University of Groningen
Full superconducting dome of strong Ising protection in gated monolayer WS2
Lu, Jianming; Zheliuk, Oleksandr; Chen, Qihong; Leermakers, Inge; Hussey, Nigel E.; Zeitler,
Uli; Ye, Jianting
Published in:
Proceedings of the National Academy of Sciences of the United States of America
DOI:
10.1073/pnas.1716781115
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Lu, J., Zheliuk, O., Chen, Q., Leermakers, I., Hussey, N. E., Zeitler, U., & Ye, J. (2018). Full
superconducting dome of strong Ising protection in gated monolayer WS2. Proceedings of the National
Academy of Sciences of the United States of America, 115(14), 3551-3556.
https://doi.org/10.1073/pnas.1716781115
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Full superconducting dome of strong Ising protection in
gated monolayer WS
2
Jianming Lua, Oleksandr Zheliuka, Qihong Chena,b, Inge Leermakersc,d, Nigel E. Husseyc,d, Uli Zeitlerc,d, and Jianting Yea,1 aDevice Physics of Complex Materials, Zernike Institute for Advanced Materials, University of Groningen, 9747 AG Groningen, The Netherlands; bDepartment of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China;cHigh Field Magnet Laboratory–European
Magnetic Field Laboratory (HFML-EMFL), Radboud University, 6525 ED Nijmegen, The Netherlands; anddInstitute for Molecules and Materials, Radboud
University, 6525 ED Nijmegen, The Netherlands
Edited by Zachary Fisk, University of California, Irvine, CA, and approved February 21, 2018 (received for review September 26, 2017)
Many recent studies show that superconductivity not only exists in atomically thin monolayers but can exhibit enhanced properties such as a higher transition temperature and a stronger critical field. Nevertheless, besides being unstable in air, the weak tunability in these intrinsically metallic monolayers has limited the exploration of mono-layer superconductivity, hindering their potential in electronic applica-tions (e.g., superconductor–semiconductor hybrid devices). Here we show that using field effect gating, we can induce superconductivity in monolayer WS2 grown by chemical vapor deposition, a typical
ambient-stable semiconducting transition metal dichalcogenide (TMD), and we are able to access a complete set of competing electronic phases over an unprecedented doping range from band insulator, superconductor, to a reentrant insulator at high doping. Throughout the superconducting dome, the Cooper pair spin is pinned by a strong internal spin–orbit interaction, making this material arguably the most resilient superconductor in the exter-nal magnetic field. The reentrant insulating state at positive high gating voltages is attributed to localization induced by the char-acteristically weak screening of the monolayer, providing insight into many dome-like superconducting phases observed in field-induced quasi-2D superconductors.
transition metal dichalcogenides
|
Ising superconductivity|
spin-orbit coupling|
monolayer|
ion-gated transistorT
he last decade has witnessed the flourishing development of isolating layered materials to their 2D limit (1). Reducing the dimensionality of an electronic system from three to two di-mensions often conserves its fundamental electronic properties while simplifying the theoretical description; hence, a number of exact solutions of important physical models exist in 2D (2, 3). Although quantum confinement is gradually enhanced with re-duced thickness, significant modifications to the electronic states sometimes are observed when the system approaches the mono-layer limit such as the massless Dirac band in graphene (4, 5) and indirect-to-direct band gap transition in MoS2(6). On the otherhand, the dimensionality of a system is not an invariable but is rather related to specific phases (7), determined by the ratio of the geometrical thickness d to fundamental electronic length scales such as the phase or superconducting coherence lengthξ. For in-stance, 2D superconductivity is well established in amorphous films of superconducting metals (8) far thicker than a single atom be-cause ξ can easily exceed d. However, due to the large carrier density in metals, the corresponding Fermi wavelengthλF of
dif-fusive electrons appearing after a quantum phase transition is typ-ically smaller than d. This means that the transition coincides with a dimensional crossover from a 2D superconductor to a quasi-2D or 3D diffusive system. Such a dimensional crossover has also been observed in superconducting interfaces and cuprates when approaching the optimal gating and doping, respectively (9, 10).
These constraints have motivated the search for truly mono-layer superconductors (11, 12). Recently, epitaxial growth on optimized substrates has given rise to elemental monolayer films (13, 14) (Pb, In, Ga, etc.), monolayer FeSe (15), as well as monolayer cuprate (16), heavy fermion (17), and organic
superconductors (18). The interaction between these monolayers and their substrates appears to be strong, with the electronic and vibrational couplings in the third dimension believed to be re-sponsible for a reduced critical temperature Tcin metallic
mono-layers and a significantly enhanced Tcin FeSe, respectively. Van der
Waals layered materials (19–21) are 2D systems where electrons are mainly confined in a covalently bonded crystalline plane. Therefore, by breaking the van der Waals stacking, monolayer superconducting transition metal dichalcogenides (TMDs) [such as NbSe2(22, 23)]
and high-Tc cuprates Bi2Sr2CaCu2O8(24) could exhibit truly 2D
characteristics. However, due to their large intrinsic carrier density, switching electronic phases in these superconductors appears to be limited (25). Another strategy is to induce superconductivity in a semiconducting TMD monolayer such as MoS2in ref. 26, though
here, the availability of possible electronic phases and their varia-tion by field effect has yet to be explored.
Here we demonstrate that monolayers of the semiconducting TMD WS2, where both carrier tunability and true 2D
charac-teristics are accessible, provide an extremely versatile option for field effect control of various quantum phases. By field effect gating, WS2 flakes evolve from a direct band insulator into a
metal that exhibits superconductivity (27–35) at low tempera-tures. The significant spin–orbit coupling in the conduction band leads to so-called Ising superconductivity (23, 36, 37) that is re-markably robust against external in-plane magnetic fields. Be-yond the peak of the superconducting dome, the normal state becomes more resistive with increasing gate bias, eventually
Significance
Compared with 3D superconductors, atomically thin super-conductors are expected to be easier to engineer for electronic applications. Here, we use field effect gating to induce super-conductivity in a monolayer semiconducting transition metal
dichalcogenide, WS2, grown by chemical vapor deposition. The
remarkable doping range allows access to a cascade of elec-tronic phases from a band insulator, a superconductor, to a reentrant insulator at high doping. The large spin-orbit
cou-pling of∼30 meV makes the Ising paring in WS2arguably the
most strongly protected superconducting state against exter-nal magnetic field. The wide tunability revealed by spanning over a complete superconducting dome paves the way for the integration of monolayer superconductors to functional elec-tronic devices exploiting the field effect control of quantum phases.
Author contributions: J.L., O.Z., U.Z., and J.Y. designed research; J.L., O.Z., Q.C., I.L., N.E.H., and J.Y. performed research; J.L., O.Z., Q.C., and J.Y. analyzed data; and J.L. and J.Y. wrote the paper.
The authors declare no conflict of interest. This article is a PNAS Direct Submission. Published under thePNAS license.
1To whom correspondence should be addressed. Email: j.ye@rug.nl.
This article contains supporting information online atwww.pnas.org/lookup/suppl/doi:10. 1073/pnas.1716781115/-/DCSupplemental.
Published online March 19, 2018.
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PHYSICAL
quenching the superconductivity, and a second distinct insulating ground state develops beyond the superconducting dome. Methods
The monolayer WS2flakes used in our experiments are grown by chemical
vapor deposition (CVD). The high quality of the as-grown crystalline sheets is confirmed by the observation of strong photoluminescence (PL) and a mo-bility ofμ ∼ 300 cm2/Vs at 10 K and at optimal gating, which is comparable to
or higher than for its cleaved counterparts (38) (Fig. S1). An electronically homogeneous part exhibiting a uniform PL is isolated by etching a standard Hall-bar from a pristine triangular monolayer (Supporting Information, section 1) and fabricated into a dual-gate configured device composed of an ionic liquid top gate (VTG) and a dielectric back gate (285 nm SiO2on a highly
doped silicon substrate, VBG) as shown in Fig. 1A. This dual-gating method
allows both coarse and fine electrostatic control of quantum phases ( Sup-porting Information, section 2). Applying first an ionic gate at T∼220 K, we can introduce an extremely strong electrostatic field effect, which is sub-sequently fixed by freezing the ionic liquid below its glass transition tem-perature Tg∼ 190 K. By grounding the ionic gate and sequentially warming
the device slightly above Tg, we are then able to create dense coarse doping
states (color coded in Fig. 1B), which can be seamlessly linked at low tem-peratures by VBG. The quasi-continuous transfer curve thus obtained (black
curve in Fig. 1B) defines electronic phases as a function of effective gate voltage Veff(Supporting Information, section 4). Note that on both sides of
optimal doping, the dependence of Hall carrier density on Veffis opposite:
positive on the left, but negative on the right, relating to the reentrant insulating phase at low temperatures (for more discussion see Fig. 4). Around optimal doping, there is a crossover linking two monotonic corre-spondences (as elaborated inFig. S5). Therefore, we use Veffinstead of Hall
carrier density to label states across the whole spectrum. Although a simple capacitance model cannot be applied directly to our dual gated device (39), Veffgenerally scales linearly with the number of charge carriers injected into
the sample, which is equivalent to the nominal stoichiometry of in-tercalated/doped bulk compound.
Results and Discussion
The Veffdependence of the sheet resistance Rs(Fig. 1B) at 2 K
(diamond), 10 K (triangle), 70 K (square), and 150 K (circle) gives an overview of the whole spectrum of electronic states. Between two insulating phases, metallic transport appears at intermediate values of Veffaccompanied by a transition into a superconducting
state. At Veff= 1,130 V, optimal transport shows the lowest Rsand
the highest superconducting transition temperature Tc.
The temperature dependence of Rson the left and right sides
of optimal doping is shown in Fig. 1 C and D, respectively. The curves reveal that superconductivity emerges from a nonmetallic state (dRs/dT < 0, Fig. 1C) when approaching optimal doping
from the low gating side and quenches into another insulating state at high gating (Fig. 1D). In this way, a full spectrum of electronic phases can be prepared using a single tuning param-eter Veff, allowing the properties of different quantum phases—
such as the quantitative dependence of superconductivity on Veff
(Insets in Fig. 1 C and D)—to be analyzed in detail.
The full phase diagram is shown in Fig. 2, with the super-conducting dome spanning the range 0.8 kV≤ Veff ≤ 1.6 kV.
(Throughout, Tcis defined as the temperature at which Rsfalls to
50% of its normal state value.) The Veffdependence of the Hall
carrier density nHall(Fig. 2, Lower) indicates that Tc is mainly
driven by changes in the carrier density. However, the separation between the maxima of Tcand nHall(10 K) suggests that Tcmay
also be affected by electron-impurity scattering, as inferred from the opposite Veff dependence of carrier mobilityμ (T = 10 K,
right axis in Fig. 2, Lower) extracted from Rs(Fig. 1B) above and
Fig. 1. Electrical transport of ion-gated monolayer WS2. (A) Schematic of measurement set-up with both ion liquid VTGand solid back gates VBG. (Inset)
Optical image of the monolayer etched into standard Hall-bar geometry. (B) Transfer characteristics measured by scanning VBGat 70 K with various VTGs were
concatenated, as indicated by the black line. The origin of effective gate voltage Veffwas extrapolated using gate dependence of Hall carrier density (Fig. S4).
Square resistance Rsat typical temperatures (150 K, circle; 70 K, square; 10 K, triangle; 2 K, diamond) are shown for many different Veffs to reveal the
evolution from an insulator to a superconductor and finally, to the reentrant insulator. Each color represents a specific VTG. (C and D) Temperature-dependent
Rsis plotted for regimes before (C) and after (D) the peak of the superconducting dome, where each curve corresponds to one Veffof the same color in B.
(Insets) Details around the superconducting–insulating transition on a linear scale.
below the Tcmaximum. Notably in MoS2(27), a similarly gated
superconducting dome follows Tc ∝ (n2D− n0)zv, where zv∼ 0.6
is the product of exponents for correlation length (z) and cor-relation time (v) in scaling theory (3, 7), in analogy to that found for LaSrO3/SrTiO3 interfaces (40). In the present monolayer
superconductor, the limited temperature range precludes a res-olution of the scaling exponents and the exact locations of the two quantum critical points (QCPs, denoted roughly by two dashed circles). Nevertheless, within the experimentally accessi-ble phase space, the voltage dependence of Tcdoes not
contra-dict the relationship seen in the other two systems.
In many quasi-2D superconductors, quasi-metallic (qM) re-gions have been inferred (7, 40, 41), in which Rs exhibits a
temperature dependence weaker than exponential although overall dRs=dT < 0. Here, we define Tmin as the temperature at
which Rsreaches a minimum (Fig. 1 C and D) presumably from
competition between electron-phonon scattering and Anderson localization. In Fig. 2, the trace of Tmin(empty squares, Upper)
marks the boundary of the qM regime. It is worth noting that the qM region here is manifest in a finite-size sample at intermediate temperatures, which might cross over to insulating behavior at lower temperatures and/or in larger samples. We leave this question open to future investigations to be conducted at milliKelvin temperatures.
An outstanding feature of the 2D superconductivity in TMD materials is the Ising pairing (23, 36, 37) that originates from the valley coupled spin texture found in monolayer TMDs. In this cir-cumstance, the spins of the Cooper pairs become pinned by a strong out-of-plane effective magnetic field that is generated by an intrinsic
Zeeman-type spin–orbit interaction (SOC) pointing oppositely in K/ K′ valleys (Fig. 3B, Inset). The Zeeman field—normally the uni-versal pair-breaking mechanism in superconductors—here strongly protects the Cooper pair against an orthogonal (in-plane) external magnetic field. Compared with other quasi-2D Ising superconduc-tors such as ion-gated multilayer MoS2, where the electronic wave
function is confined to the uppermost layer and Ising pairing is protected by SOC∼6 meV (36), the much heavier transition metal in WS2 creates SOC that is five times larger (∼30 meV) (42),
pointing to an even higher in-plane upper critical field Bc2. This
stronger SOC in WS2, and hence larger spin splitting, can result in
an archetypal spin texture for Ising pairing, which avoids the crossing of two lower lying spin-split conduction bands in MoS2
when the Fermi level moves further away from the band edge at K/ K′ points (43). More importantly, the SOC in WS2is more than one
order of magnitude larger than the superconducting order param-eter calculated from maximum Tc. In this sense, monolayer WS2
may provide an elegant platform to probe unconventional Ising pairing theoretically predicted for this system (44, 45).
Guided by the phase diagram established in Fig. 2A, we suc-ceeded to induce superconductivity in another sample B with an optimal Tc= 3.15 K (Fig. 3A, Inset). The observed lower Tchere
is possibly due to the more defective crystal, as the interaction between electrons and charged scatterers would renormalize the superconducting order parameter (46). This is also consistent with the lower mobility of sample B. The Bc2s were measured in
three representative regions of the dome, as shown in Fig. 3. Interestingly, the strongest Ising protection was measured near the lower edge of the dome, where relatively weak electric fields
Fig. 2. Phase diagram of monolayer WS2and critical
scaling of quantum phases. (Upper) Superconducting critical temperatures TCare plotted (solid circle) as a
function of the effective back gate. Quasi-metal (qM) regime is bounded by metal–insulator crossover tem-perature (empty square). The initiation and sup-pression of the superconducting dome are indicated by dashed circles. (Lower) Hall carrier density mea-sured at 160 and 10 K are plotted on the left axis; Hall mobility at 10 K on the right axis.
APPLIED
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cause a minimum Rashba effect (36) (Fig. 3A, Upper: Tc= 1.54 K
only shifted byΔTc= 0.08 K for an in-plane field B//as high as
35 T). Following mean-field theory (36) (also seeSupporting In-formation, section 6), we can estimate the contribution from Zeeman-type SOC and Rashba splitting to the enhancement of Bc2(relative to the Pauli limit Bp= 1.86 Tc). The comparison with
experimental data (solid red points) is shown in Fig. 3B (red line). Assuming a Rashba effect created through ionic gating of order 0.7 meV—that is, as found near the left QCP of MoS2(36)—the
obtained Zeeman-type SOC is found to be 30 meV, consistent with theoretical calculations. Neglecting the Rashba contribution, our data set a lower bound of 19.5 meV for Zeeman SOC. Be-cause of the very large Bc2for states at the peak (Fig. 3A, Middle)
and the upper edge (Fig. 3A, Lower) of the dome, the change of Tc
at a maximum field of 12 T is below the measurement accuracy for extracting quantitative values of the SOC.
In Fig. 3B, we compared the ratio Bc2/Bp of other
supercon-ductors where the Pauli limit is significantly violated. For the gated monolayer WS2, Bc2/Bp is at least as large as those in the
UCoGe (47) and the submonolayer Pb film (48) protected by triplet pairing and Rashba splitting, respectively. It is much larger than other recently discovered Ising-protected superconductors such as multilayer MoS2 (36) and monolayer NbSe2 (23). It is
noteworthy that the Zeeman SOC in the NbSe2 (∼70 meV,
valence band) is even larger than that in both MoS2(∼6 meV)
and WS2 (∼30 meV), yet the level of protection in monolayer
NbSe2 and bulk (LaSe)1.14(NbSe2) (49) (resembling decoupled
monolayers at low temperatures) merely approaches that found in gated MoS2. A similar mismatch also appears in TaS2(Py)0.5(50),
where the pairing occurs also in the valence band. This reduction in Ising protection could be influenced by a competing charge density wave (CDW) phase and the contributions from a spin
degenerateΓ point (51), which might effectively weaken the strong Ising pairing formed at the K/K′ valleys of NbSe2and TaS2.
Another prominent feature of the data is the reversible re-entrance into a strongly insulating state at high Veff, which is
closely related to how the superconductivity is suppressed beyond optimal doping. First, we rule out the possibility of electrochemical reaction between WS2 and ion liquid as seen from the high
re-peatability of sample performances in consecutive gating processes (comparison of transport behavior is shown inFig. S6, and more is elaborated in Supporting Information, section 3.). Second, recent advances in studies of semiconducting WS2 (42) could safely
ex-clude many exotic(intrinsic) mechanisms as well, such as the opening of a Mott, CDW, or Kondo gap, and the enhanced cor-relation effects (52, 53). Alternatively, extrinsic mechanisms, which take into account the charged ions on the sample surface (54), may be more relevant. Typical examples include narrow-band materials such as rubrene (55) and ReS2(56) where Mott- and
Anderson-type localization were proposed, respectively, and wide-band ma-terials like silicon inversion layers (54, 57, 58) with Coulomb traps and strong short-range scattering from rough surfaces. To address this universal insulating phase, in the following, we focus on the common fact that all of the above examples involve ionic gating (either by ion liquid or alkaline metal).
Inspection of Arrhenius plots (Fig. 4A) yields similar in-sulating behavior at high temperatures for both the low and high gating sides of the dome. Without knowledge of the underlying transport mechanism, we tentatively extract a characteristic en-ergy scale. As shown in Fig. 4B, although the two enen-ergy scales are similar in magnitude, their dependences on Veff have the
opposite sign. The temperature dependence of nHall also
con-firms insulating behavior at large Veff, manifesting as a freeze-out
of carriers within a large range of gate voltages including the
Fig. 3. Ising pairing over the entire superconducting dome. (A) Upper critical field Bc2was measured on the left side (Upper), the peak (Middle), and right
side (Lower) of the superconducting dome (Inset to A). Superconducting critical temperature Tcis defined by 50% of normal state resistance denoted by the
dashed line. Each state is highlighted by an empty circle in the dome. (B) Normalized Bc2with respect to the Pauli limit in WS2is denoted by the solid red circle,
which exceeds that of many well-known superconductors with high Bc2, including TMDs, triplet pairing, and monolayer Pb film. (Inset) Schematic of
Zeeman-type effective magnetic fields (green arrows) with alternating directions in K/K′ valleys in a hexagonal Brillouin zone, which stabilize electron spins (red/blue denotes spin up/down) in a Cooper pair against external in-plane magnetic field Bex.
whole superconducting dome (Vefffrom 0.8 to 1.6 kV, Fig. 4C).
In contrast, a nearly temperature-independent nHallis observed
only in the qM region near the left QCP at low Veff.
To account for the above observation about activation energy and Hall carrier density, we adopt a scenario of a gate-induced band variation as sketched in Fig. 4D, which is based on the fact that randomly arranged charged ions can trap the induced carriers (54, 58) as well as disturb periodic lattice potential (56). In such a truly 2D system, weak out-of-plane screening exposes induced carriers directly to the potential of ions lying on the surface. The localization effect depends on the distance l between induced carriers and charge centers of the cations (Fig. 4D). At low Veff<< 1.1 kV, ions
accu-mulated by the weak electric field create a uniform potential, while at large Veff>> 1.1 kV, the discreteness of the ions at a reduced l can no
longer be averaged out by the characteristically weak 2D screening effect. This increased randomness enlarges the band tail (Fig. 4E) where more carriers localize, reducing the number of free carriers available for band transport. In the high gating limit and low tem-perature, every induced carrier is localized/bounded on site by the potential of an adjacent ion—that is, forming electron–cation pairs that mimic the hydrogen impurity model (Fig. 4E, Right). Strongly
localized electrons in the reentrant regime would form an impurity band, thereby reducing the Fermi level with increasing gate voltage. When the temperature is lower, charge transport deviates from single thermal activation from impurity band to conduction band, which is likely due to an additional conduction channel involving hopping between localization centers.
With this physical picture in mind, we can understand the shift in maxima between nHall(10 K) and Tcin Fig. 2. Starting from Veff
∼1,130 V, where Tc peaks, nHall decreases from 160 K to10 K
more rapidly at higher Veff, due to the stronger localization
orig-inating from more and deeper Coulomb traps. Such localization of induced carriers neutralizes Coulomb traps (Fig. 4D, dashed line), which then acts as short-range scattering centers and leads to a decrease in mobility (Fig. 2, Lower). As a result, compared with its counterpart (with the same Tc) on the left side of the dome peak,
the state on the right side resides in a more disordered environ-ment that cancels out the effect of higher carrier density on critical temperature. In other words, the interplay between carrier density and disorder shapes the superconducting dome versus Veff.
Considering that electrostatic gating by polarizing dielectrics (polarized dipole) and ionic media (cation–anion pair) is similar
Fig. 4. Reentrant insulator induced in monolayer WS2by ionic gating. (A) Arrhenius plot of conductance defined as 1/Rsin insulating (Left) and reentrant insulating
(Right) regimes. The characteristic energy scales are extracted in terms of thermal activation transport (dashed lines). In Right, the long tail at low temperature may suggest complicated hopping mechanisms along with the increasing Veff. (B) Extracted characteristic energy is plotted as a function of effective gate voltages. Black
squares and blue triangles correspond to reentrant insulator and band insulator. (C) Normalized Hall carrier density at various gate voltages as a function of temperature. Free carriers freeze out during cooling down in the reentrant insulating regime (red), while the carrier concentration almost remains constant in the metallic regime (blue and purple). (D) Schematics of electron (blue sphere) localization in the Coulomb traps (black curve) due to the poorly screened cations (organic molecular DEME+, the positive charge center is highlighted by a solid ball in purple) in proximity to monolayer WS2film. (E) Representation of the density
of states (DOS) as a function of energy, E, in the insulating phase (left of the dome) and the reentrant insulator (right of the dome), in both of which a disorder potential results in a localized band tail below the spin–split conduction band (red and blue denote spin up and down, respectively). The insulating side has a low density of localization centers (Left), whereas overlapping of high-density localized states on the reentrant insulating side plausibly forms an impurity band.
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in principle, the competing quantum phases induced in the present study represent the high field limit with respect to those super-conducting domes reported previously (27, 29, 31–33, 40, 53) (Fig. S7), where either a very strong field effect or an isolated mono-layer crystal was missing. In this truly 2D system, localized states can now be easily formed because of the slow 1/r3decay of the ion potential, indicating that any disorder in the potential landscape has a long-range effect. In contrast, in quasi-2D systems, gate-induced carriers always extend to a finite thickness; strong gat-ing populates multiple subbands, causgat-ing crossover to 3D, which enhances screening and thereby reduces carrier localization. In this sense, the proposed scenario provides a clear understanding of the power law/logarithmic correction in the normal state re-sistance as the precursor of a reentrant insulator in ion-gated bulky materials (silicon, rubrene, etc.) and universally observed
superconducting dome in gated multilayer MoS2(27), TiSe2(31),
ZrNCl (32), as well as LaAlO3/SrTiO3interface (40, 59), where
accessing the right QCP and the insulating state subsequent to the superconducting dome is prohibited by the enhanced screening in these quasi-2D systems.
ACKNOWLEDGMENTS. We thank J. Harkema for technical support. Q.C. thanks the scholarship from The Ubbo Emmius Fund. J.Y. and Q.C. thank the Stichting voor Fundamenteel Onderzoek der Materie (FOM) (Grant FV157) and FlagERA iSpinText for financial support. J.Y. acknowledges funding from the European Research Council (Consolidator Grant 648855, Ig-QPD). U.Z. acknowledges support of HFML-RU/FOM, member of the European Magnetic Field Laboratory (EMFL) and part of this work was supported by The Netherlands Organization for Scientific Research (NWO) as part of DESCO program no. 149 by FOM.
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