Two-Stage Proximity-Induced Gap-Opening in Topological Insulator - Insulating Ferromagnet (Bi x Sb 1−x ) 2 Te 3 - EuS Bilayers
aa r X i v : . [ c ond - m a t . m t r l - s c i ] A ug Two-Stage Proximity-Induced Gap-Opening in Topological Insulator–InsulatingFerromagnet (Bi x Sb − x ) Te –EuS Bilayers Qi I. Yang
1, 2, 3, ∗ and Aharon Kapitulnik
1, 2, 4 Department of Physics, Stanford University, Stanford, CA 94305, USA Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA Stanford Institute for Materials and Energy Sciences,SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA Department of Applied Physics, Stanford University, Stanford, CA 94305, USA (Dated: October 21, 2019)To further investigate the interplay between ferromagnetism and topological insulators, thin filmsof the low-carrier topological insulator (Bi x Sb − x ) Te were deposited on the insulating ferromagnetEuS (100) in situ . AC susceptibility indicates magnetic anomalies between T ≈
30 K and T ≈
60 K,well above the Curie temperature T C ≈
15 K of EuS. When the Fermi level is close to the Diracpoint and the surface state dominates the electric conduction, sharp increases in resistance withdecreasing temperatures were observed concurrently with the magnetic anomalies. Positive-negativemagnetoresistance crossovers were observed at the Curie temperature, which seem only to appearwhen the sheet resistance exceeds the Mott-Ioffe-Regel limit h/e . A two-stage gap-opening processdue to magnetic proximity is proposed. CONTENTS
I. Main Article 1Acknowledgments 4II. Supplemental Material: Sample Fabrication andCharacterization 4References 5
I. MAIN ARTICLE
Recent studies of topological insulators (TI) empha-size their interplay with various forms of magnetism. Oneof the main objectives is the observation of QuantumAnomalous Hall Effect (QAHE), that is a quantized Halleffect without a magnetic field. Starting from a two-dimensional (2D) TI, also known as a quantum spin Hallsystem, where a pair of counter-propagating edge stateswith opposite spins exist, QAHE is realized with the in-troduction of ferromagnetic order that suppresses one ofthe spin channels.
A standard route to achieve a 2D-TIis to reduce the thickness of a 3D-TI until the two oppos-ing surfaces hybridize to form a 2D-TI. To introduce fer-romagnetism, one approach was to dope the bulk 3D-TIwith ferromagnetic ions; while in a second approach, aferromagnetic layer was brought to contact with the sur-face of the TI.
With sufficiently strong perpendicularanisotropy, time reversal symmetry should be broken atthat surface and a QAHE would be realized. To date, a“true” QAHE in zero magnetic field was achieved onlyin magnetically doped TIs, and only at temperaturesmuch lower than the ferromagnetic coupling tempera-ture. The need for low temperature has been attributedto the doping-related disorder. While bulk disorder may be alleviated in the bilayer configuration, it is replacedby interface effects.The first generation of TI–ferromagnet bilayers usedbismuth selenide (Bi Se ) as the TI platform, andEuS or GdN for the insulating ferromagnet. Rel-evant to the present study, we previously reportedmagneto-transport measurements on bilayer sampleswith europium sulfide (EuS) as the insulating ferromag-net, where a crossover between positive and negativemagnetoresistance suggested a proximity effect occurringat the Curie temperature ( T C ) of EuS. Investigatinga similar material system, Wei et al. further detecteda low temperature weak hysteresis as a signature fora developing ferromagnetic phase. Further investiga-tions by this group, using spin-polarized neutron reflec-tivity experiments, revealed interfacial magnetism thatextended ∼ ∼
20 nm Bi Se system, whichpersisted to temperatures much higher than the T C ofEuS itself. While a small increase in T C of EuS hasbeen reported before, and was attributed to the pres-ence of free bulk carriers, the much larger increasein T C was attributed solely to an interface effect. How-ever, progress in this bilayer material system has beenslow, primarily because of Bi Se quality problems suchas interstitials and vacancies, which lift the Fermi levelto the bulk conduction band, resulting in n-type bulkconductivity, thereby complicate the interpretationof experimental results.A variety of other 3D-TI materials have been stud-ied in search for an optimal TI platform. In particu-lar, like Bi Se , both Bi Te and Sb Te share the samequintuple-layer (QL) crystalline structures with similarlattice constants. However, unlike Bi Se , the Diracpoint of either compound is not well exposed in thebulk band gap. This was resolved by using the alloy(Bi x Sb − x ) Te (BST), introducing a further advantagethat electric conduction can be tuned between n-type andp-type by changing the Bi to Sb ratios. The realizationof QAHE by Cr-doping of BST, exhibiting high sam-ple quality and robust magnetism at low temperatures,which persists even when the film thickness is beyondthe 2D hybridization limit, suggests that it should alsobe tried with a bilayer configuration.In this paper we present new results on magnetic be-havior in the BST–EuS bilayer thin film system. In ad-dition to reproducing similar results as in the Bi Se –EuS bilayer system, namely a positive to negative mag-netoresistance crossover at the Curie temperature of EuS T C ≈
15 K, novel magnetic order was observed at theinterface between BST and EuS, which persists to ∼ T C of EuS. Anomalies inthe resistivity and AC Susceptibility suggest a two-stagemagnetic proximity induced gap-opening mechanism. Inthe rest of this paper, the magnetic and transport proper-ties of four representative samples are reported and com-pared.Based on existing procedures, bilayer sampleswere fabricated by growing EuS (100) and BST thin filmssequentially in situ on Si (100) substrates by pulsed laserdeposition (PLD). Here we present studies on two thinand optimally doped samples (S1 & S2), where the sur-face state should dominate the electric conduction; and,to contrast, two thicker and undoped samples (S3 & S4),where the Fermi levels intersect the bulk valance band,hence a large contribution of p-type bulk conduction isexpected (table. II). X-ray diffraction (XRD) indicates Samples Ferromagnet TI Compositions TI ThicknessesS1 EuS (100) (Bi . Sb . ) Te . Sb . ) Te Te
13 nmS4 EuS (100) Sb Te
65 nmTABLE I. Summary of samples. S1 & S2 are thin and opti-mally doped and therefore should have dominant surface con-duction; whereas S3 & S4 are undoped and thicker thereforeshould have large contribution from the bulk. Compositionand thickness are calculated from numbers of laser pulses. clear (001) orientation of the BST layers. The compo-nent of magnetization perpendicular to the films behavesimilarly to EuS thin films without the TI layer in DCmagnetometry. While useful as a bulk measurement, DC magnetome-try is less suited to detect weak interface phenomena. Inparticular, measurements above T C are especially diffi-cult when background interference dominates the SQUIDcoil centering process. AC magnetic susceptibility, onthe other hand, has been proven to be very sensitive tothermodynamic transitions as well as surface and localphenomena, as demonstrated in studies of 2D ferromag-netism, spin-glass, superparamagnetism, heavy fermionsand superconductivity.
To better study the magneticproperties of the interface in a wider temperature range,AC susceptibility of the thin optimally doped sample S1was measured with a home-made two-coil mutual induc- tance device at a drive frequency f = 71 kHz. Thepick-up coil was wound in a gradiometer configurationand mounted inside the drive coil, both casted into asmall epoxy cylinder. One end of the cylinder was thenpolished to allow the sample to be in close proximity tothe top of the two concentric coils (see e.g. ref. 41). Thesame sample was measured in a van der Pauw config-uration for DC and Hall resistance measurements. In-deed, where an unusual behavior of the bilayer systemis observed, anomalies appear in both susceptibility andresistance measurements.A striking example for the correspondence between thezero field AC susceptibility and DC resistance is shownin fig. 1. This 4 nm sample is expected to be very close
10 30 50 70 90 T (K) − χ ( a r b . un i t) + o ff s e t (b) χ ′ χ ′′ − − R (cid:3) ( h / e ) (a) FIG. 1. Temperature dependence of (a) sheet resistance, and(b) AC magnetic susceptibility of sample S1 in zero magneticfield. When an unusual behavior of the bilayer system is ob-served, anomalies appear in both susceptibility and resistance. to the 2D-TI r´egime where magnetism from the proxim-itized EuS is expected to have maximum effect. There isa clear effect at the Curie temperature of EuS ( ∼
15 K),where the sheet resistance starts its low-temperature in-crease, while the the AC susceptibility saturates in mag-nitude. However, these expected effects are just the lastof the magnetic response as we lower the temperature. Adramatic increase in resistance, associated with a cusp inthe imaginary part of AC susceptibility, is first observedat 60 K. Lowering the temperature, the sheet resistanceseems to almost saturate at ∼
30 K, at which point thereal (inductive) part of the susceptibility shows a dip andthe imaginary (dissipative) part almost saturates. Suchanomaly seems to be readily suppressed by a small per-pendicular magnetic field (fig. 2c), which is consistentwith a change in the magnetic configuration at the in-terface, such as that proposed in ref. 14. In a strongperpendicular DC magnetic field, where the magnetiza-tion in the ferromagnetic phase is forced to align withthe applied field similarly to ferromagnets measured ontheir easy axes, the real and imaginary parts of the ACsusceptibility should exhibit peaks just above and be-low T C respectively. However the as-measured data
10 20 30 40 T (K) − . . . (a) χ ′ χ ′′
10 20 30 40 0 . . (b) µ H = 0 . . χ ( a r b . un i t) + o ff s e t (c) . . χ ( a r b . un i t) + o ff s e t (d) µ H = 20 mT
10 20 30 40 T (K)0.05.0 (e)
10 20 30 40 0.05.0 (f) µ H = 2 T FIG. 2. (Color online) Real ( χ ′ , crosses) and imaginary ( χ ′′ ,circles) parts of the AC susceptibility of sample S1 as func-tions of temperatures close to the Curie temperature (dashedlines). (a, b) In zero field, (c, d) in 20 mT and (e, f) in 2 TDC fields perpendicular to the film. The left column shows as-measured data whereas the right column includes 40 ◦ phaserotations. Error bars in all figures in this paper represent theestimated 95 % confidence intervals. slightly deviate from such expected behavior (fig. 2e).This is likely due to the phase rotation and complex off-set introduced by the finite resistance, capacitance andinductance in the wiring of the cryostat and instruments.Indeed the expected behavior is recovered by applying a40 ◦ phase rotation (fig. 2f). For comparison, the ACsusceptibility in zero and 20 mT DC fields are also pre-sented with 40 ◦ phase rotations in the right column infig. 2 next to their as-measured counterparts. In par-ticular, in 20 mT DC field, where the magnetization ismostly in-plane and the anomaly above T C is suppressed,the AC susceptibility after phase rotation (fig. 2d) alsoroughly conforms with the expected behavior of a thinfilm ferromagnet measured on its hard axis. Transport data are shown in fig. 3, summarizing thezero-field sheet resistance (figs. 3a–3d) and the Hall re-sistance (figs. 3e & 3f) of the four bilayer samples. TheHall effect indicates that S2–S4 have holes as the ma-jority carrier, whereas S1 exhibits electron character. Apossible reason for a change in majority carrier types be-tween S2 and S1, from holes to electrons, could be the re-duction in thickness, hence a stronger influence from thechemical potential of the EuS layer, which has a naturaltendency to have electron donors. While a small eleva-tion of chemical potential may not produce measurableelectric conduction in EuS due to its large band gap, in the BST layer, however, if the Fermi level is belowand very close to the Dirac point, where excitationsexhibit electron-hole symmetry, even a small elevation − − R (cid:3) ( h / e ) (a) S10 . . . (b) S217 . . . R (cid:3) ( − h / e ) (c) S310 30 50 70 90 T (K)2 . . . (d) S4 0 2 4 6 8 H (T /µ ) − (f) S1 01020 R x y / Ω (e) S4S3S2
FIG. 3. (Color online) Resistive anomalies observed in sam-ples (a) S1 and (b) S2 at the same temperatures where mag-netic anomalies occur, but not in those with intrinsic thickerTI layers (c) S3 and (d) S4. (e, f) The Hall effect indicatesdecreasing carrier densities per unit area from S4 to S1 and ashift from p-type to n-type. may change the majority carrier type. Similarly to S1,a resistive transition was observed in the slightly thickeroptimally doped sample S2 (fig. 3b) near T ≈
30 K. Suchresistive transitions were neither observed in samples S3& S4 (figs. 3c & 3d) nor in the Bi Se –EuS bilayers inref. 9, where in both cases the ferromagnetism is presentbut the bulk conduction is more dominant; nor in BSTsamples near the optimal doping level reported in ref. 24,where the surface conduction dominates but in absenceof magnetism. These strongly suggest that the resistivetransition observed is a result of proximity between themagnetic order and the surface state. Indeed, the inter-face magnetization is expected to open a gap at the TI’ssurface state, hence reduce its contribution to the overallconduction, which would only be observed when the EuSlayer is highly insulating and the surface state dominatesthe conduction in the TI layer.The magnetoresistance (MR) of the bilayer sampleswas measured at representative temperatures and pre-sented in fig. 4. A positive to negative MR crossover at T C was observed in S1 (fig. 4a), similarly to previouslyreported behavior of thin Bi Se –EuS bilayers. Above T C , a sharp positive MR feature exists near zero fieldas ubiquitously observed in TI thin films; whereas be-low T C a negative MR emerges. In S2 the MR remainspositive at all measured temperatures (fig. 4b), howeverthe low-field feature is broader at 12 K than at 30 K(fig. 4b: insert), suggesting a developing negative com-ponent, similar to Bi Se –EuS bilayers close to T C . Inthicker undoped samples S3 & S4 (figs. 4c & 4d), onlypositive MR was observed, which sharpens monotonously − − H (T /µ ) − ∆ R ( H ) / R ( )( % ) (a)
2K 4K12K30K − − (b) − − (c) − − H (T /µ ) 012 ∆ R ( H ) / R ( )( % ) (d) − . . . . . − . . . . . FIG. 4. (Color online) Magnetoresistance at representativetemperatures of (a) S1, (b) S2, (c) S3 and (d) S4. (b: insert)Low-field behavior of S2 at T = 12K (triangles) and at T =30K (circles), showing reverse temperature dependence. (d:insert) Low-field features of S4. with decreasing temperature, in addition to parabolicbackgrounds that are typically observed in thicker TIfilms. While in our previous studies of Bi Se -EuS bi-layers the Fermi levels were likely well inside the bulk con-duction band, and therefore the mechanism of the emer-gent negative MR remained inconclusive; in the presentstudy, specifically for samples S1 and S2, the doping lev-els and the Hall effects suggest that the Fermi levels arevery close to the Dirac point and well inside the bulkband gap. This case was studied theoretically, suggest-ing that either gap-opening at the Dirac point orcoexistence of ferromagnetism and spin-orbit coupling as the origin for the negative MR. Finally, we note thatthe crossovers from positive to negative MR have alsobeen observed in bilayer structures with different TIs andferromagnets, interestingly only when the sheet re-sistance exceeds the Mott-Ioffe-Regel limit in two-dimensions h/e (fig. 5). While most available theorieson magneto-transport properties of TI thin films havebeen formulated in terms of weak localization, we notethat, being an orbital quantum interference effect, theconcept of weak localization is not easily applicable insuch r´egime.To summarize, (Bi x Sb − x ) Te –EuS bilayers were fab-ricated by pulsed laser deposition. AC magnetic sus-ceptibility displayed anomalies well above the bulk T C of EuS. Resistive transitions were observed concurrentlywith magnetic anomalies in thin optimally doped sam-ples, where the Fermi levels are close to the Dirac point,suggesting a gap opened at the Dirac point at the inter-face. Similarly to previous results, negative magnetore-sistance was observed below T C near zero fields whereaspositive magnetoresistance was recovered above T C . To-gether these suggest a two-stage gap-opening mechanism A B C D E F G Isources10 − − − R (cid:3) m a x ( h / e ) -ve MR +ve MR Only FIG. 5. The maximum sheet resistance of bilayer samples atzero magnetic field from a variety of sources (A: this paper,B: ref. 9 and unpublished data, C–I: refs. 50, 51, 54–57) TheMott-Ioffe-Regel limit ( R (cid:3) = h/e ) seems to separate samplesshowing signatures of negative MR below T C (violet circles),and those only display positive MR (gray crosses) at the TI surface state Dirac point as result of proximityto an insulating ferromagnet. ACKNOWLEDGMENTS
We thank Jiecheng Zhang, Sejoon Lim and Shuai Shaofor helpful discussions. The mutual inductance coil wascrafted by Alan Fang. Sample fabrication and charac-terization were partly performed at the Stanford NanoShared Facilities (SNSF), supported by the NationalScience Foundation under award ECCS-1542152. Thiswork is supported by the Department of Energy, Of-fice of Science, Basic Energy Sciences, Materials Sciencesand Engineering Division, under Contract DE-AC02-76SF00515. Initial work was supported by DARPA,MesoDynamic Architecture Program (MESO) throughthe contract number N66001-11-1-4105.
II. SUPPLEMENTAL MATERIAL: SAMPLEFABRICATION AND CHARACTERIZATION
Samples of (Bi x Sb − x ) Te –EuS bilayer thin filmswere fabricated by pulsed laser deposition (PLD). Forthe ferromagnet layer, 40 nm EuS thin films were grownon intrinsic Si (100) substrates with native oxide. Withthe previously reported recipe, high quality EuS thinfilms were consistently obtained, characterized by single(100) orientations, atomically smooth surfaces, immea-surably high sheet resistance, and magnetic anisotropyexhibiting an out-of plane component of the magnetiza-tions. To optimize the quality of the interfaces, the TIlayer was subsequently grown by PLD in situ . Basedon existing reports on both Sb Te and Bi Te , weestablished a procedure to deposit (Bi x Sb − x ) Te by al-ternating the targets of the two compounds. Follow-ing each EuS deposition carried out in high vacuum of ∼ − torr, the sample was allowed to cool to 300 ◦ Cbefore 200 millitorr of argon gas mixed with 2% hydro-gen was introduced to diffuse the plasma plumes and toprevent potential oxidation from residual gases. Sputter-ing targets (Kurt J. Lesker, 99.999%) were ablated 5 cmaway from the sample with 25 ns 248 nm KrF excimerlaser pulses at 0.55 J · cm − fluence and 5 Hz repetitionrate. The thickness of a ∼
40 nm film was measuredby atomic force profiliometry and the average depositionrate was 0 .
22 ˚A/pulse. To achieve the optimal composi-tion (5% bismuth doping), where the Fermi level is insidethe bulk band gap and closest to the Dirac point, theBi Te target was ablated by one pulse once per 19 pulseson Sb Te .The four samples studied in the main paper are de-scribed in table. II. The X-ray diffraction (XRD) spectra Samples Ferromagnet TI Compositions TI ThicknessesS1 EuS (100) (Bi . Sb . ) Te . Sb . ) Te Te
13 nmS4 EuS (100) Sb Te
65 nmTABLE II. Summary of samples. Composition and thicknessare calculated from numbers of laser pulses. of these samples (fig. 6a) indicate clear (001) orienta-tions of the (Bi x Sb − x ) Te layers. Their bulk magneticproperties were studied with a superconducting quantuminterference device (SQUID) magnetometer. Examplesare presented in figs. 6b & 6c for sample S2. The sam-ple was cooled in zero magnetic field to T = 2 K, atwhich the centering procedure of SQUID was carried out.Subsequently, the field-dependence of the magnetizationwas measured in an external magnetic field perpendic-ular to the thin film sweeping between µ H = +2 Tand µ H = − µ H = +2 T, and the tem-perature dependence of the magnetization was measuredduring warming up in zero field (fig. 6b). The com-ponent of magnetization perpendicular to the films be-haves similarly to EuS thin films without the TI layer. By fitting to the Curie-Weiss law in the paramagneticr´egime, the Curie temperature was determined to be T C = 14 . ± . ∗ [email protected] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. , 1057(2011). M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. , 3045(2010). F. D. M. Haldane, Phys. Rev. Lett. , 2015 (1988). Q. Liu, C.-X. Liu, C. Xu, X.-L. Qi, and S.-C. Zhang, Phys.Rev. Lett. , 156603 (2009). R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, andZ. Fang, Science , 61 (2010). C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang,M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji,Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C.Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, and Q.-K. Xue,Science , 167 (2013). Y. L. Chen, J.-H. Chu, J. G. Analytis, Z. K. Liu,K. Igarashi, H.-H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore,D. H. Lu, M. Hashimoto, T. Sasagawa, S. C. Zhang, I. R.Fisher, Z. Hussain, and Z. X. Shen, Science , 659(2010). Y. S. Hor, P. Roushan, H. Beidenkopf, J. Seo, D. Qu,J. G. Checkelsky, L. A. Wray, D. Hsieh, Y. Xia, S.-Y. Xu,D. Qian, M. Z. Hasan, N. P. Ong, A. Yazdani, and R. J.Cava, Phys. Rev. B , 195203 (2010). Q. I. Yang, M. Dolev, L. Zhang, J. Zhao, A. D. Fried,E. Schemm, M. Liu, A. Palevski, A. F. Marshall, S. H. Ris-bud, and A. Kapitulnik, Phys. Rev. B , 081407 (2013). A. Kandala, A. Richardella, D. W. Rench, D. M. Zhang,T. C. Flanagan, and N. Samarth, Appl. Phys. Lett. ,202409 (2013). P. Wei, F. Katmis, B. A. Assaf, H. Steinberg, P. Jarillo-Herrero, D. Heiman, and J. S. Moodera, Phys. Rev. Lett. , 186807 (2013). T. Hirahara, S. V. Eremeev, T. Shirasawa, Y. Okuyama,T. Kubo, R. Nakanishi, R. Akiyama, A. Takayama, T. Ha-jiri, S.-i. Ideta, M. Matsunami, K. Sumida, K. Miyamoto,Y. Takagi, K. Tanaka, T. Okuda, T. Yokoyama, S.-i.Kimura, S. Hasegawa, and E. V. Chulkov, Nano Lett. , 3493 (2017). X. Kou, L. Pan, J. Wang, Y. Fan, E. S. Choi, W.-L. Lee,T. Nie, K. Murata, Q. Shao, S.-C. Zhang, and K. L. Wang,Nature Communications (2015), 10.1038/ncomms9474. F. Katmis, V. Lauter, F. S. Nogueira, B. A. Assaf, M. E.Jamer, P. Wei, B. Satpati, J. W. Freeland, I. Eremin,D. Heiman, P. Jarillo-Herrero, and J. S. Moodera, Nat.Lett. , 513 (2016). Y. Shapira and T. B. Reed, Phys. Rev. B , 4877 (1972). J. Keller, J. Parker, J. Stankiewicz, D. Read, P. Stampe,R. Kennedy, P. Xiong, and S. von Molnar, IEEE Trans-actions on Magnetics , 2673 (2002), international Mag-netics Conference (Intermag Europe 2002), Amsterdam,Netherlands, Apr 28-May 02, 2002. Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Ban-sil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan,
10 20 30 40 502 θ (degrees)10 c o u n t s ( a r b . un i t) (a) S1S2S3S4EuS 003 006 009 0015 001810 20 30 T (K)0 . . . M z ( a r b . un i t) (b) T C ≈ . − . . . H (T/ µ ) − M z ( a r b . un i t) (c) FIG. 6. (Color online) (a) Semi-log X-ray diffraction spectraof the four (Bi x Sb − x ) Te –EuS bilayer samples, with thick-ness of the TI layer increasing from the top to the bottom,compared to a EuS-only thin film of similar thickness. K- β spectral contamination exists in the spectrum of sample S4due to unavailable monochromator. Dashed lines mark the ex-pected positions of the (Bi,Sb) Te [001] peaks. Magnetiza-tion of sample S2 as functions of (b) temperatures and (c) per-pendicular magnetic fields (arrows indication field sweep di-rections). A fitting to the Curie-Weiss law is shown as theblack solid curve. Error bars represent the estimated 95 %confidence intervals.Nat. Phys. , 398 (2009). L. Zhang, M. Dolev, Q. I. Yang, R. H. Hammond, B. Zhou,A. Palevski, Y. Chen, and A. Kapitulnik, Phys. Rev. B , 121103 (2013). Z. Alpichshev, R. R. Biswas, A. V. Balatsky, J. G. Ana-lytis, J.-H. Chu, I. R. Fisher, and A. Kapitulnik, Phys.Rev. Lett. , 206402 (2012). J. G. Analytis, J.-H. Chu, Y. Chen, F. Corredor, R. D.McDonald, Z. X. Shen, and I. R. Fisher, Phys. Rev. B ,205407 (2010). T. L. Anderson and H. B. Krause, Acta Crystallogr., Sect.B: Struct. Sci. , 1307 (1974). M. H. Francombe, Br. J. Appl. Phys. , 415 (1958). H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C.Zhang, Nature Physics , 438 (2009). J. Zhang, C.-Z. Chang, Z. Zhang, J. Wen, X. Feng, K. Li,M. Liu, K. He, L. Wang, X. Chen, Q.-K. Xue, X. Ma, andY. Wang, Nat. Commun. , 574 (2011). X. Kou, S.-T. Guo, Y. Fan, L. Pan, M. Lang, Y. Jiang,Q. Shao, T. Nie, K. Murata, J. Tang, Y. Wang, L. He,T.-K. Lee, W.-L. Lee, and K. L. Wang, Phys. Rev. Lett. , 137201 (2014). Q. I. Yang, J. Zhao, L. Zhang, M. Dolev, A. D. Fried, A. F.Marshall, S. H. Risbud, and A. Kapitulnik, Appl. Phys.Lett. , 082402 (2014). H. Obara, S. Higomo, M. Ohta, A. Yamamoto, K. Ueno,and T. Iida, Jpn. J. Appl. Phys. , 085506 (2009). M. Shaik and I. A. Motaleb, in
IEEE International Con- ference on Electro-Information Technology (2013) pp. 1–6. M. B. Korzenski, P. Lecoeur, B. Mercey, P. Camy, andJ.-L. Doualan, Appl. Phys. Lett. , 1210 (2001). A. Ambrosini and J.-F. Hamet, Appl. Phys. Lett. , 727(2003). See supplemental material at [URL will be inserted by pub-lisher] for details of sample fabrication and basic charac-terization, which includes refs. 21, 24, 26–30. N. Casa-Pastor, P. Gomez-Romero, and L. C. Baker, J.Appl. Phys. , 5088 (1991). R. Chiarelli, M. A. Novak, A. Rassat, and J. L. Tholence,Nature , 147 (1993). B. V. B. Sarkissian, J. Phys. F: Met. Phys. , 2191 (1981). J. L. Dormann, L. Bessais, and D. Fiorani, J. Phys. C:Solid State Phys. , 2015 (1988). Y. Ando, H. Kubota, Y. Sato, and I. Terasaki, Phys. Rev.B , 9680 (1994). P. Gegenwart, J. Custers, Y. Tokiwa, C. Geibel, andF. Steglich, Phys. Rev. Lett. , 076402 (2005). E. R. Schemm, W. J. Gannon, C. M. Wishne, W. P.Halperin, and A. Kapitulnik, Science , 190 (2014). B. Jeanneret, J. L. Gavilano, G. A. Racine, C. Leemann,and P. Martinoli, Appl. Phys. Lett. , 2336 (1989). A. Yazdani, W. R. White, M. R. Hahn, M. Gabay, M. R.Beasley, and A. Kapitulnik, Phys. Rev. Lett. , 505(1993). A. Yazdani,
Phase Transitions in Two-Dimensional Su-perconductors , Ph.D. thesis, Stanford University, Stanford,CA 94305 (1994). M. J. Dunlavy and D. Venus, Phys. Rev. B , 094411(2004). P. J. Jensen, S. Knappmann, W. Wulfhekel, and H. P.Oepen, Phys. Rev. B , 184417 (2003). S. J. Cho, Phys. Rev. , 632 (1967). W. M¨uller and W. Nolting, Phys. Rev. B , 085205(2002). Y. S. Kim, M. Brahlek, N. Bansal, E. Edrey, G. A. Kapile-vich, K. Iida, M. Tanimura, Y. Horibe, S.-W. Cheong, andS. Oh, Phys. Rev. B , 073109 (2011). I. Garate and L. Glazman, Phys. Rev. B , 035422 (2012). H.-Z. Lu, J. Shi, and S.-Q. Shen, Phys. Rev. Lett. ,076801 (2011). V. K. Dugaev, P. Bruno, and J. Barna´s, Phys. Rev. B ,144423 (2001). J. S. Lee, A. Richardella, R. D. Fraleigh, C.-X. Liu,W. Zhao, and N. Samarth, (2017), arXiv:1706.04661[cond-mat.mes-hall]. G. Zheng, N. Wang, J. Yang, W. Wang, H. Du, W. Ning,Z. Yang, H.-Z. Lu, Y. Zhang, and M. Tian, Sci. Rep. ,21134 (2016). N. F. Mott and E. A. Davis,
Electronic Processes in Non-Crystalline Materials , 2nd ed. (Oxford University Press,2012). E. Fradkin, Phys. Rev. B , 3263 (1986). Z. Jiang, F. Katmis, C. Tang, P. Wei, J. S. Moodera, andJ. Shi, Appl. Phys. Lett. , 222409 (2014). L. D. Alegria, H. Ji, N. Yao, J. J. Clarke, R. J. Cava, andJ. R. Petta, Appl. Phys. Lett. , 053512 (2014). M. Lang, M. Montazeri, M. C. Onbasli, X. Kou, Y. Fan,P. Upadhyaya, K. Yao, F. Liu, Y. Jiang, W. Jiang, K. L.Wong, G. Yu, J. Tang, T. Nie, L. He, R. N. Schwartz,Y. Wang, C. A. Ross, and K. L. Wang, Nano Lett. ,3459 (2014). S.-Y. Huang, C.-W. Chong, Y. Tung, T.-C. Chen, K.-C.
Wu, M.-K. Lee, J.-C.-A. Huang, Z. Li, and H. Qiu, Sci.Rep.7