STM and STS investigation of annealed Co-doped BaFe2As2

University of Amsterdam

MSc Physics

Advanced Matter and Energy Physics

Master Thesis

STM and STS investigation of annealed Co-doped BaFe

As

by

Gijsbert van der Geer

10115161

June 8, 2016

60 ECTS

Supervisors:

Prof. Dr. Mark Golden

MSc Shyama Varier Ramankutty

Second Examiner:

Prof. Dr. Tom Gregorkiewicz

Contents

1 Introduction 3

2 Scanning Tunneling Microscopy 4

2.1 Theory . . . 4

2.2 Scanning Tunneling Spectroscopy . . . 6

2.3 The Createc Low Temperature STM . . . 7

2.3.1 Approaching the tip to the sample . . . 8

2.4 Damping isolators of the Createc LT STM . . . 9

2.4.1 Vertical-Motion Isolator . . . 9

2.4.2 Horizontal-Motion Isolator . . . 10

2.4.3 Vibration isolation legs . . . 11

2.4.4 Comparison of the Minus-K and Newport I-2000 vibration isolators . . . 12

2.5 Tips . . . 13

2.6 Electrochemical etching . . . 14

2.6.1 Removal of the oxide layer . . . 15

2.6.2 Scanning Electron Microscope . . . 16

3 Iron pnictide superconductors 18 3.1 BCS theory . . . 18

3.2 Cuprates . . . 19

3.3 Iron pnictides . . . 21

3.4 BaCoxFe2−xAs2. . . 24

3.5 Annealing . . . 25

4 Scanning Tunneling Microscopy and Spectroscopy results on BaCoxFe2−xAs2 27 4.1 Topographs of annealed BaCoxFe2−xAs2 . . . 27

4.2 Gap map of annealed BaCoxFe2−xAs2 . . . 30

4.3 Comparison annealed and as-grown BaCoxFe2−xAs2 . . . 34

5 Conclusions 39

6 Acknowledgements 40

A Electrochemical etching 41

Abstract

There is still no consensus about what the microscopic mechanism is that drives iron pnic-tides into the superconducting state. The superconducting gap could be an important in factor in determining this mechanism. In this MSc thesis project, the spatial variations of the su-perconducting gap of an annealed Co-doped BaFe2As2 sample are measured using scanning

tunneling spectroscopy. These variations are compared to previously reported measurements carried out by Freek Massee as part of his PhD thesis project.

1

Introduction

It has been known for a long time that a particle also can exhibit the properties of a wave. One result of this wave-particle duality of matter is quantum tunneling. Quantum tunneling enables particles to overcome barriers that they are not able to overcome classically. In order words, when two objects are held close to each other, electrons can tunnel from one material to another. Scanning tunneling microscopy (STM) is based on this phenomenon and requires a sharp tip that is held close to a conducting sample. Using STM, the topographic height structure of a material can be investigated at an atomic level of precision. This widely used technique also allows the possibility of probing the electronic structure of materials. In that case, it is referred to as scanning tunneling spectroscopy (STS). In Chapter 2, STM is described in a more detailed manner. The practical issues of the Createc low-temperature (LT) STM in Amsterdam, where the experiments are carried out, are also discussed.

The phenomenon superconductivity, which is electrical conductivity without resistance, has been of huge interest for several decades after its discovery in 1911. It has a wide range of applications such as from nuclear magnetic resonance machines to low-power-loss cables. There has been a lot of research done on superconductors and this has led to a wide variety of materials that have been reported to show superconducting behavior. There are some theories that describe superconduc-tivity in either a microscopic or a macroscopic, phenomenological manner. However, these theories cannot describe all superconducting materials. Since the 1980’s, materials that did not obey the existing theories of superconductivity were discovered to be superconducting. Two groups of these materials that show unconventional superconducting behavior are the cuprates and pnictides. Dif-ferent families of pnictides have been reported of which the so-called 122 family is highlighted in particular. One material of this 122 family is BaFe2As2, which is not superconducting by itself but

requires doping to achieve the superconducting phase. The phenomenon of superconductivity and some of the different classes of superconducting materials are elucidated in more detail in Chapter 3.

In Chapter 4, the results of investigating an annealed, Co-doped BaFe2As2sample, using STM,

are shown. This includes both measurements of the topographic height structure and the electronic structure of the material. Since STM is a very sensitive technique, vibration isolators are usually installed on these systems to reduce mechanical vibrations. New Minus-K vibration isolators have been installed on the Amsterdam STM system in August 2014. These isolators replace the New-port I-2000 vibration isolators and enhance the resolution of the STM. These measurements are compared, in this thesis project, with measurements on as-grown, Co-doped BaFe2As2 carried out

by Freek Massee in 2008. In particular, the variations of the superconducting gap of both samples are compared.

Chapter 5 includes a recap of the conclusions drawn out of the investigations.

This research project is part of reaching the understanding of the physics of unconventional superconductors in these kind of materials. The electronic structure could be very important for understanding the superconducting behavior in pnictides. When the microscopic mechanism of superconductivity in these materials is completely understood, a room-temperature superconductor might be a step closer.

2

Scanning Tunneling Microscopy

Scanning Tunneling Microscopy (STM) is a technique invented by Gerb Binnig and Heinrich Rohrer for which the Nobel Prize in Physics was awarded in 1986 [1]. The technique can be used to probe the surface of a material on an atomic scale. STM is based on quantum tunneling and requires a very sharp conducting tip to be controllably positioned near a metal surface. The distance between the sample and the tip should be in the order of a few ˚Angstr¨om (˚A).

2.1

Theory

In Fig. 1, a schematic picture of an STM is shown. The tip is mounted on a piezo tube. This piezo tube can position the tip with sub-atomic resolution in three dimensions. When the tip is brought within ca. 10 ˚A of the sample and a bias voltage is applied between the tip and the sample, a tunneling current will occur as a result of the overlap of the wave functions of the electrons in the tip and the sample. The applied voltage shifts the Fermi level of the tip and sample with respect to each other [2]. When a negative bias voltage is applied to the sample, the electrons will tunnel predominantly from the occupied states of the sample to the unoccupied states of the tip. This situation is sketched in Fig. 2. If the sign of the voltage is positive, the electrons will mainly tunnel in the opposite direction.

Figure 1: A schematic picture of an STM [2]. A voltage is applied to a tip that is held close to a conducting surface. The tunneling current, caused by this voltage, is controlled by a feedback loop. This results in height variations while scanning across the surface. The piezo tube, that enables the tip to be positioned with sub-atomic resolution in all three dimensions, is highlighted in orange.

When a bias -V is placed on the sample with respect to the tip, and the tunneling from the tip to the sample is neglected, the tunneling current of electrons from the sample to the tip can be described by [2]:

Figure 2: A schematic representation of the tunneling between sample and tip in the case of a negative voltage applied to the sample [2]. In this case, electrons will predominantly tunnel from the sample to the tip. Energy is along the vertical axis.

I =−4πe ~ ∞ Z −EF (tip) |M |2_g

s(r, E)gt(E + eVb)(f (E) − f (e + eVb))dE. (1)

In this formula, M represents the matrix element between tip and sample, −e the electron charge, gsand gtthe density of states of the sample and the tip, respectively, Vbis the bias voltage

and f (E) is the Fermi distribution. This expression for the tunneling current can be simplified using two assumptions. First of all, we assume that the density of states of the tip near the Fermi level is constant. Therefore, the density of states of the tip can be taken outside the integral and treated as a constant. Furthermore, we assume that the Fermi distribution is a step function which is the case at zero temperature. This changes the limits of integration and in this way the tunneling current is simplified to:

I ≈ −4πe ~ gt(0) 0 Z −eVb |M |2_g s(r, E)dE. (2)

The integral limits in this formula are set to −eVb and 0, the latter is equivalent to the Fermi

energy of the tip. The next step is to make an approximation for the matrix element M . For an s-wave tip, the matrix element can be approximated by [3]:

|M |2_{≈ e}−2γ_{, (3)}

where γ = d q

2mφ

~2 with d the distance between tip and sample, m the electron mass and φ

the work function. The work function represents the energy an electron needs to tunnel from the material into the vacuum. Because Bardeen showed that the wave functions of sample and tip are

insignificantly influenced by each other, the matrix element M can be taken outside the integral [2]. Therefore, the resulting formula for the tunneling current is:

I ≈ −4πe ~ e−2d q_2mφ ~2 g_t(0) 0 Z −eVb gs(r, )d. (4)

In real experiments, however, the barrier is not uniform and the shape of the tip also has an influence on the tunneling current. In the constant current mode, the current is kept constant by varying the height difference between sample and tip while scanning over the sample using the piezo tube. This means that the tip follows a contour of constant integrated local density of states (LDOS) [2]. When the material is homogeneous, this contour coincides with the geometric height profile of the surface. If this is not the case, the LDOS will also affect the resulting image. Such images, received with the feedback loop on are often referred to as yielding topographic information, received in ’topographic mode’.

2.2

Scanning Tunneling Spectroscopy

Apart from topography, an STM can also investigate, in a local manner, the electronic structure of the sample. This technique is called scanning tunneling spectroscopy (STS). When the tip is kept at constant distance from the sample and the bias voltage is varied, the tunneling current will change as a result of the LDOS of the sample. Starting from the expression for the tunneling current given in Eq. 4, differentiating with respect to the bias voltage, V, yields:

dI

dV ∝ gs(EF− eVb). (5)

Thus, when the tip is kept at the position above the sample and the bias is varied, the LDOS is measured around the Fermi level. An advantage of STS is that both occupied and unoccupied states can be accessed, since the applied voltage between tip and sample can be positive or negative. The dI/dV curve can be measured directly using a lock-in technique. A small alternating voltage with constant frequency is added to the bias signal. The tunneling current will thus also vary with the same frequency, and its amplitude will be proportional to the LDOS. Since the alternating voltage frequency can be used as a reference frequency, the current signal proportional to the LDOS can be filtered using a lock-in amplifier. This yields a better signal-to-noise ratio than deriving the dI/dV numerically from the I(V ) curve. If this STS technique is used for many locations (x,y) on the sample, a 4D data set is obtained in which the tunneling current (proportional to the LDOS) is determined as function of x and y position and energy with respect to the Fermi level. This data block can then be sliced to show the real space variation of the LDOS at a chosen, constant energy. This is often referred to as an LDOS map.

The tip-sample distance in an STS experiment is set by means of the setup current. For a given setup voltage (often one ’end’ of the STS spectrum to be measured), a current value is put into the measurement software. The consequence is, that at each spatial pixel at which STS is to be done, the tip height is adjusted till the setup current is reached. The setup current originates from the integral between EF and Vb of the LDOS of the sample. In this sense, the setup current acts, via

adjustment of the tip-sample distance (i.e. junction resistance), as a normalization for STS spectra received from different spatial locations. This means that the sign and value of the setup current

and voltage can have a significant impact on whether a number of STS spectra resemble each other or not.

2.3

The Createc Low Temperature STM

The Createc low temperature (LT) STM works under ultra-high vacuum (UHV) which requires pressures well below 10−9 _{mbar. The LT STM contains three UHV compartments: the load lock,}

the preparation chamber and the main chamber. All the individual compartments are separated by valves.

The load lock is used to bring samples and tips in or out of the vacuum system. Since it is separated from the other compartments, the load lock is the only compartment that has to be vented in order to bring new samples and tips into the system. The venting of the load lock is usually done with dry nitrogen gas. After pump down of the load lock, samples can be transferred into the preparation chamber using a transfer arm. In order to obtain a high-vacuum pressure in the load lock a Pfeiffer Vacuum turbo pump and a Edwards Vacuum XDS scroll pump are used. The scroll pump is used to bring the pressure below 0.1 mbar. When this pressure is reached, the turbo pump is used to achieve a pressure in the 10−9 mbar range. Since both pumps have rotating parts, they are switched off during measurements to reduce the vibrational noise that would otherwise effect the performance of the tunnel junction.

In the preparation chamber, a manipulator arm is housed. This arm can be rotated around its long axis, translated in three dimensions and is used to transfer the sample into the STM head in the main chamber. Before the measurements commence, the sample can be cleaved, usually by means of knocking off a cleavage post that has been glued to the sample. This takes place in the preparation chamber. A station where tips and samples can be stored is also situated in the preparation chamber.

The main chamber is, just as the preparation chamber, pumped by a Leybold Heraeus ion pump and a titanium sublimation pump. An ion pump is often used for UHV systems since it can reach pressures in the 10−11 mbar range. In contrast to the pumps used for the load lock, these pumps do not have to be switched off during the measurements as they contain no moving parts. This ensures that the vacuum conditions do not change while performing measurements.

The STM head is suspended from a cryostat with springs. This cryostat is filled with liquid helium (He) to keep the temperature low. The He bath is shielded by an outer cryostat that is filled with liquid nitrogen. A full tank can keep the STM temperature at 4.2 K for approximately 72 hours.

Figure 3: Left: Image of the STM head. Right: Schematic image of the STM head. Image courtesy of Freek Massee.

In Fig. 3 the head of the STM is shown. The STM head is of a Besocke Beetle type [4]. The sample holder is stationed on the sample holder plateau. By means of a spring loaded linear translator and a system of pulleys and cables, it is possible to raise and lower the sample holder plateau. When this is pulled down to its lowest position, the complete STM assembly, mounted on its three springs, is also pulled down to contact the cryostat, thus ensuring good thermal equilibrium. At this position, the sample holder can be transferred in and out. Once a new sample holder is in place, the sample holder plateau is raised such that the sample holder is pulled against the STM head, thus facilitating the cooling of the sample holder and the sample. By doing this, the STM assembly also is pulled up and off the base of the cryostat by the three springs on which it is hanging, and vibrations are further damped by eddy current damping elements acting between the STM and the inner can of the cryostat.

2.3.1 Approaching the tip to the sample

Once a tunnel junction has been set up, the feedback loop between the tunnel current and z-position of the tip gives a good degree of stability. The issue is how this situation can be reached safely. This is called the approach. In order to approach the tip to the sample the tip has to be brought optically close to the sample first. Using a telescope, the tip and sample can be seen through windows built into the cryostat. Using the ramp controller, the three piezos acting on the ramp plate can move the tip downwards, towards the upward-facing sample surface. To be close enough to start the automatic approach routine, the tip and the reflection of the tip on the sample need to be visible. Since the ramp controller moves not only downwards but also in a horizontal direction, it is preferred to get the tip as close to the place on the sample where one wants to measure as possible. It is important that the tip and sample do not touch otherwise the tip might be damaged. When the tip is optically brought close to the sample, the automatic approach routine can be started. When the automatic approach is started, the main piezo will move from fully retracted to fully extended until a certain set tunneling current is detected. If the tunneling current is detected the approach will stop automatically and the tip is close enough to the sample to start measuring.

If no tunneling current is detected, the ramp will move one step down and the main piezo will move from fully retracted to fully extended again. This approach should be finished within 30 minutes.

2.4

Damping isolators of the Createc LT STM

STM is a very sensitive technique detecting currents in the range of pico-amperes between two objects that are within a few ˚A of each other. Therefore vibrations have to be damped as much as possible. STM setups are usually placed on vibration isolation legs, and also make use of eddy current damping in the UHV chamber. Prior to this project, the Createc STM was mounted on four Newport I-2000 vibration isolation legs, which use air pistons to damp the vibrations the STM apparatus as a whole may pick up from the building. In order to further suppress mechanical vibrations, three new legs were installed, replacing the Newport legs, which work based on the principle of a negative stiffness mechanism (NSM). These legs were bought from the company Minus-K, and installed in August 2014. One of the legs is shown in Fig. 4. Part of this MSc research project was the testing of the efficiency of these new vibration isolation legs and Chapter 4 relates STS measurements on Co-doped BaFe2As2 superconductors carried out to compare with

similar data received using the Newport dampers. In the following, a brief account will be given of the working principle of the NSM system.

Figure 4: One of the three Minus-K vibration isolation legs, installed in August 2014.

2.4.1 Vertical-Motion Isolator

The vertical-motion isolator consists of a spring and an NSM element. These combined can make the stiffness close to zero which is preferable for damping purposes [5]. In Fig. 5 an NSM is shown next to a conventional spring. The three balls, shown in the sketch of the NSM, are connected by two beams, indicated by 2 and 3 in Fig. 5, and they are pressed from the sides by load P. This NSM is in unstable equilibrium. It has two configurations where the equilibrium is stable; if the third

ball is either displaced upwards or downwards. If one moves the center ball a bit up it takes a force to keep it in equilibrium [6]. The direction of this force is downwards rather than upwards when the displacement is up. This is the opposite of a conventional spring where the force is in the same direction as the displacement. This makes the stiffness, defined as the force needed to displace the object a certain amount, of the NSM negative whereas the stiffness of a spring is positive.

Figure 5: On the left-hand side an NSM is shown, on the right-hand side a conventional spring [5]. For the NSM the force is opposing the displacement instead of in the same direction as the dis-placement as is the case for the conventional spring. The two beams are represented by the black lines numbered 2 and 3.

If an NSM and a conventional spring are combined, we get the situation sketched in Fig. 6. The weight load is supported by the spring, but the stiffness of the object is the stiffness of the spring combined with the stiffness of the NSM (K = KS− KN) [6]. In this way, the stiffness of the total

system can be made to approach zero. When the stiffness is close to zero, the system will have a very low natural resonant frequency which is beneficial for a vibrational isolator.

Figure 6: An NSM combined with a conventional spring [5]. In this configuration the effective stiffness K is the stiffness of the spring KS minus the stiffness of the NSM KN.

2.4.2 Horizontal-Motion Isolator

The horizontal-motion isolator in the Minus-K damping system makes use of flexible rods, also called beam columns. If there is no weight added to the beam columns, they will behave as horizontal springs as can be seen in Fig. 7 and the stiffness of the beam column is just simply KS =F_δS. With

an added weight load there is an additional force which causes the system to behave as an NSM and a spring combined and the stiffness is again K = KS− KN. Thus, the more weight is put on

the beam column the more negative the stiffness gets. In the middle of the beam there is a point where the curvature changes. Effectively, this can be seen as two cantilever beams; one from the bottom and one from the top [6].

Figure 7: A beam column without (left-hand side) and with a weight load added (right-hand side) [7]. The added weight load causes the configuration to behave as a spring and an NSM combined.

Now, consider the configuration shown in Fig. 8. The payload is supported by two upper columns and two lower columns that work like described above. If the weight load changes, the negative stiffness increases on the upper columns. On the lower columns it has the opposite effect. If the system is well tuned the low natural frequency remains unchanged when the load is changed [6].

Figure 8: A schematic representation of the horizontal-motion isolator [5].

2.4.3 Vibration isolation legs

Both the vertical-motion isolator and the horizontal-motion isolator are combined in the setup for the vibration-isolation legs, see Fig. 9. In this system, additional damping is used to isolate even better. In order to isolate the system from tilt-motion a tilt pad is used. The compression load and thus the vertical stiffness can be changed by the vertical-stiffness adjustment screw. So the negative-stiffness flexures and the spring behave exactly as the isolator shown in Fig. 6. The lower column plate is connected to the upper column plate via beam columns. With a weight load added, it isolates in the same manner as the horizontal-motion isolator in Fig. 8.

Figure 9: A schematic of the vibration isolator where both the horizontal-motion isolator and the vertical-motion isolator are integrated [7].

2.4.4 Comparison of the Minus-K and Newport I-2000 vibration isolators

In order to show why the replacement of the legs has taken place, the performance of both sets of vibration isolators is compared. The transmissibility curves for the Newport I-2000 are dissimilar in horizontal and vertical directions. Both are shown in Fig. 10 for the maximal recommended load. These isolators have a vertical resonant frequency smaller than 1.1 Hz and a horizontal resonant frequency smaller than 1.5 Hz.

Figure 10: The vertical transmissibility versus frequency curve of the Newport I-2000 isolators is shown on the left-hand side. On the right-hand side, the horizontal transmissibility versus frequency curve of the Newport I-2000 isolators is plotted. These curves are taken from the manual of the Newport I-2000 isolation legs.

A typical performance curve for the Minus-K vibration isolators is shown in Fig. 11. A vertical resonant frequency of 0.5 Hz can be reached as well as a horizontal frequency of 0.5 Hz near the nominal load.

Figure 11: A typical transmissbility versus frequency curve for the Minus-K legs. The dashed line represents the performance of other Minus-K vibration isolators and is shown for comparison. This curve is taken from the manual of the Minus-K legs.

This illustrates that a smaller eigenfrequency can be achieved with the Minus-K vibration iso-lators, meaning that the resolution of the STM can be expected to be enhanced as a consequence of the new legs.

2.5

Tips

For STM, a very sharp tip with a featureless density of states near the Fermi level is required. Most tips used for STM are either made of an alloy of platinum and iridium (PtIr) or made of tungsten (W). Because of the hardness of W, a tip made of W will not deform easily during measurements and therefore, it is relatively stable during scanning [8]. Another result of this hardness is that the tip has to be electrochemically etched before usage. The major drawback of the usage of W as the tip material is its high reactivity which causes an insulating oxide layer to be formed at the surface when the tip is stored in air. This layer can prevent electrons from tunneling and thus no tunneling current will be detected. PtIr is much less hard than W. This has the advantage that cutting a piece of PtIr wire under an acute angle while holding the wire under tension can result in successful tip preparation, meaning that electrochemical etching is not required. On the other hand, a PtIr tip is less stable and can deform during measurements more easily than an electrochemically etched W tip.

The tips used in the LT STM are made of PtIr with a ratio of 80/20. The length of the tip is important in this system and should be 2.3 mm since the range of the STM head coarse approach is limited. The tips are made by cutting a piece of 0.25 mm diameter PtIr wire under a large angle. All tips are well tested on an Au sample first before measuring on the desired sample. Cutting of a

PtIr wire has resulted in sufficiently sharp and stable tips before, but not in all cases. For instance, spectroscopy measurements of the topological insulator Bi2−xSbxTe3−ySey(BSTS) did not lead to

successful results. This indicates that sometimes a W tip rather than a PtIr tip would be beneficial and therefore the possibility of using a W tip in the Createc LT STM has been investigated in this thesis project. In the next paragraph, the process of etching a W tip is described.

2.6

Electrochemical etching

To etch a W tip a piece of wire is immersed into an electrolyte solution in which a counter electrode is placed and a voltage is applied between the electrodes such that the tip is the anode and the etching process is allowed to run until a sharp tip is created.

The electrochemical etching reaction is given by [9]:

cathode : 6H2O + 6e−→ 3H2(g) + 6OH− (6)

anode : W (s) + 8OH−→ W O2−

4 + 4H2O + 6e− (7)

total : W (s) + 2OH−+ 2H2O → W O2−4 + 3H2 (8)

At the interface between the air and the electrolyte, the tungsten reacts with the OH− ions resulting from the reduction of the water to form tungstate anions that are soluble in water. At the cathode, OH− _{ions and gaseous bubbles of H}

2are formed.

Figure 12: A schematic representation of the drop-off method [10]. In a) the meniscus is formed and in b) up until e) a necking phenomenon is observed and the downward flow of W O2−₄ is indicated, which results in a dense layer of W O₄2− around the lower part of the wire. In f) the drop off has occurred.

The process of etching is shown in Fig. 12. Because of capillary forces, a meniscus is formed around the wire that is immersed in the solution. A concentration gradient of OH− is formed due to the diffusion of OH− ions towards the anode [11]. Because of this gradient, the reaction will occur more slowly at the top of the meniscus than at the bottom. Moreover, the W O2−₄ will flow downwards creating a viscous layer around the bottom part of the wire [10]. This layer slows down the etching reaction at that the bottom part of the wire. Consequently, in the part where the etching happens at the fastest rate a necking phenomenon is observed, causing the wire to break at a certain moment. This results in two parts of the wire with a sharp end. One part will drop down and therefore this method is called the drop-off method. It is very important to switch off the voltage immediately after the drop-off has occurred. The drop-off causes a sudden drop in voltage which can be used to detect the drop-off and thus, to switch off the voltage at the appropriate time. If the voltage is not switched off instantly after the drop-off, the sharp end of the wire will

be etched away resulting in a blunt tip. The part of the wire that drops will have the sharpest end so it is preferable to use that part of the wire but the other end of the wire can also be used. In the used setup, the wire has to be in a tip holder before etching, hence, the part of the wire that drops is generally not used.

There are a few parameters that are important for the result of the etching. Before the etching is carried out, one could use pre-etching to result in a much smoother wire to etch. Although only a small amount of material is removed by the pre-etching, it has been argued to improve the result of the etching process [12].

For the applied voltage, one could either use an AC voltage or a DC voltage. An AC voltage, however, produces a lot of bubbles that could disturb the etching process and therefore, a DC voltage is preferred [13]. A voltage that is too high causes the etching to happen very rapidly. As a result, the drop-off occurs before well-developed necking takes place and a sharp wire end has been realized. On the other hand, when a voltage that is too low is used, the etching will take a long time and in that case it is more likely that vibrations occur. In the experiments reported here, DC voltages around 7 V have been used.

The result of etching is also influenced by the shape of the meniscus. Since a symmetric tip is desirable, the shape of the meniscus should be symmetric as well. To get a symmetric meniscus and tip the wire has to be oriented perpendicular to the surface of the liquid. This can be quite tricky since the wire has to be bent in order to fit into the tip holder (see Appendix A).

The etching solution that has been used and the concentration of this solution also plays its part in the chances of success. Both NaOH and KOH have been used as an electrolyte solution with satisfying results but there is still debate about which of these solutions yields better results [8]. A concentration of either NaOH or KOH that is too high will cause the meniscus to drop whereas a too low concentration increases the etching time and thus, the chance that the meniscus is disturbed by particles resulting from the etching process.

Another factor of importance is the length of the wire that is immersed into the solution. It has been claimed that a large dipping length yields a sharp tip [14]. On the other hand, it has also been claimed that a small dipping length is favorable [9]. In our own experiments, comparison of large versus small dipping lengths yielded no conclusive evidence for either of the claims, indicating that this factor is not the dominating one for achieving sharp tips.

2.6.1 Removal of the oxide layer

The oxide layer is the major drawback of the preparation of a W tip by electrochemical etching. This insulating oxide layer can be removed in several ways. The tip could be dipped into the very powerful acid, HF. HF does not react with tungsten, but it does react with all its oxides [15]. The disadvantage of this method is that HF is very dangerous and since this is an ex-situ method, the oxide layer will start to form again after the dipping has been done. Another method is electron bombardment which is an in-situ treatment and therefore more convenient. A filament is placed in proximity of the tip. When a voltage is applied, either the tip or the filament serves as an electron source depending on the sign of the voltage. The WO−2₄ layer will react into WO2at around 1000

K and this will sublimate. Although the melting temperature of W is much higher than 1000 K, raising the temperature could make the tip more blunt [16].

2.6.2 Scanning Electron Microscope

After a tip has been etched, one can verify the gross structure of the tip apex using a scanning electron microscope (SEM). Fig. 13 illustrates the working of an SEM, schematically. In contrast to other microscopes, an SEM uses electrons rather than photons. Since the tip can be damaged by the process of making an SEM image, this should be done only if the etching process has not been optimized yet, or as a spot-check of an otherwise reproducible etching process.

Figure 13: A schematic illustration of an SEM. Adapted from [17].

An SEM contains an electron gun which usually consist of a W filament through which a current is flowing. This will produce an electron cloud near the filament. When a cathode and an anode with a hole in it are placed near the filament, the electrons are attracted by the anode and will move through the hole of the cathode. Because the electrons are accelerated, they will also move through the hole of the anode and an electron gun is created.

However, when the electrons have passed the anode they will diverge. Since an electron beam is required, an SEM makes use of electromagnetic lenses. A cylinder with an iron core and coil wires around is placed on each side of the beam. When a current is applied to this coil wires an electromagnetic field will be created which has the same function as a lens [18]. An SEM makes use of electromagnetic lenses: at least one condenser lens and an objective lens. The condenser lens controls the beam size and the objective lens focuses the beam onto a spot on the sample.

When the beam impinges on the sample there are three possible events: (a) there is no interaction and the electron moves through the sample. (b) The beam electron collides with an electron of the sample and as a result a secondary electron is created. (c) The electron from the beam collides with an atom in the nucleus of the sample and is backscattered. Usually the electrons that are being detected are the secondary electrons but backscattered electrons can also be used [17]. By applying a positive potential over the detector, the secondary electrons are attracted to the detector. In this way even the electrons that are not in the line of sight of the detector can be detected.

In order to scan over the sample scanning coils are used. By varying the potential between these coils the beam will be deflected and this way the beam can be scanned over the sample. The position of the beam is synchronized with the position of the beam spot on the detection screen such that an image is created.

The SEM used in this case is a Hitachi TM3000 and makes use of a backscattered electron detector. An acceleration voltage of 15 kV has been used for verifying the gross structure of the etched tips.

3

Iron pnictide superconductors

In 1918, Heike Kamerlingh-Onnes discovered the resistance of mercury (Hg) dropped rapidly to zero at a temperature below 4.2 K. This experiment, first carried out in Leiden, is nowadays considered as the first proof of superconductivity. After the experiment of Kamerlingh-Onnes, another important step in exploring superconductivity was taken in 1933 by Walther Meissner and his student Robert Ochsenfeld. They discovered that applied magnetic fields were expelled by superconductors when cooled below their transition temperature. This phenomenon is distinct from zero resistance and is called the Meissner effect. This effect is nowadays considered as a proof that superconductivity occurs. In 1950, Ginzburg and Landau came up with a phenomenological description that specified the macroscopic properties of superconductivity which is now known as Ginzburg-Landau theory. Seven years later, the first theory that describes superconductivity on a microscopic scale was developed by Bardeen, Cooper and Schrieffer. They called it BCS theory, after their initials, and for this theory they received the Nobel Prize in Physics in 1972.

3.1

BCS theory

An important insight on which the BCS theory is based is that the effective forces between electrons can be attractive in a solid. Cooper stated that as long as the force is attractive, no matter how weak, two electrons just outside the Fermi surface can form a stable pair bound state, a Cooper pair [19]. Cooper’s model is based on a completely filled Fermi surface at zero temperature. If two extra electrons are added just outside the Fermi surface, they will attract each other as long as their energy is in the energy range F < k < F+ ~ωD, where ωD is the Debye frequency [19]. As

a result, a condensate of electron pairs will be formed in the ground state. For a Cooper pair to be broken up, an energy of 2∆ is required. This means there is a range where the energy is insufficient to break the Cooper pair, and this is known as the superconducting gap. This gap is centered at the Fermi energy. BCS theory predicts the value of this superconducting gap at zero temperature to depend on the critical temperature Tc as follows:

2∆(0) = 3.52kBTc. (9)

This is one of the famous results of BCS theory. Although in experiments a temperature of 0 K can never be acquired, the BCS 2∆ value is a good approximation at low temperatures. This gap can also be described for all temperatures by [19]:

2∆(T ) = 2∆(0)tanh(π 2

r Tc

T − 1). (10)

One of the important parameters for superconductors is the coherence length, denoted as ξ, which is related to the spatial distribution of the Cooper pair wave function. The value of ξ can be shown to be [20]:

ξ ∼ EF kF∆

. (11)

Another parameter of importance is the mean free path length l. This describes the length over which a particle can travel without collisions. The mean free path length for the Cooper pairs is described as:

l = τ vF, (12)

where τ is the time between collisions of the conduction electrons with impurities and vF is the

Fermi velocity. The ratio between these two parameters decides whether the superconductor is in the dirty or the clean limit. When l << ξ, the superconductor is in the dirty limit meaning that electrons will be scattered when traveling distances much smaller than the Cooper pair distance. When l >> ξ, the superconductor is in the clean limit and the electrons can move over distances larger than the Cooper pair distance without being scattered.

The s-wave superconducting density of states is given by:

nsc= ( 0 if E < ∆, E √ E2_−∆2 if E ≥ ∆. (13)

Apart from the superconducting gap between −∆ and ∆, this equation indicates that there will be a peak in the density of states at the borders of the superconducting gap, −∆ and ∆.

For conventional superconductors, BCS theory correctly predicts the isotope effect which states that the critical temperature of a superconductor is inversely proportional to the mass of the isotope of the material.

Tc ∝ M−α. (14)

For many superconductors an α of 0.5 agrees well with experiments. Later in the 20th century, superconducting materials were found that surely do not obey BCS theory, and these will be mentioned briefly in the following section.

3.2

Cuprates

In 1986, the first high temperature superconductor was found by Bednorz and M¨uller [21]. Its critical temperature was around 35 K which was quite a lot higher than for all other superconductors found at that time. Until 2008, all of the high temperature superconductors found were cuprates. The word cuprate refers to a class of copper oxides. All cuprates that are superconducting have a quasi-two-dimensional CuO2 plane in their perovskite structure (see Fig. 14). The CuO2 plane consists

of a square of O2− ions and a Cu2+ ion in the middle of this square. A lot of superconducting cuprates have been found so far, of which YBa2Cu3O7 is one of the most studied materials. The

cuprates clearly do not obey the BCS theory since they have a too high transition temperature, YBa2Cu3O7 has for example a Tc of 93 K, and gap values of the cuprates do not coincide with

the values expected from BCS theory. Furthermore, the optimally doped cuprate superconductors do not support the isotope effect described by BCS theory. Moreover, the simplest version of BCS theory only supports s-wave symmetry of the superconducting order parameter, whereas hole-doped cuprates show d-wave symmetry [22]. d-wave superconductivity means that the superconducting wave function has l=2 and possesses line nodes in k-space at which the superconducting gap is zero. The differences between the different pairing symmetries will be elucidated in more detail later. For the electron-doped cuprates, it is not yet agreed upon what symmetry order parameter they possess.

Without doping, cuprates are Mott insulators. Mott insulators are insulators that should con-duct according to conventional band theory. Due to electron-electron interactions that are insuffi-ciently taken into account in conventional band theory, Mott insulators do not conduct. Although

superconductivity in cuprates has been the subject of a lot of research, there is still no consensus as to what drives the electrons to form Cooper pairs in these materials at such high temperatures.

Figure 14: The structure of La2−xSrxCuO4[23]. The generic structure of superconducting cuprates

always includes two-dimensional CuO2 planes.

In Fig. 15, a generic phase diagram for the cuprates is illustrated. This phase diagram shows that, without doping, the cuprates are anti-ferromagnetic insulators, but as a result of the doping the superconducting state arises. The superconducting state occurs both upon hole- and electron-doping. In the hole-doped area of the phase diagram, there is a pseudogap phase. This pseudogap phase is only sketched since that particular region of the phase diagram is not yet understood completely. It is still a matter of debate whether the pseudogap is a precursor to the superconducting state or represents a competing order parameter.

Figure 15: The phase diagram for the electron- and hole-doped cuprates, left and right for Nd2−xCexCuO4 and La2−xSrxCuO4 respectively [23]. The anti-ferromagnetic state (AF) and the

superconducting state (SC) are colored light gray and dark gray, respectively. The pseudogap area for the hole-doped cuprates is not completely understood.

3.3

Iron pnictides

In 2008, superconductivity was discovered in a layered iron arsenide material with a transition temperature of 26 K [24]. This material, LaFeAsO, was not a superconductor by itself but by replacing the oxygen atoms by fluorine atoms the material became superconducting. This material is the first iron pnictide proven to be a superconductor. An iron pnictide is a compound that consists of iron and arsenic, although sometimes also iron selenides/tellurides are also included in this designation. The iron pnictides have many similarities with the cuprates, but also some important differences as will be elucidated in this paragraph. Five different crystal structures of these materials have been reported to show superconductivity [25]. The different crystal structures are shown in Fig. 16. All these five different structures have a tetragonal symmetry at room temperature and consist of the same building block, highlighted in Fig. 16a and shown in more detail in Fig. 16b. This block contains a square of iron atoms and phosphorus, arsenic, selenium or tellurium atoms below and above this square. In contrast to the Cu-O building block of the cuprates, this Fe2Pn2building block is three-dimensional. In the simplest crystal structure (FeSe),

there are no interstitial layers between the building blocks. There is at least one interstitial layer between the blocks in all the other structures.

Figure 16: In a) the five different crystalline structures for iron-based superconductors are shown, adapted from [25]. In b) the three-dimensional Fe2Pn2 building block that is present in every

structure is shown. The Fe atoms are red, the As/Se atoms are yellow.

As for LaFeAsO, most iron pnictides require doping or applied pressure to arrive at the super-conducting state. Without doping, pnictides are metallic at low temperatures, and also in contrast to the cuprates, the iron pnictides can be doped to superconductivity directly into the active pairing layer [25].

The AEFe2As2structure, also called the 122 structure, is the most studied structure, where AE

is an alkaline-earth material. Often, Ba is used as alkaline-earth material which makes it the Ba122 structure. In this structure, the FeAs plane is sandwiched between two layers of Ba2+ _{atoms. The}

distance between the Fe atoms in the square highlighted by the dashed line in Fig. 16b is roughly 2.8 ˚

A. The As atoms that surround this square of Fe atoms have a lattice constant of 3.9 ˚A [26]. For this Ba122 structure, there are several ways to reach the superconducting phase. All three components can be partially replaced by another material (see Fig. 17). The highest critical temperature of 38 K can be reached by partially replacing Ba with K (hole doping) [27]. Other options are partially replacing Fe with Co (electron doping), as will be discussed in the next paragraph, or substituting P for As. Without doping, BaFe2As2has anti-ferromagnetic order, but due to the doping this ordered

magnetic phase gets destroyed. The superconducting phase appears when doping is increased and is more or less centered around the doping level for which the anti-ferromagnetic order is destroyed. This differs from the LaFeAsO structure where the anti-ferromagnetic and the superconducting state do not exist at the same doping concentration. The dotted line in Fig. 17 indicates the transition from the paramagnetic to the anti-ferromagnetic state which coincides with a structural transition from tetragonal to orthorhombic [25]. In the tetragonal structure, the a and b lattice constants are identical (see Fig. 16b). In the orthorhombic structure, the lattice parameter of the a axis is roughly 1% smaller than that of the b axis [28].

Although there are a lot of possibilities to achieve superconductivity in the Ba122 structure, it is not yet known what causes the superconductivity in this system. However, it has been pointed out that electron-phonon coupling is too low for pnictides to be the cause of superconductivity [29]. It has been argued that magnetic spin fluctuations are the cause of the electrons to form Cooper pairs, but so far there has not been a conclusive proof [30].

Figure 17: Phase diagram of the BaFe2As2 system as a function of doping, from [25]. All of three

components (Ba, Fe, As) can be (partially) replaced to reach the superconducting state (SC) by K, Co and P, respectively. The dotted line indicates the transition from a tetragonal structure (T) to an orthorhombic structure (O). This corresponds to the paramagnetic (PM) to anti-ferromagnetic (AFM) transition in the parent compound.

The band structure could be the key in determining the cause of superconductivity in these materials. The band structures of these superconducting pnictides have been calculated using density functional theory (DFT) calculations [25]. The electronic states at the Fermi level are dominated by the Fe 3d states with some influence of the As 4p states. The electronic structure of Co-doped BaFe2As2 is shown in Fig. 18a. The electronic structure consists of several distinct

Fermi surfaces, that correspond to different bands crossing the Fermi level. The hole-like bands are situated in the center of the Brillouin zone (Γ point) and in Fig. 18a are highlighted in purple and blue. The electron-like bands are at the corners of the Brillouin zone (M points) and colored red and yellow. The five bands crossing EF indicate that all the Fe 3d orbitals play a role in the

electronic structure of these materials.

The symmetry of the order parameter (OP) of BCS superconductors is s-wave, whereas hole-doped cuprates have d-wave symmetry. In the simplest case, that of isotropic s-wave supercon-ductivity, the order parameter does not depend on momentum, ∆(k) = ∆0. If d-wave symmetry

occurs, there will be nodes and sign changes in the order parameter as a function of momentum as ∆(k) = ∆0cos(2φ) where φ is the angle of the k-vector. For pnictides, the pairing symmetry is still

a matter of debate. Three possible candidates are shown in Fig. 18b.

Figure 18: In a) the Fermi surfaces of BaFe2As2 with 10% Co-doping are shown, calculated

us-ing DFT calculations. In b) the k-dependence of the superconductus-ing gaps for different pairus-ing symmetries are shown, adapted from [25]. The left image represents the isotropic s± state, the middle the anisotropic s± state and the right image represents the d state. Single electron (e) and hole (h) pockets are shown for multiple bands. The shaded regions represent the multi-gap pairing symmetries on hole and electron pockets in red and blue, respectively.

The simplest s-wave symmetry (not shown in Fig 18) has been ruled out based on experimental evidence [25]. In contrast to cuprates, pnictides have four or five bands crossing the Fermi level rather than one. This could lead to multi-band superconductivity and multiple gaps as is the case for MgB2, which has a double gap [31].

3.4

BaCo

Fe

As

Replacing Fe by Co induces electron-doping since Co has an extra 3d electron compared to Fe. An optimal Co-doping level for BaCoxFe2−xAs2is obtained at x = 0.14. Therefore, a Co-concentration

of less than 0.14 is referred to as under-doped and a concentration higher than 0.14 is called over-doped. The possibility of a pseudogap in Co-doped BaFe2As2 has been ruled out, since the

superconducting gap was seen to close at the critical temperature for all doping levels in early STM experiments [32].

In the Ba122 structure, the Fe-As blocks are sandwiched between two layers of Ba2+ _atoms.

When this structure is cleaved to expose the clean surface required for STM experiments, there are several possibilities. Since the Fe-As bonds are very strong, the crystal will not cleave in this layer. Therefore, it can either cleave between the Ba and the As layer, or within the Ba layer. It has been claimed that the remaining layer after cleavage is the As layer [33], but it has also been claimed that the remaining surface after cleavage is half a Ba layer [34].

Considering the charge of the surface, a cleave leaving half a Ba layer behind is most likely to occur. When a full Ba layer were to remain on top, the repeating charges of the layers would be (+2, -3, +4, -3, +2), causing a dipole moment. A full As layer results in (-3,+4, -3, +2), also containing a dipole moment. However, when half a Ba layer were to remain after cleavage the repeating charges of the layers would be (+1,-3, +4, -3,+1) since half a layer of Ba atoms carries half the charge of a full layer of Ba atoms. In these simple gedanken experiments, we assume that half of the Ba layer is on top of the cleaved crystal and the other half is on the other cleavage

surface. The fact that this system terminated by a half Ba layer is non-polar, is a reason to expect the sample to cleave within the Ba layer.

Energy calculations have been performed on this system to resolve which structure is the most energetically favorable [35]. When the system is cleaved within the Ba layer, half of the Ba atoms should remain on the surface as uniformly as possible to balance the chemical valence. Hence, the surface can be reconstructed in a (2x1) or in a (√2 x √2) structure. In the calculations the energies of both reconstructions have been compared to the unreconstructed (1x1) As plus (1x1) Ba surface. Both structures have a negative relative energy. This means that both reconstructions are energetically favorable compared to a full As layer and a full Ba layer as the crystal termination. It has been shown that the energy of the (√2 x√2) reconstruction is lower than that of the (2x1) reconstruction and thus, energetically favorable [35].

Overall, a cleavage within the Ba layer is the most likely option leaving half a layer of Ba at the surface. Furthermore, the surface structure of the Ba122 system seems to depend on the cleavage temperature [34]. At low cleavage temperatures, the Ba surface atoms are argued to be not mobile enough to re-arrange into the energetically most favorable (√2 x √2) reconstruction. Therefore, metastable reconstructions, such as the (2x1) reconstruction can be obtained. At higher cleavage temperatures, the (√2 x √2) reconstruction occurs more frequently, because the Ba atoms are mobile enough to re-arrange themselves. As a result, the cleavage surfaces of the alkaline earth-122 material family can display several different surface structures, depending on the way the Ba atoms remain after cleavage. Several reconstructions have been observed. Apart from the (2x1) and (√2 x√2), combinations of both of those structures, a rib cage structure and a maze-like structure have been reported [16, 34]. In Fig 19, these structures are shown schematically.

Figure 19: Several reconstructions of a cleaved Ba122 surface with half a Ba layer on the surface, from [16, 34].

3.5

Annealing

Annealing is a heating technique which can change the physical properties of a sample of a material, for example by modifying the crystal structure. An annealing step can also help to remove

contam-ination from a surface. Upon annealing, because of increasing temperature the bonds between the atoms can be broken, and hence the rate of diffusion will be increased. This can cause dislocations to disappear, dopants to rearrange so as to lower disorder, can remove contaminants from the surface and can also cause the recrystallization of the surface atoms. So far in the research carried out in the group hosting this MSc project, mostly as-grown samples of BaCoxFe2−xAs2have been studied.

In the next chapter, the results of our measurements on annealed samples of Co-doped BaFe2As2

will be discussed and compared to measurements on as-grown Co-doped BaFe2As2samples carried

4

Scanning Tunneling Microscopy and Spectroscopy results

on BaCo

Fe

As

In this section, the results of our measurements on annealed BaCoxFe2−xAs2 are discussed and

compared with previous measurements on as-grown BaCoxFe2−xAs2 that were carried out as part

of the PhD thesis project done by Freek Massee. The BaCo0.2Fe1.78As2 sample studied in this

thesis project was annealed for 75 hours at 800 K and cleaved in-situ at 85 K. After annealing, the critical temperature was enhanced to 25.6 K [36] as can be seen in Fig. 20. The measurements were performed at 4.2 K in a commercial LT STM from Createc. The tips were made by cutting a PtIr wire of 250 µm thickness. Most of the tips used in this study were characterized and conditioned on an Au (788) surface.

Figure 20: Resisitivity data of the annealed BaCo0.2Fe1.78As2sample (red) compared to an as-grown

BaCo0.2Fe1.78As2sample (blue). Adapted from [36].

I will start with discussing the topography and the surface structure of annealed BaCoxFe2−xAs2

and then move onto the spectroscopy part and the superconducting gap maps which will be com-pared with the ones on as-grown samples.

4.1

Topographs of annealed BaCo

Fe

As

In this section, an overview of the topographs that were obtained on annealed BaCoxFe2−xAs2 is

given. In Fig. 21a, a typical (2x1) reconstructed surface is shown on a (250 ˚A)2_{patch. This structure}

looks similar to earlier reported (2x1) structures of the Ba122 system [16, 34]. Fig. 21b shows the line scan taken where the red line is drawn. The distance between the rows of approximately 8 ˚

A corresponds to 2a where a is the lattice constant. The white dots (lower right and lower left of the field of view) are from a different layer, since the height difference is larger than the inter-layer distance. The Fourier Transform (FT) of the topograph is shown in Fig. 21c, where the two peaks corresponding to the (2x1) reconstruction can be seen clearly and are marked by red circles. The separation of the two peaks corresponds to 2a. The atoms along the (2x1) rows are not well

distinguished, which explains why there are no other peaks corresponding to the lattice parameter a visible on the FT.

Figure 21: (a) Constant current image (topograph) taken on annealed BaCo0.2Fe1.78As2showing a

clear (2x1) reconstruction (Vbias = 50 mV, I = 50 pA). (b) Line scan indicated in (a). (c) A zoom

of the Fourier transform of the topograph.

The (2x1) reconstruction is by far the most commonly occurring structure, but also other struc-tures such as the (√2 x √2) reconstruction are seen (Fig. 22). In both directions, the distance between the atoms was estimated to be 5.4 ˚A which is within 0.2 ˚A of the expected value for the (√2 x√2) reconstruction (5.6 ˚A). It has been shown using first principles calculations that the (√2 x√2) reconstruction is the most energetically favorable structure [35]. The (√2 x √2) structure was seen only rarely on the cleaves done during the course of this thesis project, and when present, was not seen to exist over large distances. This indicates that the cleavage temperature of 85 K is still not high enough for most atoms to rearrange into the most energetically favorable structure.

Figure 22: (a) Constant current image taken on annealed BaCo0.2Fe1.78As2 of a (

√

2 x √2) recon-struction (Vbias= 50 mV, I = 50 pA). In b) and c) the line scans indicated in a) are shown.

Also more complex structures were seen, such as in Fig. 23. This structure has troughs in the direction of the rows in (2x1) reconstruction. There is no specific pattern in which the troughs occur. The depth of the troughs is ca. 0.5 ˚A which is significantly smaller than the inter-layer distance of 1.5 ˚A. This means that either this structure consists of one crystallographic layer or the tip is not sharp enough to obtain the height difference correctly. This structure has similarities with other disordered structures reported previously on as-grown samples [16, 34].

Figure 23: Constant current image taken on annealed BaCo0.2Fe1.78As2(Vbias= 50 mV, I = 50 pA).

The cleavage surface structure is more complex, showing neither the (2x1)/(1x2) reconstruction nor the (√2 x√2) of Fig. 21 and Fig. 22, respectively. In b) the line scan indicated in panel a) is shown.

In Fig. 24, a (2x1) structure running in a different direction than the one in Figure 21 is shown. Since this structure is seen from the same cleave as the one in Fig. 21, and the structure runs in the perpendicular direction, it validates that the tip is not double. This (2x1) structure came with thick lines (of about 10 ˚A) running perpendicular to its structure. These new structures are about 1.2 ˚A high, which is close to the inter-layer distance of 1.4 ˚A.

Figure 24: Constant current image in a) showing a (2x1) reconstruction (Vbias = 50 mV, I = 50

pA). The blue and red lines indicates where the line scan of b) and c) were taken, respectively.

Overall, the structures seen on the surface look similar to earlier studies of the Ba122 system. This suggests that the annealing does not have a significant influence on the crystallographic surface structure. This also validates that our sample is comparable to previously measured Ba122 sam-ples. The (2x1) reconstruction is by far the most commonly occurring surface structure, indicating that the cleavage temperature of 85 K is not high enough for atoms to rearrange into the most energetically favorable (√2 x√2) reconstruction.

4.2

Gap map of annealed BaCo

Fe

As

There is no consensus about the origin of the superconductivity in the iron pnictides. Understanding the electronic structure of these pnictides is therefore of huge importance. Thus, techniques that can access the electronic structure of materials, such as STS, play an important role in the research of iron pnictides.

STS will give us the dI/dV which is in turn proportional to the LDOS of the sample under study. To do the spectroscopy, the tip is positioned above the sample using a setup voltage and current. Keeping the tip at this position, the bias voltage is varied and the change in the tunnelling current recorded. This will give an I/V plot. A dI/dV curve can either be measured using a lock-in amplifier or got by numerically differentiating the measured I/V spectra. The former procedure is used to get dI/dV throughout this thesis project. To do this, the DC sample bias voltage is superimposed with a small, suitably high frequency AC sinusoidal signal (dV) and then the lock-in

will record the AC component of the tunneling current (dI) which is in phase with the modulation given. This will essentially give the required dI/dV . This way we can make a big dI/dV map on a real surface ranging over a few hundred ˚A, depending on the stability of the tip when the feedback is switched off. That means one needs a very noise-free (both electrical and mechanical) environment over a period of 48 hours in our case to get a mapping done over an area of (340 ˚A)2_.

Now plotting the superconducting gap measured from each spectrum in real space gives us a gap map.

In an s-wave superconductor, the density of states is zero for a region of 2∆ centered around the Fermi level, with 2∆ being the energy required to break up the Cooper pair. Thus on tunneling in or out single electrons, two peaks will be measured at +∆ and at −∆ from the Fermi level. An ad-vantage of the STS technique compared to, for instance, angle-resolved photoemission spectroscopy (ARPES) is that it can also probe states above the Fermi level. Hence, also the unoccupied states can be accessed using this technique.

Because no experiments can be done at zero temperature, the finite temperature has to be taken into account. This causes a broadening which can be approximated by kBT .

Fig. 26 shows the gap map taken on a (341 ˚A)2 _{area on a (2x1) reconstructed surface. The gap}

map size used was 86 x 86 individual dI/dV spectra (7396 in total). The topograph of the patch, where the gap map was made, and its FT can be seen in Fig. 25. The topograph shows a typical (2x1) structure similar to the one showed in Fig. 21.

Figure 25: The topograph of an (341 ˚A)2 _{area of the BaCo}

0.2Fe1.78As2 sample (Vbias = 50 mV, I

= 50 pA, Tc = 25.6 K). This is the same topographic field of view as where the gap map, shown in

Fig. 26, was taken. It coincides with previously reported (2x1) reconstructions. On the right-hand side, its FT is shown.

Fig. 26 shows the gap map taken on the topographic field of view shown in Fig. 25. The value of 2∆, the superconducting gap, differs between 10 and 16 meV as can be seen in the color scale bar. This bar ranges from red (10 meV) to blue (16meV). Fig. 26b shows the histogram belonging to the gap map. All the values for the superconducting gap of 2∆ are plotted in a histogram and fitted with a Gaussian function. This function has a standard deviation of 0.9 meV and contains a peak at a value of 12.8 meV.

Figure 26: (a) A gap map taken on a (341 ˚A)2 _{patch of a (2x1) reconstruction on the surface of}

BaCo0.2Fe1.78As2 (Vbias = 50 mV, I = 50 pA, frequency = 731.9 Hz, amplitude = 2 mV, Tc =

25.6 K). The color scale is given on the right-hand side of the map, ranging from 10 meV (red) to 16 meV (blue). The histogram of the superconducting gap values is shown in b). The blue line represents a Gaussian fit to the histogram yielding an average value of 12.8 meV and a standard deviation of 0.9 meV.

An important parameter for superconductors is their _k2∆

BTc value which is often used to decide whether a superconductor is conventional or not. Using the value for 2∆ of 12.8 and the critical temperature of 25.6 K, a modal value of 5.7 for this so-called reduced gap is obtained. This reduced gap value ranges from 4.5 to 7.1, calculated from the gap map shown in Fig. 26. The reduced gap is an indication of the coupling in the superconductor and its value for s-wave BCS superconductors is 3.52 and 4.3 for d-wave BCS superconductors [37]. The value for BaCoxFe2−xAs2is well above these

BCS values. For cuprates, it has been shown that the reduced gap does not depend on the doping concentration, since 2∆ and Tc change in the same way [38]. For the Co-doped BaFe2As2 system

however, the reduced gap value has been shown to increase as the level of doping is increased [16]. This could be caused by scattering as a result of the Co-doping. As a consequence, the critical temperature decreases while the superconducting gap does not change and thus, the 2∆

kBTc value is enhanced. For as-grown over-doped BaCoxFe2−xAs2 a reduced gap value of over 10 has been

reported [16]. The value obtained here for the annealed BaCoxFe2−xAs2is well below 10 and thus,

among other factors, the reduction in _k2∆

BTc can be due to the increased critical temperature, as a result of annealing.

In Fig. 27, five dI/dV spectra are plotted. Each of these spectra represents an average of eight spectra taken from pixels with the corresponding color on the gap map. For every gap value, the superconducting gap is clearly visible, meaning that the sample was in the superconducting state at every position. From this graph, it looks like the smaller the peak-to-peak energy of the gap, the greater the zero bias conductance is. The red curve has the smallest gap energy and the highest zero bias conductance, whereas the dark blue curve has the smallest zero bias conductance and the largest gap value. The maximum-minimum ratio (in the range from -20 meV to 20 meV for the bias voltage) for the red curve is the smallest and this ratio is the largest for the blue curve.

Figure 27: Five averages, each of eight spectra taken on the corresponding color of the gap map, that is shown in Fig. 26.

Another piece of important that can be extracted from such a gap map is the correlation length. This gives information about the range over which interactions between the electrons occur. The autocorrelation coefficient of the gap map is plotted in Fig. 28. The correlation length is significantly larger than 10 ˚A. This can be compared to the coherence length which is the length over which the superconducting gap is seen to vary. The coherence length for BaCo0.2Fe1.8As2 is 12 ˚A [39], which

is close to the distance over which the superconducting gap is seen to vary in the gap map shown in Fig. 26.

Figure 28: The autocorrelation of the gap map. On the y-axis the correlation coefficient is given and on the x-axis the distance.

Looking qualitatively at the topograph and the gap map, it would not seem too far-fetched that there is some degree of correlation between them. In Fig. 29, the extreme values of the topograph are shown on the left-hand side, and they are stacked on top of the gap map on the right-hand side. The extreme values are determined by, in succession, averaging around zero, raising to the power six and filtering in such a way that only the values greater than 0.5 are shown. This shows that there is definitely some correlation between the topograph and the gap map. However, there are also some places where the superconducting gap is seen to vary on an area where no significant

features appear on the topograph, as is for example the area indicated by the white circle. This indicated that at least at these positions, the superconducting gap does not simply depend on the apparent height of the termination of the cleaved crystal. Thus, these gap signatures picked up using STS are more likely originating from the AsFeAs block(s) beneath the surface.

Figure 29: On the left-hand side, the extreme values of the topograph are shown. On the right-hand side, these extreme values are stacked on top of the gap map. The white circle represents an area where the superconducting gap is seen to vary and no extreme topographic features are seen.

4.3

Comparison annealed and as-grown BaCo

Fe

As

The measurements on as-grown BaCo0.14Fe1.86As2 were performed by Freek Massee on the same

Createc LT STM using PtIr tips and at 4.2 K. At the time of these measurements, the system was installed on Newport I-2000 vibration isolation legs rather than on the Minus-K vibration isolation legs. The BaCo0.14Fe1.86As2 crystal was grown in self flux, as were those which were subsequently

annealed, data from which have been presented in the preceding paragraphs. The as-grown sample had a transition temperature of 22 K. All data have been processed in the same way as in the case of the data from the annealed sample. It should be noted that the Co-concentration of the as-grown sample is a bit lower than that for the annealed sample, 0.14 compared to 0.2. It has been reported that the gap structure does not undergo major changes with increasing doping level [40] and thus, a reasonable comparison can be made.

The topograph where the gap map was taken and its FT are shown in Fig. 30. The topograph shows no (2x1) reconstruction but a more complicated, maze-like structure. The gap map has been argued to be independent of the surface reconstruction [16] and thus, the gap map on this surface can be compared to the one made one the (2x1) reconstruction.

Figure 30: The topograph of as-grown BaCo0.14Fe1.86As2, from which the gap map was taken, and

its FT. Data from [16].

The gap map of the as-grown sample is shown in Fig. 31 along with the histogram of the gap map. It has to be noted that the settings used for this experiment (such as bias voltage, current and modulation amplitude), are slightly different from the ones used for the annealed sample (see Table 1).

Annealed BaCoxFe2−xAs2 As-grown BaCoxFe2−xAs2

x 0.2 0.14

Vbias 50 mV 35 mV

I 50 pA 40 pA

Fq 731.9 Hz 427.3 Hz

Amp 2 mV 2 mV

Vibration Isolators Minus-K Newport I-2000

Table 1: The different doping levels, settings and vibration isolators for both samples.

The value of the superconducting gap varies from below 8 meV to greater than 20 meV. The range of this gap is significantly greater than the 10-16 meV range for the annealed sample. For the as-grown sample, the global peak in the histogram is situated at 12.7 meV which is within 0.1 meV from the peak of the annealed sample. The 2∆

kBTc value for the as-grown BaCo0.14Fe1.86As2 ranges from 4.2 to 10.5 with a modal value of 7.8. This reduced gap value naturally has a larger range, and it also has a larger value compared to the reduced gap value of the annealed one. This difference in reduced gap value is at least in part caused by the difference in transition temperature, since the average 2∆ values for both samples are comparable. The annealed sample has a higher transition temperature and therefore, a lower reduced gap value. For the histogram, the gap value distribution for the as-grown crystal is much broader above the average than that below it. This suggests the possibility of a double gap situation and two corresponding Gaussian distributions. The histogram provides better fit results when fitted with the combination of the two separate Gaussian distributions. The separate distributions are plotted in Fig. 31 in black and the total fit function in blue. Apart from the fact that the two-gap distribution fits give a broader histogram,