Photocurrent manipulation in topological insulators with light polarisation

Universiteit van Amsterdam

Faculty of Science

Report of Bachelorproject Physics- and Astrophysics, content 15 EC, conducted between 30-03-2015 and 03-07-2015

Photocurrent manipulation in topological insulators with light

polarisation

Abstract

Topological insulators (TIs) are materials that have a spin polarized photocurrent response to electromagnetic radiation, due to the presence of a unique surface electronic structure. Such helicity dependent photocurrents have recently been observed by McIver et al. [2011]. The goal of this experiment is to build a setup that can be used to detect such photocurrents. I have build a fully automatized setup that can map the photocurrent response as function of position on the sample and as function of the incident polarisation state of a HeNe laser. I have detected photocurrents in a 1% Sn doped Bi2T e2S esample that show a similar response as

was observed by McIver et al. [2011]. At the same time, I have also found clear differences with the results obtained by McIver et al. [2011]. In particular, I have observed photocurrents that may have a pure surface state origin. These results need to be further verified in future experiments. The sample gave a current due to the laser, which alternated under change of polarisation in a similar way as in the experiment executed by McIver et al. [2011].

Populaire samenvatting

Topologische isolatoren (TIs) zijn isolerende materialen die een geleidend opper-vlak hebben. Deze nieuwe materialen hebben unieke eigenschappen die uitzicht bieden op toepassingen in de elektronica. Een van die eigenschappen is dat elek-tronen in het materiaal niet makkelijk naar een hogere energietoestand kunnen verstrooien, zoals ge¨ılustreerd in het energie tegen snelheid diagram in figuur 1.

Figure 1: Energie tegen snelheid diagram van elektronen op het op-pervlak (Junck et al. [2013])

In de figuur kun je zien, dat de lage energietoestanden gevuld zijn (blauw) en de hogere energietoestanden leeg (wit). In geleidende materialen kunnen de elek-tronen van deze gevulde toestand naar een hogere en-ergie toestand springen als je er een stroom door heen laat lopen. De elektronen uit deze stroom zullen tegen de kernen van het materiaal aan botsen, waardoor de elektronen van het materiaal genoeg energie krijgen om naar een lege toestand te springen, waardoor het materiaal opwarmt. In topologische isolatoren kan dit niet. Dit komt doordat de spin (het magnetische mo-ment, of draairichting van het elektron) in het hogere energieniveau omgekeerd is aan de spin in de bezette energietoestand. Een elektron kan alleen maar naar een hogere enrgietoestand gaan als de lege toestand de juiste spin heeft. Doordat een elektron dus niet zonder de spin om te draaien naar hoger energieniveau zal er veel minder warmte ontwikkeling plaatsvinden (link-erkant van figuur 1). Omdat er minder warmte on-twikkeling is , verlies je zo minder energie. De hoop is dat op deze manier nieuwe elektronica (spintronica) ontworpen kan worden de veel energie zuiniger is. In

eigen-schap van een topologische isolator die hier zeker niet los van staat. We hebben in ons experiment geprobeerd een stroom te laten lopen door het materiaal door er licht op te schijnen. Niet zo maar licht, maar circulair en lineair gepolariseerd licht. Circulair gepolariseerd licht zou namelijk kunnen doen wat ons elektron eerder niet kon, de spin van het elektron omdraaien (rechterkant van figuur 1). Rechtsom circulair gepolariseerd licht draait de spin op zo een manier dat de elek-tronen aan de rechterkant van figuur 1 de juiste spinrichting krijgen en naar een hoger energie niveau kunnen, dit gebeurd echter niet aan de linkerkant. Door deze onbalans in elektronen aan de linkerkant en elektronen aan de rechterkant gaat een stroom lopen. Die stroom hebben we geprobeerd te meten. We hebben een opstelling gebouwd, waarbij een laser op een sample schijnt met daar tussen op-tische elementen die het licht van polarisatie kunnen laten veranderen. Door te kijken naar het verschil tussen stroom bij circulaire polarisatie en lineaire polar-isatie konden we zien dat er inderdaad een photostroom (stroom door licht) ging lopen.

Acknowledgements

I would like to thank Erik van Heumen for supervising me during this project and helping me write my thesis. I want to thank Hugo Schlatter for helping me prepare the sample and taking me to AMOLF to make the contacts. I would also like to thank Gerrit Hardeman for programming labview, Hans Ellermeijer for building our first mount and Johan Mozes for building the automated mount. I also want to thank them for helping with all the other technicalities that Erik and I couldn’t do ourselves. Further, I want to thank Yu Pan for helping me put wires on our sample. At last I would like to thank Alona Tytarenko for answering my questions and giving me advice when Erik was not around.

Contents

1 Introduction 6

2 Theory 7

2.1 Introduction . . . 7

2.2 Previous experimental work . . . 8

2.3 Theoretical interpretation . . . 9

3 Experimental Setup and Method 11 3.1 Sample preparation . . . 11

3.2 Setup . . . 12

3.3 Apparatus . . . 13

3.4 Method . . . 18

4 Results 20

Chapter 1

Introduction

In recent years topological insulators have arrived as a hot topic in condensed matter physics. These materials are bulk insulators with metallic surfaces. What makes them different from ordinary band insulators? The surface states in a TI stay metallic, even under strong disorder because the states are protected by time-reversal symmetry. They are also helical, which means that each surface-momentum state has a unique spin direction. Due to this helical property of the surface states, a photocurrent can be observed in response to electromagnetic ra-diation (McIver et al. [2011]). Theorists have proven that there indeed should be a photocurrent in this case.[Junck et al., 2013]

The goal of this bachelor thesis’ experiment is to investigate photocurrents gen-erated in topological insulator materials. The earlier experiments showed that the current response is determined by several effects that occur simultaneously (bulk effects, surface effects, effect due to light and effects due to temperature). Starting from the theoretical predictions we will try to provide a recipe to disentangle the photocurrent associated with the topological surface states from the other sources mentioned above. Such a recipe could provide us with a new tool to investigate or detect topological surface states.

This thesis will describe the development of a new setup that was used to in-duce and measure photocurrents in the topological insulator S n0.01Bi1.99T e2S e. In

Chapter 2 the theory will be described, Chapter 3 describes the sample prepa-ration, the experimental setup and the method. The results are represented in Chapter 4 and these results will be discussed in Chapter 5.

Chapter 2

Theory

2.1

Introduction

Figure 2.1: Dirac cone in k-space, the electron spin points perpenidcularly to the momentum. Adapted from Qi and Zhang [2011]

As was said in the introduction, topo-logical insulators are states of mat-ter with insulating bulk and conduct-ing surface states that are invariant un-der time-reversal. The topological pro-tected surface states consist of Dirac fermions (massless, charged, spin 1/2 particles). Due to the strong spin-orbit interaction in these materials the topo-logical surface states are helical, this means that the electron spin points per-pendicularly to the momentum, form-ing a left handed helical structure in k-space (figure 2.1). The spin-momentum locking prevents the he-lical edge states from backscattering. This helical structure presents itself as a Dirac cone, which has been ob-served in many materials using angle resolved photoemission spectroscopy

(ARPES). Materials with helical surface states are expected to have a rather unique photocurrent response to electromagnetic radiation. This is due to

spin-selection rules: Looking at a 2D Dirac cone (figure 2.2) you can see clearly, that for an electron to excite to the top level of the cone, a spin needs to be flipped. When the material is illuminated with circularly polarised light, an electron on one side of the cone will be able to make a transition, while the electron on the other side of the cone will not be able to do this for the same handedness of the circular polarisation. As a result this imbalence in the momentum distribution leads to a current. [Junck et al., 2013]

2.2

Previous experimental work

Experimentally, we can use a polariser and a λ₄ wave plate to provide circular po-larised light. This wave plate (or phase retarder) will change the polarisation of the light from left handed circular to right handed circular, with linear polarisation in between. When the polarisation is vertical (or 0◦) and the the wave plate is rotated over an angle α, the light will change from linear (α= 0◦_{), to right handed}

circu-lar (α = 45◦), to linear (α = 90◦), to left handed circular (α = 135◦) etc.. When

Figure 2.2: Dirac cone in k-space. Circularly polarised light will excite the elec-tron on the left side of the cone, but not on the right, inducing a current. Adapted from Junck et al. [2013]

the polarisation is horizontal this will be the same except that the order of left and right circular polarisation is reversed. In McIver et al. [2011] the current was mea-sured in the x- and y-direction and (with the y-direction perpendicular to the plane of incidence), with an 56◦angle of incidence and normal incidence. For current in the y-direction was also measured for normal incidence. The polarisation was P-polarised, which means that the polarisation is parallel to the plane of incidence. The current they measured could be described by the following function.

j(α)= D + C sin(2α) + L1sin(4α)+ L2cos(4α) (2.1)

In this function, C and L1are helicity dependent and thus responsible for the

pho-togalvanic effect (utilizing the generation of a potential difference between two electrodes by illumination). D and L2 are terms with bulk origin, probably

orig-inating in the photon drag effect (effective mass increase of conduction electrons or valence holes due to interactions with the crystal lattice in which the electron moves). The measurement in the y direction gave a current with a large positive C term and the other term negative, but approximately the same size. They also measured the current in the x-direction, which gave a current twice as small as the one measured in the y-direction. The dominating term (after D) was L2which

means that the current generated in this direction has almost no surface origin. When the light is normally incident, C vanishes completely. From this they con-cluded that the C-term arises from the asymmetric optical excitation of the helical Dirac cone. [McIver et al., 2011]

2.3

Theoretical interpretation

Cand L1originating from the surface is also supported by a theoretical article by

Junck et al. [2013]. In this article the equation given for photocurrent for the ideal Dirac spectrum in the y-direction is,

jy(α)= C sin(2α) + L1sin(4α) (2.2)

(reference frame and constants changed to match McIver et al. [2011]). For pho-tocurrent for the ideal Dirac spectrum in the x-direction another equation was used,

where L2is a constant. This means that measurements of current in the x-direction

should give the same value for left circular polarised light as for right circular polarised light. From the same article also followed that p-polarised light won’t give a photocurrent, but s-polarised will.[Junck et al., 2013]

Chapter 3

Experimental Setup and Method

3.1

Sample preparation

The sample that was used was S n0.01Bi1.99T e2S e. It was approximately 6 mm

in length, 2.5 mm in width and 1 mm in thickness. S n0.01Bi1.99T e2S eis a likely

candidate material to be a topological insulator, since it’s a close relative of the known TI Bi2T e2S e.

To make well-defined contacts on the sample, the middle of the the sample was covered with a piece of plastic. The whole surface was subsequently covered with a 100 nm layer of gold by sputtering. By removing the plastic, two clear Au contacts remained on the sides of the sample. The wire contacts were glued with silver paint on these contacts as seen in figure: 3.1.

(a) Schematic

(b) Foto

Figure 3.1: Sample with nano-layer gold on the sides and two contacts glued with silver paint.

3.2

Setup

The setup of this experiment is shown in Figure 3.2. A 50mW/cm2 laser beam was sent through a polariser, a λ₄ wave plate and a lens, before hitting the sample with an angle of incidence of 45◦. The sample was connected to ground and to an amplifier, which was connected to the lock-in amplifier. A signal generator was used to modulate the laser intensity with a sine wave reference frequency. The λ₄ wave-plate and the sample holder were both equipped with a stepper motor. This enabled automated rotation of λ₄ and high precision x, y movement of the

Figure 3.2: Setup of experiment. Laser was sent through a polariser, aλ₄ wave plate (automated with a stepper motor) and a lens before hitting the sample at variable angle of incidence. The sample holder was equipped with a x-y stepper motor and connected to an amplifier. This amplifier connected to the lock-in amplifier. The controller of the stepper motors and the lock-in were both connected to a pc.

Since we want to make use of horizontal and vertical polarised light, the laser was mounted with it’s main axis of polarisation under 45◦_{. This allows us to}

obtain both horizontal and vertical polarised light with equal intensity using a single rotatable polariser. The λ₄ wave plate changed the polarisation of the laser beam from linear to circular and back. If the polariser was vertical (θ = 0◦_{) and the}

wave plate started with it’s fast axis vertical (let’s say α= 0◦), the polarization was changed from vertical polarised (α= 0◦), to right circularly polarised (α= 45◦), to vertical polarised again (α= 90◦_{), to left circular (α}= 135◦_{) and that would repeat}

itself for the rest of the rotation. For horizontal polarisation this was of course the same only with a phase difference of 90◦, and horizontal linear polarised light (so, horizontal, left circular, horizontal, right circular, etc.). After the λ₄ wave plate a lens was placed to focus the beam. The sample was mounted in a small aluminium box (Figure 3.3a) in order to reduce electromagnetic interference in the photocurrent circuit. A small slit in the box provided optical acces to the sample. Inside the box one side of the sample was connected to the ground (a screw in contact with the outside of the box), the other side of the sample was connected to an output for a coax cable. The wires of the sample were connected to these by means of a printed circuit board. In the sample box several resistors and other outputs where present, these were not necessary in this experiment, but might be of use in future experiments. The sample was attached to the box by fastening the top part between two plastic plates that were screwed to the box, so that the sample is not in contact with the ground (figure 3.3b). The sample box was attached to a mount that could move in the x- and y-direction controlled by stepper motors, that could change the position with an accuracy of 2µm. For most measurements the step size was 10µm or 100µm. The stepper motors were all controlled by a computer program in Labview, this will be dealt with in Section 3.3. A current amplifier was used to convert the current to a voltage with a 106 amplification factor. The lock-in amplifier further amplified the signal and filtered away a large part of the noise using a modulation- demodulation technique. This will be explained in detail in Section 3.3.

3.3

Apparatus

Lock-in amplifiers are used to detect and measure very small AC signals using phase-sensitive detection to single out the component of the signal at a specific reference frequency and phase. The lock-in amplifies the signal it measures and multiplies it by the lock-in reference. The output of the phase-sensitive detector

(a) Outside of sample box. (b) Inside the sample box.

Figure 3.3: Sample with nano-layer gold on the sides and two contacts glued with silver paint.

will be the following: [Stanford Research Systems, 2002]

Vpsd = VsigVLsin(ωrt+ θsig) sin(ωLt+ θre f)

= 1

2VsigVLcos([ωr−ωL]t+ θsig−θre f)− 1

2VsigVLcos([ωr+ ωL]t+ θsig+ θre f)

(3.1)

When signal is passed through a low pass filter, the AC signals are removed. No signal will be left except when ωrequals ωL, the difference frequency component

will be a DC signal. The output of the phase sensitive detector (PSD) becomes:

Vpsd =

1

2VsigVLcos(θsig−θre f) (3.2) This way the noise will be filtered out; the PSD and low pass filter only detect sig-nals whose frequencies are very close to the lock-in reference frequency filtering out disturbances for whisch ωR not close to ωL. θ is the phase difference between

the signal and the lock-in reference oscillator. By adding a second PSD the phase dependency can be eliminated and two outputs arise. One proportional to cos(θ) and one to sin(θ),

Y = Vsigsin(θ) (3.4)

The phase dependency is removed by computing the magnitude (R) of the signal,

R= (X2+ Y2)1/2 = Vsig (3.5)

The phase difference between the lock-in reference and the signal can be calcu-lated using:

θ = arctan(Y/X) (3.6)

In Labview a program was made that recorded the lock-in outputs X and Y and stored them into a text file. It was programmed to measure a specified number of points, then move over the sample or rotate the wave-plate (or both), and start measuring again. Other than just storing some measurements, the program had a lot more capabilities. In Figure 3.4 a screenshot can be seen of the program. In the yellow framed box all settings that are also on the lock-in amplifier are present. These settings can be changed before and during a measurement. From the mo-ment the program is started, the values that the lock-in measures can be followed in the purple framed windows. The top one with the X values and the bottom one with the Y values. Having these windows is very convenient when you want to check if what you are measuring makes sense without having to put the data files into the analysing program. The scan selector is framed in green, it is a drop down menu in which a scan can be selected, choices can be made between scanning x, y (of the sample) and rotate (of the wave plate), in all possible combinations. The red framed part is where the sort of scan can be further specified; which part of the sample you want to scan (in µm) and how much you want to rotate the λ₄ plate (in◦_{) in a certain amount of steps. The small boxes above the red frame indicate}

number of measuring points per step and the time that is measured per point. On the bottom of the screen, framed by a blue line, there is a set position option. With the three variables (x, y, and angle) the sample can be moved, and the wave plate rotated.

The data is analysed using a routine programmed in Igor (screenshot figure: 3.5). This program averages over the points measured for one position (or rotation) and calculate the current J. It could do this using al three degrees of freedom that the stepper motors used and create 2D and 3D graphs. The program also fits the current to the following function:

Figure 3.4: Screenshot of Labview program: Yellow, options that are also present on the lock-in amplifier. Green, scan selector and start/stop sweep button. Red, range in which the measurement takes place, and the distance between steps. Blue, Set position. Purple, monitor window.

Which is the same equation as was used in the article of McIver et al. [2011]. In the screenshot in figure 3.5 a scan over the x-direction can be seen, while rotating the wave plate for every step in that scan. In the graph in the top left corner this data is plotted as position versus rotation, with the colours indicating what the value of the current is (blue is the lowest value and red the highest). The red lines in the graph indicate the cut that can be seen in the other two graphs. The horizontal line can be seen in the top right corner and shows current versus rotation. The vertical line can be seen in the bottom right corner and shows current versus position. The data is loaded into the program using the indicators framed by the green box. These indicators are the same as the ones used to start the

measurement in Labview (Figure: 3.4, red box). In the yellow frame it is possible to change the cuts of the measurement, so basically changing the position of the red lines in the top left graph. The orange framed part is were the data can be fitted. The values for D, D1, D2, C, L1and L2 can be put in and fixed if necessary.

It is also possible to fit more cuts of the data at the same time by inserting a start and an end position, and hitting ’fit all’. The values of D, D1, D2, C, L1and L2will

be stored in a table, so it will be easy to compare them with each other.

Figure 3.5: Screenshot of Igor program. Top right corner, graph of position versus rotation versus current (blue being the lowest current and red the highest). Top left corner, cut of the data, plotting current versus rotation. Bottom left corner, cut of the data, plotting current versus position. Green framed, indicators of the range in which the data was measured and the step size. The data can be loaded by hitting ’Load data’. Yellow framed, way to browse trough the data and take other cuts (for the graphs top right and bottom right). Orange framed, indicators to fit the data to equation 3.7. Indicators can be locked if deemed necessary and more cuts can be fitted at the same time.

3.4

Method

The goal of this experiment is to measure photocurrent and build a setup that can reproduce the experiment of McIver et al. [2011]. Unfortunatly photocurrents are not the only thing that will arise when illuminating the sample, but also thermo-electric currents. These thermothermo-electric currents emerge because when the sample is illuminated by a laser, it will only partly warm up, creating thermoelectric cur-rents. In the paper of McIver et al. [2011] they tackled this problem by scanning over the sample with the laser while measuring the current. The results of this are shown in figure 3.6a. The current goes from positive to negative close to the mid-dle of the sample. In the midmid-dle of the sample thermoelectric currents should be zero, since the thermoelectric currents from both sides of the sample will cancel each other. The current in the article of McIver et al. [2011] shows a non-zero current in the centre, indicating a that there is an additional contribution. This is the location were they measured the current with the rotation of the λ₄ wave plate. The result of this measurement (under a 56◦_{angle of incidence in the y-direction)}

can be seen in figure 3.6b. The sample used in the article of McIver et al. [2011] was Bi2S e3 and was 3µm by 5µm by 120nm (figure3.6c). They also used a laser

bigger than the sample (100µm), constantly illuminating the whole sample. We used a different sample (S n0.01Bi1.99T e2S e) because Bi2S e3has a relatively large

bulk conduction. At the WZI a large effort has been made to make TIs with a high bulk resistivity resulting in samples including ours. It is hoped that the sur-face state contribution will be larger than the bulk contribution because of the

(a) Position scan over the sam-ple.

(b) Current measured under ro-tation of λ₄ wave plate.

(c) The sample, 3µm by 5µm by 120nm

Figure 3.6: The position scan, rotation measurement and the sample of McIver et al. [2011]

improved bulk resistivity. This may make the identification of surface state cur-rents more clear.

In the following chapter we will follow the same procedure to try to identify pho-tocurrents.

Chapter 4

Results

The first measurement that was done was the position scan of the sample. Since our sample was bigger than the sample of McIver et al. [2011] and our laserspot smaller than the sample, we made an XY-scan over the sample surface, while mea-suring the current for every 10µm, as can be seen in figure 4.1b. The data in this figure looks slightly more complicated than the data in the article of McIver et al. [2011], but a laser induced current can be seen, which was the first goal of this experiment. The figure shows a map of the sample where red and blue give the maxima and minima of the current. Most minima and maxima can be observed on a diagonal line over the sample where also an irregularity can be seen (figure 4.1c). These minima and maxima might be seen in this position because the irreg-ularity causes this part of the sample to have a larger effective surface area. Since we don’t have a simple picture with the current going from zero, to negative, to positive and again to zero as can be seen in figure 3.6a (McIver et al. [2011]), we didn’t know on which position it was best to do a photocurrent measurement. That’s why we chose to measure over a small range of positions on the sample, where the current went from positive to negative (just like in the article of McIver et al. [2011]). In the figure 4.2, the first exploratory measurement can be seen. In this measurement we chose a position with maximum current close to x = 2 mm and y = 0,8 mm in figure 4.1b. We used horizontal polarised (p-polarised) light and measured with the contacts in the y-direction. This measurement corresponds closest to the geometry used by McIver et al. [2011] underlying figure 3.6b. After the exploratory measurement, a rotation scan was conducted over a small range (200µm) in position over the sample as was explained above. This mea-surement was executed for vertical and horizontal polarisation with contact ori-entated along the x- and y-direction. In figure 4.3 and 4.4 the results of these

(a) Sample with contacts. (b) Map of the sample where red and blue give_{the minima and maxima of the current.}

(c) Picture of the sample and the map of the sample on top of each other. The green dot indicates the the the size of the of the laserspot. The scale is in mm.

Figure 4.1: Figure 4.1c shows that the top peaks of the current are present in particular on the left contact and on the diagonal scratch on the sample.

measurements can be seen. Figure 4.3a shows a wide range scan of the current, for current measured in the y-direction. Also indicated are two coloured areas (red, blue) corresponding to the panels shown in 4.3b and 4.3c. Figure 4.4a also shows a wide range scan of the current, but with contacts orientated along the x-direction. Here the coloured areas (green and dark blue) correspond to figure 4.4b and 4.4c. The top figures of figure 4.3b, 4.3c, 4.4b and 4.4c show the pho-tocurrent for linear polarisation measured over a narrow range along the sample.

3.8 3.6 3.4 3.2 current (nA) 300 200 100 0 rotation (°) data fit C = 0.14 L1 = 0.02 L2 = 0.33

Figure 4.2: Current versus rotation, fitted to equation 3.7. The current was mea-sured for horizontal polarisation in the y-direction.

The bottom figures show an (y,α) map (or (x,α) map depending on orien-tation of the contacts) with a color scale ranging from −3nA (blue) to 5nA (red). The figure in the middle of ev-ery framed box is the most interesting. It shows the values of the C, L1and L2

terms of equation 3.7 for every posi-tion in the measured range. A compar-ison of these four experiments displays an interesting recurrence. In the loca-tion where the photocurrent becomes 0 for linear polarisation, a finite current appears for circularly polarised light. In the article of McIver et al. [2011],

only measurements with horizontal polarisation where done, but they did do ex-periments with contacts along the x- and y-direction. They showed that a mea-surement of the current in the y-direction should give a clear photocurrent, with the C term large and positive, and L1 and L2 approximately the same magnitude

but negative. Our measurement gave us similar results for some positions on the sample. In the same article it was also shown that for contacts in the x-direction, all three of these terms should become at least 4 times smaller. This result was ab-sent from our measurements. However, in order to change the contacts the sample needs to rotate and we are not sure that we have located the same position. Most likely not given figure 4.3a and 4.4a.

The current for the rotation of the λ₄ wave plate on the position where the current is very close to zero and the fit can be seen in figure 4.5. The figure shows the cur-rent for horizontal polarisation with contacts orientated in the x- and y-direction (the current for vertical polarisation looks similar). In these two data figures it can be clearly seen that the sin(2α) is dominant (C) and that the sin(4α) and the cos(4α) are almost absent (L1 and L2). This sin(2α) is characteristic for a

pho-tocurrent in the y -direction, but in combination with the other two terms. In the x-direction there shouldn’t be a sin(2α) term at all for a photocurrent (Junck et al. [2013]). Another observation is a 45◦phase difference between current in the x-and y-direction. Although it is tempting to assign the photocurrent in figure 4.5a to the TI surface states, the result of 4.5b may cost some doubt on this conclusion. This sin(2α) is supposed to become very small for a small angle of incidence if it truly belongs to the photocurrent of the surface state (McIver et al. [2011]). To see

(a) Big range (1mm) position scan in the middle of the sample in the y direction, horizontal polarisation.

(b) Horizontal polarisation. _{(c) Vertical polarisation.}

Figure 4.3: Current in the y-direction under horizontal (framed blue) and vertical (framed red) polarisation. From top to bottom: First, small range (200µm) position scan. Second, position versus rotation, the colorscale ranges form −3nA (blue) to 5nA (red) and at the bottem the values of C, L1 and L2 if the data is fitted to

if the result in 4.5a is really a surface state photocurrent we decided to also mea-sure under a smaller angle of incidence (15◦_{). These results can be seen in figure}

4.6 and 4.7. Figure 4.6a and 4.6b show again the current against position mea-surement, and figure 4.6c and 4.6d show the (y,α) maps with a color scale ranging from −3nA (blue) to 5nA (red). In contrast to figure 4.4 and 4.3 the fit coefficients L1 and L2 in figure 4.6f and 4.6e are now zero over the entire measured range ,

while C shows an oscillatory behaviour. In figure 4.7 the fitted data can be seen for a position on the sample with high current. There is again a phase difference between horizontal en vertical polarisation, but this time of approximately 15◦. These results are quite similar to the results seen in figure 4.5.

(a) Big range (2mm) position scan in the middle of the sample in the x direction, hotizontal polarisation

(b) Horizontal polarisation. _{(c) Vertical polarisation.}

Figure 4.4: Current in the x-direction under horizontal (framed green) and vertical (framed dark blue) polarisation. From top to bottom: First, small range (200µm) position scan. Second, position versus rotation, the color scale ranges form −3nA (blue) to 5nA (red) and at the bottem the values of C, L1and L2if the data is fitted

0.2 0.1 0.0 -0.1 current (nA) 300 200 100 0 rotation (°) data fit

(a) Current in the y direction, horizontal po-larisation. 0.30 0.20 0.10 0.00 current (nA) 300 200 100 0 rotation (°) data fit

(b) Current in the x direction, horizontal po-larisation.

Figure 4.5: Current versus rotation, fitted to equation 3.7. Location on the sample with almost zero current.

(a) Position scan vertical polarisation. (b) Position scan horizontal polarisation.

(c) Position versus rotation versus current, the color scale ranges form −3nA (blue) to 5nA (red). Vertical polarisation.

(d) y-position versus rotation versus current, the color scale ranges form −3nA (blue) to 5nA (red). Horizotal polarisation.)

0.10 0.08 0.06 0.04 0.02 0.00 value 300 200 100 0 y position (µm) C L1 L2

(e) Values the constants C, L1 and L2 from

equation: 3.7, versus rotation. Vertical po-larisation. 0.10 0.08 0.06 0.04 0.02 0.00 value 300 200 100 0 y position (µm) C L1 L2

(f) Values the constants C, L1 and L2 from

equation: 3.7, versus rotation. Horizontal polarisation.)

Figure 4.6: Data for angle of incidence 15◦. Vertical polarisation and horizontal polarisation.

2.70 2.65 2.60 2.55 current (nA) 300 200 100 0 rotation (°) data fit

(a) Horizontal polarisation

2.75 2.70 2.65 2.60 2.55 current (nA) 300 200 100 0 rotation (°) data fit (b) Vertical polarisation

Figure 4.7: Data fits of current versus rotation in measurement with 15◦angle of incidence.

Chapter 5

Discussion and Conclusion

In our experiment we have found three key observations:

• We have observed photocurrent, but with some deviations from the litera-ture.

• We found locations on the sample with similar polarisation dependence as McIver et al. [2011], but also positions that seem to be dominated by purely helicity dependent photocurrent.

• We have not observed large differences between orientation/polarisation as was predicted.

The positions on the sample which seemed to be dominated by purely helicity dependent photocurrent (figure 4.5a) look a lot like the photocurrent measured under a 15◦angle of incidence (figure 4.7a), which shouldn’t be helicity dependent at all according to McIver et al. [2011] and Junck et al. [2013].

The photocurrent observed in the y-direction for p-polarisation (horizontal) and s-polarisation (vertical) under a 45◦angle of incidence didn’t differ much from each other, while from the theory (Junck et al. [2013]) followed that there shouldn’t be a current for p-polarised light, there should be a current for s-polarised light when measuring pure surface state photocurrent. Since there are also other effects that cause current it is logical that we don’t see zero current for p-polarisation, but we should at least see a difference between the two polarisations.

Measurements with smaller sample might explain more , since it would give less influence from the bulk. Moving the laser over the sample instead of moving the sample itself in respect to laser spot, will give a better accuracy in which can be

measured. The sample box is a lot heavier than the laser, which can cause the stepper motor to skip over points. These preliminary measurements do however show that this new setup can provide a good basis for further research.

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