Andreev Reflection without Fermi surface alignment in High T_{c}-Topological heterostructures
Parisa Zareapour, Alex Hayat, Shu Yang F. Zhao, Michael Kreshchuk, Zhijun Xu, T. S. Liu, G.D. Gu, Shuang Jia, Robert J. Cava, H.-Y. Yang, Ying Ran, Kenneth S. Burch
AAndreev Reflection without Fermi surface alignmentin High T c -Topological heterostructures Parisa Zareapour , Alex Hayat , Shu Yang F. Zhao ‡ ,MichaelKreshchuk , Zhijun Xu , T. S. Liu § , G.D. Gu , Shuang Jia (cid:107) ,Robert J. Cava , H.-Y. Yang , Ying Ran , and Kenneth S.Burch Department of Physics and Institute for Optical Sciences, University of Toronto, 60St George Street, Toronto, Ontario, Canada M5S 1A7 Department of Condensed Matter Physics and Materials Science (CMPMS),Brookhaven National Laboratory, Upton, New York 11973, USA Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA Department of Physics, Boston College, 140 Commonwealth Avenue, Chestnut Hill,MA 02467E-mail: [email protected]
Abstract.
We address the controversy over the proximity effect between topologicalmaterials and high T c superconductors. Junctions are produced betweenBi Sr CaCu O δ and materials with different Fermi surfaces (Bi Te & graphite).Both cases reveal tunneling spectra consistent with Andreev reflection. This isconfirmed by magnetic field that shifts features via the Doppler effect. This is modeledwith a single parameter that accounts for tunneling into a screening supercurrent. Thusthe tunneling involves Cooper pairs crossing the heterostructure, showing the Fermisurface mis-match does not hinder the ability to form transparent interfaces, which isaccounted for by the extended Brillouin zone and different lattice symmetries. Submitted to:
New J. Phys. ‡ Present Address: Department of Physics, Harvard University, Boston MA USA § Present Address: School of Chemical Engineering and Environment, North University of China,China (cid:107)
Present Address: International Center for Quantum Materials, School of Physics, Peking University,Beijing 100871, China a r X i v : . [ c ond - m a t . s up r- c on ] M a y ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures (b) S S’ Ny he B x >0I s ∆ r ∆ i ∆ (a) S S’ N ∆ (z) B x =0 he (c) Figure 1: (a) Andreev reflection process at the superconductor-normal interface withoutmagnetic field. (Red) order parameter, ∆ r the gap at the superconductor surface, and ∆ i theinduced gap. (b) Affects of applied magnetic field. (c) Fermi surfaces in the extended Brillouinzone. Dotted lines are boundaries of the zones, solid lines are the Fermi surfaces, with blackBi2212, red graphite, and orange Bi Te .
1. Introduction
Potential novel optical effects[1, 2] and non-abelian anyons[3, 4, 5, 6, 7, 8] havereinvigorated interest in the superconducting proximity effect. Various approaches tohigh temperature superconducting proximity have claimed success[9, 10, 11, 12, 13, 14,15, 16, 17], including the recent report of a proximity effect between Bi Sr CaCu O δ and Bi Se or Bi Te ,[18, 19] via the mechanical bonding technique. Using thin films andARPES, another group has claimed such interfaces result in an s-wave superconductorin the surface states[20]. One theoretical study suggested this is due to the mis-match incrystal symmetries[21], though another finds the d-wave channel is dominant[22]. Twoother thin film/ARPES studies suggest the proximity effect is not possible due to theFermi surface mis-match that suppresses the interface transparency.[23, 24]We test this hypothesis with tunneling experiments on junctions betweenBi Sr CaCu O δ (Bi-2212) and Bi Te or graphite in magnetic field. These materialsare chosen as they form mechanical junctions with different Fermi surfaces. The Bi Te is hole doped with a Fermi surface close the Γ point,[25] whereas graphite is a semimetalwith pockets close to the zone boundary (see figure 1(c))[26]. By establishing Andreevreflection and proximity, we show that our original efforts which focused on the similarmaterials (Bi Te and Bi Se ), are not a special case. The ability to obtain Andreevdespite the Fermi surface mis-match is explained by considering the extended zonescheme, where the Fermi surfaces meet.The heterostructure is probed using differential conductance (dI/dV) to look forAndreev reflection, the process where a quasi-particle converts into a Cooper pair andtravels from the normal material into the superconductor (see figure 1(a)). AndreevReflection is responsible for the proximity effect and is a stringent test of a transparentinterface.[27, 28, 29, 30] In metals with no attractive potential one expects,[31] andobserves[32] a pair amplitude that can result in a minigap whose size depends ondevice geometry and superconducting phase of the contacts. In confined devices, with ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures Te /graphite have been shown tosuperconduct,[37, 38] we do not anticipate nABS playing a crucial role in our resultsand the induced gaps result from a proximity induced state. As described later, themagnetic field dependance of our spectra is inconsistent with previous measurements ofnABS or induced pair amplitudes.
2. Experimental Details
We measured numerous devices with either a high or low barrier. In high barrierdevices we observe tunneling spectra consistent with those measured in previous planarjunctions, point contact or STM experiments (see figure 2(b)).[39, 40, 41, 42, 43, 44,45, 46] In addition they are well described by an accepted theory of tunneling into thec-axis of a d-wave superconductor,[30, 42] with the correct value of the superconductinggap (40 meV). In both Bi Te and graphite heterostructures with low-barriers, theconductance is enhanced below T c , consistent with Andreev reflection in a proximityinduced region. This interpretation is further confirmed by the application of a magneticfield, which generates super-currents. Tunneling into these supercurrents shifts themomentum of the quasi-particles and ultimately their energy. Since this only occurs forthe superconducting quasi-particles, the observation of the Doppler effect confirms thepresence of Andreev reflection as established in numerous theoretical and experimentalworks.[47, 48, 49, 50, 51, 52, 53, 54, 55, 44, 56, 45, 57]The Doppler effect manifests as a shift in the Andreev features to lower voltages.This is seen in Bi Te and graphite junctions, confirming they are not due to the normalmaterials’ field dependence. Due to the large size of our devices and the applicationof the field in the ab-plane, we expect effectively random or no observable shift inABS. All field dependent spectra are well described by including the Doppler shiftin a previously established model of the Andreev reflection for proximity junctions.Furthermore, no hysteresis or splitting of any features is observed, as had been seen inprevious measurements of ABS due to the sign change at the 110 surface (dABS).[40, 42]Taken together our results confirm Andreev reflection between Bi Sr CaCu O δ andthe normal materials, implying the relative alignment of the Fermi surface is not crucialin these heterostructures. This likely occurs due to the different lattice symmetries thatallows the Fermi surfaces to overlap in the extended zone (see figure 1(c)).To form planar junctions between the normal material and Bi-2212 (T c ∼
90 K) weemployed the mechanical bonding method as described in reference [18, 19]. In an inertglove box both materials are cleaved, then the Bi-2212 was placed on top of the Bi Te or graphite, and GE varnish applied to the Bi-2212 corners (figure 2(c)). Four-pointtransport measurements were performed at various temperatures ranging from 290 K to10 K. To further clarify the nature of the interface we performed extensive AFM on the ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures Te andgraphite produced step edges with atomically flat regions typically tens of microns across(figure 2(e)). Some regions showed mesas jutting out (Fig 2 d). Given the geometry ofour devices, this suggests the tunneling is along the c-axis of both materials and occursat planar junctions formed by these mesas touching the Bi-2212. The dI/dV were highlyreproducible regardless of field, temperature, and voltage approach taken. To confirmthe dI/dV spectra originate from the junction, for every device we checked different setsof contacts and different combinations of those contacts. Thus our tunneling probesdirectly the interface between the materials whereas previous studies probed the topsurface.[22, 20, 23, 24]The features we observe might not arise from tunneling given the large contactarea. However it is well established that the superconductivity occurs within the Cu-O plane, while the outer layers of the Bi Sr CaCu O δ are insulating Bi-O and Sr-Oenabling interlayer josephson junctions and tunneling within a single crystal.[39] Thuswe speculate that the Bi-O layer forms the tunnel barrier with the normal materialenabling the dI/dV to provide spectra. The large contact area also suggests scatteringin either side could occlude the observation of tunneling. This is not the case for ourjunctions, as shown by the high barrier device (Fig 2 a). Consistent with previousexperiments and the d-wave gap,[39, 40, 41, 42, 43, 44, 45, 39, 46] we see a v like shapeat low T that gradually fills in as temperature is raised. Furthermore the data are welldescribed by the standard approach to d-wave tunneling in the c-axis producing a propergap at 40 mV.[30, 42, 41] The fit required a broadening parameter Γ ≈ → meV , muchsmaller than any of the features observed. This is likely due to the large mobilities of thenormal materials used and the c-axis nature of the tunneling, reducing the likelihood ofscattering.Confirmation that none of the measured features arise from the within the materialsis provided by extensive measurements of various contact configurations and applicationof magnetic field. Four-point and two-point measurements on only one side of thejunction were independent of voltage and all reported features were only observed whencurrent and voltage were measured across the interface. Two-point measurements on oneside of the junction resulted in resistances 1 →
10Ω at low T. Swapping the current andvoltage leads on the normal material only produced a slight, voltage independent offset ofa few Ω, while high barrier devices had resistances > k Ω and low barrier junctions had dV /dI ≈ Te ). Consistent with STM measurements we find no field dependenceof the spectra,[41] and a slight, voltage independent offset due to the graphite magneto-resistance. ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures [ d I / d V ] S / [ d I / d V ] N
21 (a)-60 -40 0-20 604020Voltage (mV) (e)(c)(d) 4.5321 [ d I / d V ] S / [ d I / d V ] N Contacts c-axisVarnish
Figure 2: (a) dI/dV normalized to its value at T c from a high-barrier Bi Te junction.Purple line shows a fit with an energy independent lifetime and maximum gap of 40 meV.(b) High barrier junction with offsets due to extra resistance in the graphite upon applyingin-plane magnetic field every Tesla from 0 (blue) to 5T (orange). (c) Photo of the device. (d)and (e) AFM from the cleaved surface of Bi Te revealing atomically flat regions, with someraised mesa’s and step edges. Color bar indicates the height in nm.
3. Model
To understand the dI/dV from the low-barrier junctions, we review what is expected,observed in proximity devices by tunneling[18, 19, 58, 59, 60, 61, 29] and confirmed withARPES[62]. The superconducting order parameter is induced into the normal materialby the conversion of a quasi-particle current into a supercurrent via Andreev reflection.This involves an electron crossing the interface by forming a Cooper pair resulting in adoubling of conductance (figure 1 (a)). In less transparent interfaces, the conductanceat zero bias is smaller than two and the shape at finite voltage is altered[60, 30]. The ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures i ) and reduced gap(∆ r ) at the interface (figure 1(b)). These produce Andreev features in the dI/dV thatare tell-tale signs of the proximity effect[60, 18, 19, 61, 29, 62, 58, 59].The observed features are reproduced by modifying a standard approachto tunneling into d-wave superconductors.[60, 30, 63] Specifically, the differentialconductance below T c [dI/dV] S , divided by the normal state conductance [dI/dV] N is given by the half-sphere integration over solid angle Ω: σ ( E ) = (cid:82) d Ω cosθ N σ S ( E ) (cid:82) d Ω σ N cosθ N (1)where E is the quasiparticle energy and θ is the incidence angle (relative to theinterface normal) in the normal material, σ N is the conductance from normal to normalmaterial with the same geometry, and σ S = σ N (1 + σ N | k + | + ( σ N − | k − k + | )1 + ( σ N − | k − k + | exp ( iφ − − iφ + ) (2)where k ± = E − √ | E |−| ∆ ± || ∆ ± | and ∆ ± = | ∆ ± | exp ( iφ ± ), electron-like and hole-likequasiparticle effective pair potentials with the corresponding phases iφ ± . In the caseof c-axis tunneling, the hole-like and the electron-like quasiparticles transmitted intothe superconductor experience the same effective pair potentials, which have similardependence on the azimuthal angle α in the AB-plane ∆ + = ∆ − = ∆ cos (2 α ).Scattering-induced energy broadening (Γ) is included in the calculation by adding animaginary term to the energy of the quasi-particles. The real part of the resulting σ S then gives the differential conductance (G) with broadening from the normal materialincluded via the Γ term ( G (∆ , Γ , V ) = Re [ σ ], where V is the applied bias).[64, 65]The total Andreev reflection spectrum at zero magnetic field is obtained bycalculating the reflection and the transmission in the proximity region, followed byreflection at the interface between the two materials[66]. Incoming quasiparticleswith energies smaller than ∆ i , Andreev-reflect at the first interface. This gives riseto a G (∆ induced , Γ , V ), which is expected to consist of a central peak with a widthtypically much smaller than the bulk gap of Bi-2212, corresponding to the inducedgap in the normal material ( G (∆ induced , Γ , V )). Quasiparticles with higher energies donot Andreev-reflect off the first interface, and instead transmit as normal particles.The transmission rate is 2- G (∆ induced , Γ , V ), where the 2 accounts for the fact thatAndreev reflection involves a charge of -2e due to the conversion of two normal quasi-particles into a cooper pair (figure 1 B). Quasiparticles with energies between ∆ i and∆ r Andreev-reflect at the second interface and give rise to a term G (∆ reduced , Γ , V ).We expect G (∆ reduced , Γ , V ) to consist of peaks at an energy smaller than the bulkgap of Bi-2212 (∆ reduced ), due to the suppression of superconductivity at the interface. ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures G (∆ bulkgap , Γ , V ), which can arise due to theinhomogeneity in the tunnel junction (a few high-barrier junctions in parallel withthe low-barrier proximity junction). The total dI/dV is calculated using G total = f × [ G (∆ induced , Γ , V ) + (2 − G (∆ induced , Γ , V )) G (∆ reduced , Γ , V )] + f × G (∆ bulkgap , Γ , V ).The parameters f and f account for the different relative areas of the proximity andhigh barrier junctions. Specifically the two types of junctions are in parallel such thattheir total conductance is equal to their relative volume fractions ( f , ) times theirintrinsic conductivity. The calculated spectra in this model with the barrier strength (Z),scattering-induced energy broadening (Γ), and the superconducting gap (∆) used as fitparameters, show excellent agreement with the experimental conductance measurements(purple lines in figure 2 (a), 3 (c) & (d)).
4. Results and Discussion
The temperature dependent, dI/dV of Bi-2212/Bi Te junctions are shown in Fig 3 a.The dI/dV, when normalized to T c , reveals a zero bias peak that emerges just below T c and eventually evolves into three features at low temperature. The first is an Andreevreflection peak near zero bias, whose width is much smaller then the full gap of Bi-2212(labeled ∆ i ). This feature could be a dABS.[40, 42, 30] However, at low T, the featurereaches an amplitude of nearly twice the normal state conductance, consistent withstandard Andreev reflection. Furthermore, ab-plane tunneling only reveals a narrowpeak at zero-bias and at the full gap at Bi-2212 (∆ ). The full gap is also seen in ourdata, it’s temperature dependence matches well that observed in high barrier devices(Fig 2) and established trends for the cuprates. Another peak in our data (∆ r ) around20 meV also approaches 2. Taken together these three peaks are consistent with theproximity effect (Fig 1 a). Specifically we expect perfect Andreev reflection since thereis effectively no barrier between the normal material and the induced superconductor,while the inverse proximity effect reduces the size of the gap at the interface resulting ina peak at the reduced (∆ r ) gap, and at the full gap (∆ ). We find similar spectra andtemperature dependence from a low-barrier device with graphite as the normal material(figure 3(b)). The fact that we observe a zero-bias feature of height nearly 2 and the fullgap at 40 meV, adds confidence that these features arise from Andreev reflection and donot require the normal material’s Fermi surface to directly overlap the superconductor’s.To confirm these features result from Andreev reflection, we use an in-planemagnetic field B = ∇ × A ( r ), which dramatically affects the ABS but causes littlemagneto-resistance in the normal materials. The superconducting order parameterwill acquire an inhomogeneous phase ( φ ( r ) = − πφ (cid:82) A ( r (cid:48) ) dr (cid:48) ), with φ the fluxquantum. This produces a diamagnetic screening current where the Cooper pairsacquire a momentum ¯ hk s = ∇ γ . Since Andreev reflection involves tunneling intothis supercurrent, they are Doppler shifted by: E D = − ¯ h k ⊥ k s m e , where k ⊥ is thetransverse wavenumber. Thus magnetic fields shift Andreev reflection features by∆ E = − v F P S sinθ (where v F , P S , and θ are the normal material Fermi velocity, Cooper ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures -60 -40 0-20 6040205431 [ d I / d V ] S / [ d I / d V ] N Voltage (mV)2 (a) - Δ - Δ r Δ i [ d I / d V ] S / [ d I / d V ] N (b) (a) i - Δ r Δ r - Δ Δ i - Δ r Δ r - Δ Δ (c) (e)0 2 4Field (T)1.50.51 [ d I / d V ] S / [ d I / d V ] N (b)(a) i - Δ r Δ r - Δ Δ i - Δ r Δ r - Δ Δ (c) -60 -40 0-20 6040204321 [ d I / d V ] S / [ d I / d V ] N Voltage (mV)- Δ - Δ r Δ r Δ Δ i (b) (b)(a) i - Δ r Δ r - Δ Δ i - Δ r Δ r - Δ Δ (c) (f)211.50 2 4Field (T) [ d I / d V ] S / [ d I / d V ] N [ d I / d V ] S / [ d I / d V ] N Figure 3: (a,c,e) Bi-2212/ Bi Te and (b,d,f) Bi-2212/graphite. (a-b) Offset, normalizeddI/dV of Bi Te (75K, 60K, 50K, 40K, 30K and 20K), and graphite data every 10 K from T c to 70 K, then every 5K till 25K, and finally 11K. Three Peaks due to Andreev reflection intoinduced (∆ i ), reduced (∆ r ) and full gaps (∆ ). (c-d) dI/dV in parallel magnetic field, withthe fits shown in purple. For Bi Te the fields are (0.05, 0.1, 0.25, 0.5, 1, 2, 3, 4, 5, 6, 7, and7.5 T), while for graphite they are (every 0.1 T till 1T, then 1.1, 1.25, 1.5, 2, 3, 4 and 5T)Features shift due to the Doppler effect. (e-f) Dots show the measured data at 43 mV (blue)and 0 mV (red) versus field. The black lines are fits with Doppler. ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures P S ) is linearly proportional to B and includes a geometricfactor whose exact size is difficult to estimate in proximity devices.[47, 48, 49, 50, 40,42, 53, 54, 44, 56, 45] Thus for features involving tunneling of cooper pairs, we expecta Doppler shift: ∆ E = D × B , where D is a constant.In studies of dABS in Bi-2212, magnetic field split and/or suppressed the zerobias peak due to the Doppler effect, except when the field was aligned in the ab-plane.[40, 42] Alternatively, in S/N/S or N/S/N one can observe nABS due to multipleAndreev reflections between the interfaces. These nABS, which can play a crucial role inthe proximity effect and supercurrents, have an energy defined by the phase differenceacross the confined region, ∆ and the transparency of the barrier.[33] In a confinedstructure with an induced pair amplitude, the resulting minigap was reduced upon bya perpendicular magnetic field,[32] as expected from theory[31] due to φ between thesuperconducting contacts.The situation in our devices is quite different than typically observed in low T c structures. Due to the large H c ≈ T , we do not expect significant shifts in ∆ forthe fields applied here ( ≤ . T ).[67] However, if nABS emerged due to the small mesasseen in AFM, then their energy of will be periodic in the magnetic field as the phasewinds through 2 π .[33, 34, 35, 36] Using the cross-sectional area of our Bi Sr CaCu O δ ( ≈ − m ) or accounting for the small size of the mesas, we find the features wouldreach zero energy at B ≈ − T . Thus if our features arise from nABS, their shiftswith field would essentially be random for the sizes of the fields we apply. FurthermorenABS should only appear below the induced gap. Hence the feature at 40 meV shouldbe tunneling into the full gap of Bi Sr CaCu O δ , whereas the features at lower energycould be nABS. As such while the field may tune the zero-bias peak and the peak at∆ r , the full gap will not be affected.In figure 3(c&d) we show the dI/dV spectra at 6.5 K with magnetic field. The sizeof the dI/dV at zero bias and 43 mV is shown in figure3(e&f), revealing a systematicsuppression of the spectra, suggesting this may be the result of dABS. However thefull gap, reduced gap and width of the induced gap feature all move to zero bias uponapplying the magnetic field. This provides strong evidence against ABS as the full gap(∆ ) should be field independent, as seen in high barrier junctions (figure 2 (b)). Thuswe attribute the magnetic field induced changes to the Doppler effect.This is confirmed by including the Doppler effect in our calculation of the c-axisconductance spectra using the formalism developed for anisotropic superconductors[30].As described in reference [18, 19], we modified this formalism to include contributionsfrom the induced, reduced and fully gapped regions. A proper theoretical approachwould self-consistently calculate the gap and account for potential multiple reflectionsdue to the gradual change in the gap. However since we do not investigate confinedstructures, and our minimal model captures our results, we believe it is appropriate toinvestigate the effects of magnetic field. Once the zero-field spectra are captured byour model, we follow the established procedure for the Doppler effect by calculating the ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures Figure 4:
The width of the induced gap in graphite at 11 K at various applied fields.
Andreev reflection probability a ( ˜ E ) with ˜ E = E + ∆ E . The entire field dependenceis reproduced using only the Doppler factor D. The resulting dI/dV and their valuesat fixed bias are shown in Figs. 3. The excellent agreement, despite only one freeparameter, confirms the field dependence is governed by Andreev reflection and theDoppler effect.Before closing, let us discuss some alternate possibilities. For example, Andreevbound states formed at the 110 interface between a d-wave superconductor/normalmetal can create a peak at zero bias[40, 43, 30]. However, the central peak in our datais very different from an Andreev bound state. We observe a reduced gap as well as thecentral gap, in spite of the Andreev bound state only showing up as a zero-bias peak.Lastly, the Andreev bound states are expected to split by the application of magneticfield, while the central peak (the induced gap) in our data, not only does not split, butthe width decreases with field. (Fig 4 A) [40, 43]Other bound states such as geometrical resonances (McMillan-Rowel and Tomaschoscillations)[68, 69] can create peaks in the differential conductance spectra. However,these peaks emerge at certain voltage positions in the Andreev spectra. Tomaschoscillations are due to resonances in the superconductor and create resonance features indI/dV at voltages given by: eV n = (cid:114) (2∆) + ( nhv fS d S ) , with ∆ being the superconductingenergy gap, v fS being the Fermi velocity in the superconductor, d S being the thicknessof the superconductor, and n being the dip number). McMillan-Rowell oscillations occurdue to geometrical resonances in the normal material and the voltages of the oscillatoryfeatures are linear with n (∆ V = hv fN ed N , with v fN being the Fermi velocity in the normalmaterial and d N being the thickness of the normal layer at which the reflections occur.Neither of these oscillations agree with the peaks we observe in our data. Furthermore,these oscillations typically create features at finite bias, in contrast to our data where weobserve a zero-bias conductance peak. [68] Nonetheless, the magnetic field dependenceof McMillan-Rowell and Tomasch oscillations are different from our data. These bound ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures Te /graphite, and their poor c-axis transport. What about the mis-match in theFermi surfaces between Bi-2212 and the normal materials? Since the normal materials’lattice symmetries are quite distinct from Bi-2212, the Fermi surfaces touch in theextended Brillouin zone.[26, 25, 70] This is shown in figure 1(c), where the Fermi levelof the hole doped Bi Te is around the Dirac point[71], and the graphite is of ABABstacking.[72] This argument holds for a wide range of Fermi levels.Strong similarities between Bi Te and graphite devices may suggest our resultsare intrinsic to Bi-2212. For example, the junctions could lead to strain that producesmechanical breaks. Indeed, some devices had sharp features in the dI/dV as seen inpoint contact.[73] These result from reaching the critical current in the inhomogeneoussuperconductor. However such devices did not show the features reported here, and thesharp peaks were suppressed much faster in applied magnetic field then expected fromDoppler. Furthermore the Andreev features only appear in measurements performedacross the interface. Acknowledgments
The work at the University of Toronto was supported by the Natural Sciences andEngineering Research Council of Canada, the Canadian Foundation for Innovation,and the Ontario Ministry for Innovation. KSB acknowledges support from theNational Science Foundation (grant DMR-1410846). The work at Brookhaven NationalLaboratory (BNL) was supported by DOE under Contract No. DE-AC02-98CH10886.The crystal growth at Princeton was supported by the US National Science Foundation,grant number DMR-0819860. [1] Suemune I, Akazaki T, Tanaka K, Jo M, Uesugi K, Endo M, Kumano H, Hanamura E, TakayanagiH, Yamanishi M and Kan H 2006
Japanese Journal of Applied Physics Phys. Rev. B (9) 094508[3] Oreg Y, Refael G and von Oppen F 2010 Physical Review Letters
Physical Review Letters arXiv.org ( Preprint cond-mat/0005069v2 )[6] Fu L and Kane C L 2009
Physical Review Letters arXiv.org ( Preprint )[8] Kitaev A Y 2007
Physics-Uspekhi Physical Review Letters AppliedPhysics Letters ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures [11] Bozovic I, Logvenov G, Verhoeven M A, Caputo P, Goldobin E and Beasley M R 2004 PhysicalReview Letters JapaneseJournal of Applied Physics Physical Review Letters Physical Review B Physical Review B Physical Review B (21) 214511[17] Golod T, Rydh A, Krasnov V M, Marozau, Uribe-Laverde M A, Satapathy D K, Wagner T andBernhard C 2013 Physical Review B Nature communications Phys. Rev. B (24) 241106[20] Wang E, Ding H, Fedorov A V, Yao W, Li Z, Lv Y F, Zhao K, Zhang L G, Xu Z, Schneeloch J,Zhong R, Ji S H, Wang L, He K, Ma X, Gu G, Yao H, Xue Q K, Chen X and Zhou S 2013 Nature Physics Physical Review B Physical Review B Physical Review Letters
Physical Review B Journal of Materials Chemistry C Reviews of modern physics Journal of Low Temperature Physics
Journal of Applied Physics Journal of superconductivity Physical Review B Superlattices and Microstructures Physical Review Letters
Physical Review B (Condensed Matter and MaterialsPhysics) [34] Dirks T, Hughes T L, Lal S, Uchoa B, Chen Y F, Chialvo C, Goldbart P M and Mason N 2011 Nature Physics Nat Phys http://dx.doi.org/10.1038/nphys1811 [36] Stehno M P, Orlyanchik V, Nugroho C D, Ghaemi P, Brahlek M, Koirala N, Oh S and vanHarlingen D J 2016 Physical Review B et al. Proceedings of the National Academy of Sciences
Physical ReviewLetters Physical Review B Physica C: Superconductivity and its applications
Phys. Rev.Lett. (7) 1536–1539 ndreev Reflection without Fermi surface alignment in High T c -Topological heterostructures [42] Deutscher G 2005 Reviews of Modern Physics Physical Review Letters Phys. Rev. B (22)R14681–R14684[45] Dagan Y, Krupke R and Deutscher G 2000 EPL (Europhysics Letters) Journal of the Korean Physical Society Physical Review B Physical ReviewB Physical Review B Physica C: Superconductivity
Phys. Rev. Lett. (2) 027001[52] Fridman I, Kloc C, Petrovic C and Wei J Y T 2011 Applied Physics Letters Phys. Rev.B (10) 104504[54] Park W K, Sarrao J L, Thompson J D and Greene L H 2008 Physical Review Letters
Physica B: Condensed Matter
Phys. Rev. B (9) 094522[57] Jank´o B 1999 Phys. Rev. Lett. (23) 4703–4706[58] Wolf E L and Arnold G B 1982 Physics Reports Physical Review Letters Physical review. B, Condensed matter Physical Review B [62] Xu S Y, Alidoust N, Belopolski I, Richardella A, Liu C, Neupane M, Bian G, Huang S H, SankarR, Fang C, Dellabetta B, Dai W, Li Q, Gilbert M J, Chou F, Samarth N and Hasan M Z 2014 Nature Physics SuperconductorScience and Technology https://is.gd/uMgb7E [64] Dynes R C, Narayanamurti V and Garno J P 1978 Physical Review Letters Physical Review Letters
Physical Review B Phys. Rev. Lett. (25)5763–5766[68] Shkedy L, Aronov P, Koren G and Polturak E 2004 Physical Review B Physica C: Superconductivity
PhysicalReview B et al. Physical Review B Physical Review B Phys. Rev. Lett.107