We report on the experimental observation of the proximity induced superconductivity in an indium gallium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting electrodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantum well-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conductance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expression VSD = 2Δ/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B which decreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductance maxima close to B = 0 T are observed. Our results help to pave the way to the development of integrated coherent quantum circuitry.Authors acknowledge financial support from EPSRC grant numbers EP/M009505/1 and EP/J017671/1. K. Delfanazari is grateful to Dr. H. Asai for helpful discussions

Cao, M

Delfanazari, K

Farrer, I

Gul, Y

Joyce, H

Kelly, M

Ma, P

Puddy, R

Ritchie, D

Smith, C

Yi, T

K. Delfanazari

R.K. Puddy

P. Ma

T. Yi

M. Cao

Y. Gul

I. Farrer

D.A. Ritchie

H.J. Joyce

M.J. Kelly

C.G. Smith

Crossref

Journal of Magnetism and Magnetic Materials

Proximity induced superconductivity in indium gallium arsenide quantum wells

We report on the experimental observation of the proximity induced superconductivity in an indium gallium arsenide (In 0.75 Ga 0.25 As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting electrodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In 0.75 Ga 0.25 As quantum well-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conductance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expression V SD [U+202F]=[U+202F] 2δ/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B which decreases by increasing B. When decreasing B to below ±0.4[U+202F]T, a hysteresis and shift of the conductance maxima close to B[U+202F] =[U+202F]0 T are observed. Our results help to pave the way to the development of integrated coherent quantum circuitry

Puddy, RK

Ritchie, DA

Joyce, HJ

Kelly, MJ

Smith, CG

UCL Discovery

Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxxContents lists available at ScienceDirectJournal of Magnetism and Magnetic Materialsjournal homepage: www.elsevier .com/locate / jmmmResearch articlesProximity induced superconductivity in indium gallium arsenidequantum wellshttps://doi.org/10.1016/j.jmmm.2017.10.0570304-8853/ 2017 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).⇑ Corresponding author at: Electrical Engineering Division, University ofCambridge, Cambridge CB3 0FA, UK.E-mail address: kd398@cam.ac.uk (K. Delfanazari).Please cite this article in press as: K. Delfanazari et al., Proximity induced superconductivity in indium gallium arsenide quantum wells, Journal onetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.10.057K. Delfanazari a,b,⇑, R.K. Puddy b, P. Ma b, T. Yi b, M. Cao b, Y. Gul c, I. Farrer b,d, D.A. Ritchie b, H.J. Joyce a,M.J. Kelly a,b, C.G. Smith baCentre for Advanced Photonics and Electronics (CAPE), Electrical Engineering Division, University of Cambridge, Cambridge CB3 0FA, UKbDepartment of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UKcDepartment of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UKdDepartment of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKa r t i c l e i n f o a b s t r a c tArticle history:Received 10 July 2017Received in revised form 10 October 2017Accepted 14 October 2017Available online xxxxWe report on the experimental observation of the proximity induced superconductivity in an indium gal-lium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting elec-trodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantumwell-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conduc-tance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expressionVSD = 2D/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B whichdecreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductancemaxima close to B = 0 T are observed. Our results help to pave the way to the development of integratedcoherent quantum circuitry. 2017 The Authors. Published by Elsevier B.V. This is an open access articleunder the CCBY license (http://creativecommons.org/licenses/by/4.0/).1. IntroductionThe proximity effect in hybrid superconductor-semiconductor(S-Sm) structures, e.g. superconducting correlations and supercur-rent transport in a semiconductor connected to a superconductormediated by phase coherent Andreev reflections [1–3], providesthe possibility to study some fascinating fundamental physics suchas Kondo-enhanced Andreev tunnelling [4], supercurrent reversalin quantum dots [5], Josephson quantum electron pumps [6]. Therehas been renewed interests in such systems after the observationof Majorana fermions states at the S-Sm interfaces [7–9]. This isbecause Majorana Zero modes have potential to support topologi-cally protected quantum computing [10]. Yet, the fundamentaltechnological problem is to fabricate a highly transparent contactbetween a superconductor with a high Fermi energy Ef and a semi-conducting material with a low Ef.In this regard, here we present our experimental results onproximity induced superconductivity in a high-mobility two-dimensional electron gas (2DEG) in an indium gallium arsenide(In0.75Ga0.25As) heterostructure. The symmetric and planarNb-2DEG-Nb Josephson junction was fabricated on an InGaAs chipin which each junction consists of two identical Nb superconduct-ing electrodes. The junction was measured by using a lock-inmeasurement technique in a dilution fridge with a basetemperature of 40 mK.Andreev reflections and bound states due to the electron andhole like quasiparticle correlations at the Nb-In0.75Ga0.25As quan-tum well interfaces lead to the observation of a U-shape dip atlow-bias voltage of the differential resistance dV/dI (VSD) plot, aswell as the subharmonic energy gap structures (SGS) at V = 2D/newhere the D is Nb superconducting gap. Both the induced gapand SGS features suppress significantly as temperature T and mag-netic field B are applied to the system – due to the T and B depen-dences of DNb – leading to a shift of the SGS toward zero bias [11].Sweeping dI/dV vs. B, results in the observation of a hysteresis for0.25  B (T)  0.25 and a shift in the differential conductancemaximum close to B = 0 T.2. Materials and methodsThe In0.75GaAs/In0.75AlAs/GaAs quantum well were grown bymolecular beam epitaxy (MBE) [11,12]. Eight identical and sym-metric Josephson junctions (results for one junction is discussedhere) were patterned and fabricated on a single chip. The 30 nmthick 2DEG with density ns = 2.24  1011 (cm2) and mobilityf Mag-2 K. Delfanazari et al. / Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxxle=2.5  105 (cm2/Vs) was formed 120 nm below the wafer’ssurface.Niobium (Nb) superconducting contacts were made by standardphotolithography technique. First, we created a 120–140 nm deeptrench by wet etching and then a 130 nm of Nb was deposited byDC magnetron sputtering in an Ar plasma. The 130 nm thickness ofNb is about three times larger than the London penetration depthof 40 nm.The junction has a width w = 4 lm and a length L = 850 nm inthe shortest path between the two Nb electrodes (see inset inFig. 1). The ohmic contacts were made of AuGeNi and placed100 lm away from the junctions to prevent the influence of thenormal electrons on Nb-quantum well interfaces. The quantumtransport measurements were performed using a standardlock-in technique by superimposing a small ac signal at a fre-quency f = 70 Hz, and amplitude of 5 lV to the junction dc biasvoltage and the measurements were taken in a dilution fridge atT = 50 mK and up to 800 mK.3. ResultsThe false color Scanning Electron Micrograph (SEM) image ofthe planar Nb-In0.75Ga0.25As-Nb Josephson junction is shown inthe inset of Fig. 1. The device is in the ballistic regime as thedistance between two Nb electrodes L = 850 nm is an order ofmagnitude shorter than the corresponding elastic mean free pathof ‘e = e1⁄lep2pns 2 lm [11].The temperature dependence of the induced superconductivityis shown in Fig. 1 where the differential resistance (dV/dI) versusbias voltage (VSD) graphs at temperatures between 50 and 800mK are plotted. A pronounced supercurrent of up to 0.2 lA wasobserved at zero magnetic field B and at temperature T = 50 mK.Because of the electron- and hole-like quasiparticles correlations(Andreev reflections) below the junction’s Tc and for voltage biaseswithin the superconducting gap, the induced gap and subharmonicenergy gap structures (SGS) are observed.Fig. 1. The superconductor-semiconductor-superconductor Josephson junction: The diff800 mK. Inset: the false color scanning electron micrograph (SEM) image showing a topcontacts are Niobium (Nb) as shown in dark-gold color in the figure. The gap size betwepath. (For interpretation of the references to color in this figure legend, the reader is rePlease cite this article in press as: K. Delfanazari et al., Proximity induced supenetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.1The ratio of L/nN, where nN is the Bardeen-Cooper-Schrieffer(BCS) coherence length [13–15] have influence on the shape ofthe gap and SGS. The SGS consists of a set of pronounced conduc-tance maxima at V = 2D/ne where the D is Nb superconductinggap, and n is an integer number. In the case of the present junction,the proximity effect induces a minigap into the 2DEG withDind = 1.76 kBTc  100 leV. This suggests that our junction with alength L = 850 nm and nN = hmFN/pDind = 2 lm is in the shortchannel regime (L/nN 1). For this junction, the dimensionlessinterface barrier strength Z < 0.2 and therefore an averagetransmissivity T = 1/(1 + Z2) > 0.96 were estimated [11]. The flatdV/dI (VSD) observed within the superconducting gap is consistentwith BTK model [13] (see Ref. [11] for more details).The magnetic field dependence of the induced superconductiv-ity is shown in Fig. 2 where the plot of dV/dI as a function of appliedvoltage VSD at B = 1 mT is shown in the inset. Here, the SGS corre-sponding to 2D/3e (blue), 2D/4e (green), and 2D/6e (red) areshown by arrows. We could not observe the SGS correspondingto 2D/5e. This may be due to the geometry of our junction (seethe inset of Fig. 1). Here, the 2DEG and Nb both extend beyondthe narrow area L  w where induced superconductivity isexpected. Dephasing from the 2DEG regions either side of the junc-tion (which are in normal state) may influence the SGS. The corre-sponding voltage points of the observed SGS are plotted as afunction of B in Fig. 2. It is found that the SGS are strongly B depen-dent, with the position of the peaks bending toward zero voltage asB is increased and being totally washed out at 0.2 T.The dI/dV versus B shows a maximum at zero Bwhich decreasesby increasing B up to 0.25 T (see Fig. 3). Above this point it reachesa constant value indicating that the junction turns into the normalstate. When decreasing B to below ±0.25 T, vortex pinning in theNb electrodes causes a hysteresis in dI/dV (B) plot. The dI/dV curvein Fig. 3 shows a symmetric shift of conductance close to zero Bfield for both positive and negative fields.Here, the applied B field and the vortex penetrating the elec-trodes are parallel. However, when the sign of the applied B fielderential resistance (dV/dI) versus bias voltage VSD at temperatures between 50 andview of a symmetric Nb-In0.75Ga0.25As-Nb Josephson junction. The superconductingen two Nb electrodes has a length L = 850 nm and a width w = 4 lm at the shortestferred to the web version of this article.)rconductivity in indium gallium arsenide quantum wells, Journal of Mag-0.0570.00 0.02 0.04 0.06 0.08 0.100.10.20.30.40.50.60.7VSD (mV)B (T) 2 e 2 e 2 e-0.8 -0.4 0.0 0.40.00.10.20.3dV/dI (k)VSD (mV)T= 50 mK, B= 1 mTFig. 2. Magnetic field dependence of the induced superconductivity in a ballisticJosephson junction: The blue, green and red circles (see their corresponding arrowsin inset) indicate the magnetic field evolution of the induced- and subharmonic-gapstructures. Inset is the dV/dI (V) measured at B = 1 mT and T = 50 mK. Arrowscorrespond to SGS: 2D/3e (blue), 2D/4e (green), and 2D/6e (red). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.43.63.84.04.24.44.6T= 50 mK dI/dV (mS)B (T)Fig. 3. Magnetoconductance oscillations and hysteresis on the differentialconductance of the Nb-In0.75Ga0.25As-Nb Josephson junction: Differentialconductance (dI/dV) vs. applied magnetic field B perpendicular to the junction’splane at temperature 50 mK. Arrows indicate the B sweep directions.K. Delfanazari et al. / Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxx 3changes (e.g. B < 0 to B > 0), B and the pinned vortex becomes anti-parallel [16,17]. The pinned vortex may cause a phase change atthe interface, and causes the appearance of the dI/dV oscillationsand zero B shift.Please cite this article in press as: K. Delfanazari et al., Proximity induced supenetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.1Such oscillations have also been observed in different systemssuch as granular Sn wires [18], superconducting Pb nanobridges[19], and gold nanowires [20].4. ConclusionWe have experimentally studied the proximity inducedsuperconductivity in a hybrid Nb-In0.75Ga0.25As-Nb ballisticJosephson junction. We demonstrated the formation of highlytransparent interfaces between Nb and In0.75Ga0.25As quantumwells. The temperature and magnetic field dependences of theinduced superconducting gap and subharmonic gap structureswere discussed. The presented platform may be helpful for thedevelopment of integrated quantum circuitry.AcknowledgmentAuthors acknowledge financial support from EPSRC grantnumbers EP/M009505/1 and EP/J017671/1. K. Delfanazari is grate-ful to Dr. H. Asai for helpful discussions. The data presented in thispaper can be accessed at https://doi.org/10.17863/CAM.13774.References[1] A.F. Andreev, Thermal conductivity of the intermediate state ofsuperconductors, Sov. Phys. JETP 19 (1964) 1228.[2] Z. Wan et al., Induced superconductivity in high-mobility two-dimensionalelectron gas in gallium arsenide heterostructures, Nat. Commun. 6 (2015)7426, https://doi.org/10.1038/ncomms8426.[3] M. Kjaergaard et al., Quantized conductance doubling and hard gap in a two-dimensional semiconductor–superconductor heterostructure, Nat. Commun. 7(2016) 12841, https://doi.org/10.1038/ncomms12841.[4] T. Sand-Jespersen, J. Paaske, B.M. Andersen, K. Grove-Rasmussen, H.I.Jørgensen, M. Aagesen, C.B. Sørensen, P.E. Lindelof, K. Flensberg, J. Nygard,Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots, Phys.Rev. Lett. 99 (2007) 126603.[5] J.A.V. Dam, Y.V. Nazarov, E.P.A.M. Bakkers, S.D. Franceschi, L.P. Kouwenhoven,Supercurrent reversal in quantum dots, Nature 442 (2006) 667–670.[6] F. Giazotto, P. Spathis, S. Roddaro, S. Biswas, F. Taddei, M. Governale, L. Sorba, AJosephson quantum electron pump, Nat. Phys. 7 (2011) 857–861.[7] V. Mourik et al., Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336 (2012) 1003–1007.[8] L.P. Rokhinson, X. Liu, J.K. Furdyna, The fractional a.c. Josephson effect in asemiconductor-superconductor nanowire as a signature of Majorana particles,Nat. Phys. 8 (2012) 795–799.[9] M.T. Deng et al., Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354 (2016) 1557–1562.[10] A.Yu. Kitaev, Fault-tolerant quantum computation by anyons, Ann Phys 303(2003) 2–30.[11] K. Delfanazari, R.K. Puddy, P. Ma, T. Yi, M. Cao, Y. Gul, I. Farrer, D.A. Ritchie, H.J.Joyce, M.J. Kelly, C.G. Mith, On chip Andreev devices: hard gap and quantumtransport in ballistic Nb-In0.75Ga0.25As quantum well-Nb Josephson junctions,Adv. Mater. 29 (2017) 1701836.[12] C. Chen, I. Farrer, S.N. Holmes, F. Sfigakis, M.P. Fletcher, H.E. Beere, D.A. Ritchie,Growth variations and scattering mechanisms in metamorphic In0.75Ga0.25As/In0.75Al0.25As quantum wells grown by molecular beam epitaxy, J. Cryst.Growth 425 (2015) 70–75.[13] G.E. Blonder, M. Tinkham, T.M. Klapwijk, Transition from metallic to tunnelingregimes in superconducting microconstrictions: excess current, chargeimbalance, and supercurrent conversion, Phys. Rev. B 25 (1982) 4515.[14] K. Flensberg, J.B. Hansen, M. Octavio, Subharmonic energy-gap structure insuperconducting weak links, Phys. Rev. B 38 (1988) 8707.[15] H.Y. Günel, N. Borgwardt, I.E. Batov, H. Hardtdegen, K. Sladek, G. Panaitov, D.Grützmacher, Th. Schäpers, Crossover from Josephson effect to single interfaceAndreev reflection in asymmetric superconductor/nanowire junctions, NanoLett. 14 (9) (2014) 4977–4981.[16] Y. Takagaki, Transport properties of semiconductor-superconductor junctionsin quantizing magnetic fields, Phy. Rev. B 57 (1998) 4009.[17] Y. Asano, Magnetoconductance oscillations in ballistic semiconductor-superconductor junctions, Phys. Rev. B 61 (2000) 1732.[18] A.V. Herzog, P. Xiong, R.C. Dynes, Magnetoresistance oscillations in granular Snwires near the superconductor-insulator transition, Phys. Rev. B 58 (1998) 21.[19] Jian Wang et al., Semiconductor-superconductor transition andmagnetoresistance terraces in an ultrathin superconducting Pb nanobridge, J.Vac. Sci. Technol. B 28 (2010), https://doi.org/10.1116/1.3437016.[20] J. Wang, C. Shi, M. Tian, Q. Zhang, N. Kumar, J. Jain, T. Mallouk, M.H.W. Chan,Proximity-induced superconductivity in nanowires: minigap state anddifferential magnetoresistance oscillations, Phys. Rev. Lett. 102 (2009) 247003.rconductivity in indium gallium arsenide quantum wells, Journal of Mag-0.057

Apollo (Cambridge)

We report on the experimental observation of the proximity induced superconductivity in an indium gallium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting electrodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantum well-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conductance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expression VSD = 2Δ/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B which decreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductance maxima close to B = 0 T are observed. Our results help to pave the way to the development of integrated coherent quantum circuitry

Delfanazari, K.

Puddy, R.K.

Ma, P.

Yi, T.

Cao, M.

Gul, Y.

Farrer, I.

Ritchie, D.A.

Joyce, H.J.

Kelly, M.J.

Smith, C.G.

Enlighten

Journal of Magnetism and Magnetic Materials 459 (2018) 282–284Contents lists available at ScienceDirectJournal of Magnetism and Magnetic Materialsjournal homepage: www.elsevier .com/ locate/ jmmmResearch articlesProximity induced superconductivity in indium gallium arsenidequantum wellshttps://doi.org/10.1016/j.jmmm.2017.10.0570304-8853/ 2017 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).⇑ Corresponding author at: Electrical Engineering Division, University ofCambridge, Cambridge CB3 0FA, UK.E-mail address: kd398@cam.ac.uk (K. Delfanazari).K. Delfanazari a,b,⇑, R.K. Puddy b, P. Ma b, T. Yi b, M. Cao b, Y. Gul c, I. Farrer b,d, D.A. Ritchie b, H.J. Joyce a,M.J. Kelly a,b, C.G. Smith baCentre for Advanced Photonics and Electronics (CAPE), Electrical Engineering Division, University of Cambridge, Cambridge CB3 0FA, UKbDepartment of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UKcDepartment of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UKdDepartment of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKa r t i c l e i n f o a b s t r a c tArticle history:Received 10 July 2017Received in revised form 10 October 2017Accepted 14 October 2017Available online 16 October 2017We report on the experimental observation of the proximity induced superconductivity in an indium gal-lium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting elec-trodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantumwell-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conduc-tance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expressionVSD = 2D/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B whichdecreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductancemaxima close to B = 0 T are observed. Our results help to pave the way to the development of integratedcoherent quantum circuitry. 2017 The Authors. Published by Elsevier B.V. This is anopenaccess article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).1. IntroductionThe proximity effect in hybrid superconductor-semiconductor(S-Sm) structures, e.g. superconducting correlations and supercur-rent transport in a semiconductor connected to a superconductormediated by phase coherent Andreev reflections [1–3], providesthe possibility to study some fascinating fundamental physics suchas Kondo-enhanced Andreev tunnelling [4], supercurrent reversalin quantum dots [5], Josephson quantum electron pumps [6]. Therehas been renewed interests in such systems after the observationof Majorana fermions states at the S-Sm interfaces [7–9]. This isbecause Majorana Zero modes have potential to support topologi-cally protected quantum computing [10]. Yet, the fundamentaltechnological problem is to fabricate a highly transparent contactbetween a superconductor with a high Fermi energy Ef and a semi-conducting material with a low Ef.In this regard, here we present our experimental results onproximity induced superconductivity in a high-mobility two-dimensional electron gas (2DEG) in an indium gallium arsenide(In0.75Ga0.25As) heterostructure. The symmetric and planarNb-2DEG-Nb Josephson junction was fabricated on an InGaAs chipin which each junction consists of two identical Nb superconduct-ing electrodes. The junction was measured by using a lock-inmeasurement technique in a dilution fridge with a basetemperature of 40 mK.Andreev reflections and bound states due to the electron andhole like quasiparticle correlations at the Nb-In0.75Ga0.25As quan-tum well interfaces lead to the observation of a U-shape dip atlow-bias voltage of the differential resistance dV/dI (VSD) plot, aswell as the subharmonic energy gap structures (SGS) at V = 2D/newhere the D is Nb superconducting gap. Both the induced gapand SGS features suppress significantly as temperature T and mag-netic field B are applied to the system – due to the T and B depen-dences of DNb – leading to a shift of the SGS toward zero bias [11].Sweeping dI/dV vs. B, results in the observation of a hysteresis for0.25  B (T)  0.25 and a shift in the differential conductancemaximum close to B = 0 T.2. Materials and methodsThe In0.75GaAs/In0.75AlAs/GaAs quantum well were grown bymolecular beam epitaxy (MBE) [11,12]. Eight identical and sym-metric Josephson junctions (results for one junction is discussedhere) were patterned and fabricated on a single chip. The 30 nmthick 2DEG with density ns = 2.24  1011 (cm2) and mobilityK. Delfanazari et al. / Journal of Magnetism and Magnetic Materials 459 (2018) 282–284 283le=2.5  105 (cm2/Vs) was formed 120 nm below the wafer’ssurface.Niobium (Nb) superconducting contacts were made by standardphotolithography technique. First, we created a 120–140 nm deeptrench by wet etching and then a 130 nm of Nb was deposited byDC magnetron sputtering in an Ar plasma. The 130 nm thickness ofNb is about three times larger than the London penetration depthof 40 nm.The junction has a width w = 4 lm and a length L = 850 nm inthe shortest path between the two Nb electrodes (see inset inFig. 1). The ohmic contacts were made of AuGeNi and placed100 lm away from the junctions to prevent the influence of thenormal electrons on Nb-quantum well interfaces. The quantumtransport measurements were performed using a standardlock-in technique by superimposing a small ac signal at a fre-quency f = 70 Hz, and amplitude of 5 lV to the junction dc biasvoltage and the measurements were taken in a dilution fridge atT = 50 mK and up to 800 mK.3. ResultsThe false color Scanning Electron Micrograph (SEM) image ofthe planar Nb-In0.75Ga0.25As-Nb Josephson junction is shown inthe inset of Fig. 1. The device is in the ballistic regime as thedistance between two Nb electrodes L = 850 nm is an order ofmagnitude shorter than the corresponding elastic mean free pathof ‘e = e1⁄lep2pns 2 lm [11].The temperature dependence of the induced superconductivityis shown in Fig. 1 where the differential resistance (dV/dI) versusbias voltage (VSD) graphs at temperatures between 50 and 800mK are plotted. A pronounced supercurrent of up to 0.2 lA wasobserved at zero magnetic field B and at temperature T = 50 mK.Because of the electron- and hole-like quasiparticles correlations(Andreev reflections) below the junction’s Tc and for voltage biaseswithin the superconducting gap, the induced gap and subharmonicenergy gap structures (SGS) are observed.Fig. 1. The superconductor-semiconductor-superconductor Josephson junction: The diff800 mK. Inset: the false color scanning electron micrograph (SEM) image showing a topcontacts are Niobium (Nb) as shown in dark-gold color in the figure. The gap size betwepath. (For interpretation of the references to color in this figure legend, the reader is reThe ratio of L/nN, where nN is the Bardeen-Cooper-Schrieffer(BCS) coherence length [13–15] have influence on the shape ofthe gap and SGS. The SGS consists of a set of pronounced conduc-tance maxima at V = 2D/ne where the D is Nb superconductinggap, and n is an integer number. In the case of the present junction,the proximity effect induces a minigap into the 2DEG withDind = 1.76 kBTc  100 leV. This suggests that our junction with alength L = 850 nm and nN = hmFN/pDind = 2 lm is in the shortchannel regime (L/nN  1). For this junction, the dimensionlessinterface barrier strength Z < 0.2 and therefore an averagetransmissivity T = 1/(1 + Z2) > 0.96 were estimated [11]. The flatdV/dI (VSD) observed within the superconducting gap is consistentwith BTK model [13] (see Ref. [11] for more details).The magnetic field dependence of the induced superconductiv-ity is shown in Fig. 2 where the plot of dV/dI as a function of appliedvoltage VSD at B = 1 mT is shown in the inset. Here, the SGS corre-sponding to 2D/3e (blue), 2D/4e (green), and 2D/6e (red) areshown by arrows. We could not observe the SGS correspondingto 2D/5e. This may be due to the geometry of our junction (seethe inset of Fig. 1). Here, the 2DEG and Nb both extend beyondthe narrow area L  w where induced superconductivity isexpected. Dephasing from the 2DEG regions either side of the junc-tion (which are in normal state) may influence the SGS. The corre-sponding voltage points of the observed SGS are plotted as afunction of B in Fig. 2. It is found that the SGS are strongly B depen-dent, with the position of the peaks bending toward zero voltage asB is increased and being totally washed out at 0.2 T.The dI/dV versus B shows a maximum at zero B which decreasesby increasing B up to 0.25 T (see Fig. 3). Above this point it reachesa constant value indicating that the junction turns into the normalstate. When decreasing B to below ±0.25 T, vortex pinning in theNb electrodes causes a hysteresis in dI/dV (B) plot. The dI/dV curvein Fig. 3 shows a symmetric shift of conductance close to zero Bfield for both positive and negative fields.Here, the applied B field and the vortex penetrating the elec-trodes are parallel. However, when the sign of the applied B fielderential resistance (dV/dI) versus bias voltage VSD at temperatures between 50 andview of a symmetric Nb-In0.75Ga0.25As-Nb Josephson junction. The superconductingen two Nb electrodes has a length L = 850 nm and a width w = 4 lm at the shortestferred to the web version of this article.)0.00 0.02 0.04 0.06 0.08 0.100.10.20.30.40.50.60.7VSD (mV)B (T) 2 e 2 e 2 e-0.8 -0.4 0.0 0.40.00.10.20.3dV/dI (k)VSD (mV)T= 50 mK, B= 1 mTFig. 2. Magnetic field dependence of the induced superconductivity in a ballisticJosephson junction: The blue, green and red circles (see their corresponding arrowsin inset) indicate the magnetic field evolution of the induced- and subharmonic-gapstructures. Inset is the dV/dI (V) measured at B = 1 mT and T = 50 mK. Arrowscorrespond to SGS: 2D/3e (blue), 2D/4e (green), and 2D/6e (red). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.43.63.84.04.24.44.6T= 50 mK dI/dV (mS)B (T)Fig. 3. Magnetoconductance oscillations and hysteresis on the differentialconductance of the Nb-In0.75Ga0.25As-Nb Josephson junction: Differentialconductance (dI/dV) vs. applied magnetic field B perpendicular to the junction’splane at temperature 50 mK. Arrows indicate the B sweep directions.284 K. Delfanazari et al. / Journal of Magnetism and Magnetic Materials 459 (2018) 282–284changes (e.g. B < 0 to B > 0), B and the pinned vortex becomes anti-parallel [16,17]. The pinned vortex may cause a phase change atthe interface, and causes the appearance of the dI/dV oscillationsand zero B shift.Such oscillations have also been observed in different systemssuch as granular Sn wires [18], superconducting Pb nanobridges[19], and gold nanowires [20].4. ConclusionWe have experimentally studied the proximity inducedsuperconductivity in a hybrid Nb-In0.75Ga0.25As-Nb ballisticJosephson junction. We demonstrated the formation of highlytransparent interfaces between Nb and In0.75Ga0.25As quantumwells. The temperature and magnetic field dependences of theinduced superconducting gap and subharmonic gap structureswere discussed. The presented platform may be helpful for thedevelopment of integrated quantum circuitry.AcknowledgmentAuthors acknowledge financial support from EPSRC grantnumbers EP/M009505/1 and EP/J017671/1. K. Delfanazari is grate-ful to Dr. H. Asai for helpful discussions. The data presented in thispaper can be accessed at https://doi.org/10.17863/CAM.13774.References[1] A.F. Andreev, Thermal conductivity of the intermediate state ofsuperconductors, Sov. Phys. JETP 19 (1964) 1228.[2] Z. Wan et al., Induced superconductivity in high-mobility two-dimensionalelectron gas in gallium arsenide heterostructures, Nat. Commun. 6 (2015)7426, https://doi.org/10.1038/ncomms8426.[3] M. Kjaergaard et al., Quantized conductance doubling and hard gap in a two-dimensional semiconductor–superconductor heterostructure, Nat. Commun. 7(2016) 12841, https://doi.org/10.1038/ncomms12841.[4] T. Sand-Jespersen, J. Paaske, B.M. Andersen, K. Grove-Rasmussen, H.I.Jørgensen, M. Aagesen, C.B. Sørensen, P.E. Lindelof, K. Flensberg, J. Nygard,Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots, Phys.Rev. Lett. 99 (2007) 126603.[5] J.A.V. Dam, Y.V. Nazarov, E.P.A.M. Bakkers, S.D. Franceschi, L.P. Kouwenhoven,Supercurrent reversal in quantum dots, Nature 442 (2006) 667–670.[6] F. Giazotto, P. Spathis, S. Roddaro, S. Biswas, F. Taddei, M. Governale, L. Sorba, AJosephson quantum electron pump, Nat. Phys. 7 (2011) 857–861.[7] V. Mourik et al., Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336 (2012) 1003–1007.[8] L.P. Rokhinson, X. Liu, J.K. Furdyna, The fractional a.c. Josephson effect in asemiconductor-superconductor nanowire as a signature of Majorana particles,Nat. Phys. 8 (2012) 795–799.[9] M.T. Deng et al., Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354 (2016) 1557–1562.[10] A.Yu. Kitaev, Fault-tolerant quantum computation by anyons, Ann Phys 303(2003) 2–30.[11] K. Delfanazari, R.K. Puddy, P. Ma, T. Yi, M. Cao, Y. Gul, I. Farrer, D.A. Ritchie, H.J.Joyce, M.J. Kelly, C.G. Mith, On chip Andreev devices: hard gap and quantumtransport in ballistic Nb-In0.75Ga0.25As quantum well-Nb Josephson junctions,Adv. Mater. 29 (2017) 1701836.[12] C. Chen, I. Farrer, S.N. Holmes, F. Sfigakis, M.P. Fletcher, H.E. Beere, D.A. Ritchie,Growth variations and scattering mechanisms in metamorphic In0.75Ga0.25As/In0.75Al0.25As quantum wells grown by molecular beam epitaxy, J. Cryst.Growth 425 (2015) 70–75.[13] G.E. Blonder, M. Tinkham, T.M. Klapwijk, Transition from metallic to tunnelingregimes in superconducting microconstrictions: excess current, chargeimbalance, and supercurrent conversion, Phys. Rev. B 25 (1982) 4515.[14] K. Flensberg, J.B. Hansen, M. Octavio, Subharmonic energy-gap structure insuperconducting weak links, Phys. Rev. B 38 (1988) 8707.[15] H.Y. Günel, N. Borgwardt, I.E. Batov, H. Hardtdegen, K. Sladek, G. Panaitov, D.Grützmacher, Th. Schäpers, Crossover from Josephson effect to single interfaceAndreev reflection in asymmetric superconductor/nanowire junctions, NanoLett. 14 (9) (2014) 4977–4981.[16] Y. Takagaki, Transport properties of semiconductor-superconductor junctionsin quantizing magnetic fields, Phy. Rev. B 57 (1998) 4009.[17] Y. Asano, Magnetoconductance oscillations in ballistic semiconductor-superconductor junctions, Phys. Rev. B 61 (2000) 1732.[18] A.V. Herzog, P. Xiong, R.C. Dynes, Magnetoresistance oscillations in granular Snwires near the superconductor-insulator transition, Phys. Rev. B 58 (1998) 21.[19] Jian Wang et al., Semiconductor-superconductor transition andmagnetoresistance terraces in an ultrathin superconducting Pb nanobridge, J.Vac. Sci. Technol. B 28 (2010), https://doi.org/10.1116/1.3437016.[20] J. Wang, C. Shi, M. Tian, Q. Zhang, N. Kumar, J. Jain, T. Mallouk, M.H.W. Chan,Proximity-induced superconductivity in nanowires: minigap state anddifferential magnetoresistance oscillations, Phys. Rev. Lett. 102 (2009) 247003.

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Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxxContents lists available at ScienceDirectJournal of Magnetism and Magnetic Materialsjournal homepage: www.elsevier .com/locate / jmmmResearch articlesProximity induced superconductivity in indium gallium arsenidequantum wellshttps://doi.org/10.1016/j.jmmm.2017.10.0570304-8853/ 2017 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).⇑ Corresponding author at: Electrical Engineering Division, University ofCambridge, Cambridge CB3 0FA, UK.E-mail address: kd398@cam.ac.uk (K. Delfanazari).Please cite this article in press as: K. Delfanazari et al., Proximity induced superconductivity in indium gallium arsenide quantum wells, Journal onetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.10.057K. Delfanazari a,b,⇑, R.K. Puddy b, P. Ma b, T. Yi b, M. Cao b, Y. Gul c, I. Farrer b,d, D.A. Ritchie b, H.J. Joyce a,M.J. Kelly a,b, C.G. Smith baCentre for Advanced Photonics and Electronics (CAPE), Electrical Engineering Division, University of Cambridge, Cambridge CB3 0FA, UKbDepartment of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UKcDepartment of Electronic and Electrical Engineering, University College London, London WC1E 7JE, UKdDepartment of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UKa r t i c l e i n f o a b s t r a c tArticle history:Received 10 July 2017Received in revised form 10 October 2017Accepted 14 October 2017Available online xxxxWe report on the experimental observation of the proximity induced superconductivity in an indium gal-lium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting elec-trodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantumwell-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conduc-tance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expressionVSD = 2D/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B whichdecreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductancemaxima close to B = 0 T are observed. Our results help to pave the way to the development of integratedcoherent quantum circuitry. 2017 The Authors. Published by Elsevier B.V. This is an open access articleunder the CCBY license (http://creativecommons.org/licenses/by/4.0/).1. IntroductionThe proximity effect in hybrid superconductor-semiconductor(S-Sm) structures, e.g. superconducting correlations and supercur-rent transport in a semiconductor connected to a superconductormediated by phase coherent Andreev reflections [1–3], providesthe possibility to study some fascinating fundamental physics suchas Kondo-enhanced Andreev tunnelling [4], supercurrent reversalin quantum dots [5], Josephson quantum electron pumps [6]. Therehas been renewed interests in such systems after the observationof Majorana fermions states at the S-Sm interfaces [7–9]. This isbecause Majorana Zero modes have potential to support topologi-cally protected quantum computing [10]. Yet, the fundamentaltechnological problem is to fabricate a highly transparent contactbetween a superconductor with a high Fermi energy Ef and a semi-conducting material with a low Ef.In this regard, here we present our experimental results onproximity induced superconductivity in a high-mobility two-dimensional electron gas (2DEG) in an indium gallium arsenide(In0.75Ga0.25As) heterostructure. The symmetric and planarNb-2DEG-Nb Josephson junction was fabricated on an InGaAs chipin which each junction consists of two identical Nb superconduct-ing electrodes. The junction was measured by using a lock-inmeasurement technique in a dilution fridge with a basetemperature of 40 mK.Andreev reflections and bound states due to the electron andhole like quasiparticle correlations at the Nb-In0.75Ga0.25As quan-tum well interfaces lead to the observation of a U-shape dip atlow-bias voltage of the differential resistance dV/dI (VSD) plot, aswell as the subharmonic energy gap structures (SGS) at V = 2D/newhere the D is Nb superconducting gap. Both the induced gapand SGS features suppress significantly as temperature T and mag-netic field B are applied to the system – due to the T and B depen-dences of DNb – leading to a shift of the SGS toward zero bias [11].Sweeping dI/dV vs. B, results in the observation of a hysteresis for0.25  B (T)  0.25 and a shift in the differential conductancemaximum close to B = 0 T.2. Materials and methodsThe In0.75GaAs/In0.75AlAs/GaAs quantum well were grown bymolecular beam epitaxy (MBE) [11,12]. Eight identical and sym-metric Josephson junctions (results for one junction is discussedhere) were patterned and fabricated on a single chip. The 30 nmthick 2DEG with density ns = 2.24  1011 (cm2) and mobilityf Mag-2 K. Delfanazari et al. / Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxxle=2.5  105 (cm2/Vs) was formed 120 nm below the wafer’ssurface.Niobium (Nb) superconducting contacts were made by standardphotolithography technique. First, we created a 120–140 nm deeptrench by wet etching and then a 130 nm of Nb was deposited byDC magnetron sputtering in an Ar plasma. The 130 nm thickness ofNb is about three times larger than the London penetration depthof 40 nm.The junction has a width w = 4 lm and a length L = 850 nm inthe shortest path between the two Nb electrodes (see inset inFig. 1). The ohmic contacts were made of AuGeNi and placed100 lm away from the junctions to prevent the influence of thenormal electrons on Nb-quantum well interfaces. The quantumtransport measurements were performed using a standardlock-in technique by superimposing a small ac signal at a fre-quency f = 70 Hz, and amplitude of 5 lV to the junction dc biasvoltage and the measurements were taken in a dilution fridge atT = 50 mK and up to 800 mK.3. ResultsThe false color Scanning Electron Micrograph (SEM) image ofthe planar Nb-In0.75Ga0.25As-Nb Josephson junction is shown inthe inset of Fig. 1. The device is in the ballistic regime as thedistance between two Nb electrodes L = 850 nm is an order ofmagnitude shorter than the corresponding elastic mean free pathof ‘e = e1⁄lep2pns 2 lm [11].The temperature dependence of the induced superconductivityis shown in Fig. 1 where the differential resistance (dV/dI) versusbias voltage (VSD) graphs at temperatures between 50 and 800mK are plotted. A pronounced supercurrent of up to 0.2 lA wasobserved at zero magnetic field B and at temperature T = 50 mK.Because of the electron- and hole-like quasiparticles correlations(Andreev reflections) below the junction’s Tc and for voltage biaseswithin the superconducting gap, the induced gap and subharmonicenergy gap structures (SGS) are observed.Fig. 1. The superconductor-semiconductor-superconductor Josephson junction: The diff800 mK. Inset: the false color scanning electron micrograph (SEM) image showing a topcontacts are Niobium (Nb) as shown in dark-gold color in the figure. The gap size betwepath. (For interpretation of the references to color in this figure legend, the reader is rePlease cite this article in press as: K. Delfanazari et al., Proximity induced supenetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.1The ratio of L/nN, where nN is the Bardeen-Cooper-Schrieffer(BCS) coherence length [13–15] have influence on the shape ofthe gap and SGS. The SGS consists of a set of pronounced conduc-tance maxima at V = 2D/ne where the D is Nb superconductinggap, and n is an integer number. In the case of the present junction,the proximity effect induces a minigap into the 2DEG withDind = 1.76 kBTc  100 leV. This suggests that our junction with alength L = 850 nm and nN = hmFN/pDind = 2 lm is in the shortchannel regime (L/nN  1). For this junction, the dimensionlessinterface barrier strength Z < 0.2 and therefore an averagetransmissivity T = 1/(1 + Z2) > 0.96 were estimated [11]. The flatdV/dI (VSD) observed within the superconducting gap is consistentwith BTK model [13] (see Ref. [11] for more details).The magnetic field dependence of the induced superconductiv-ity is shown in Fig. 2 where the plot of dV/dI as a function of appliedvoltage VSD at B = 1 mT is shown in the inset. Here, the SGS corre-sponding to 2D/3e (blue), 2D/4e (green), and 2D/6e (red) areshown by arrows. We could not observe the SGS correspondingto 2D/5e. This may be due to the geometry of our junction (seethe inset of Fig. 1). Here, the 2DEG and Nb both extend beyondthe narrow area L  w where induced superconductivity isexpected. Dephasing from the 2DEG regions either side of the junc-tion (which are in normal state) may influence the SGS. The corre-sponding voltage points of the observed SGS are plotted as afunction of B in Fig. 2. It is found that the SGS are strongly B depen-dent, with the position of the peaks bending toward zero voltage asB is increased and being totally washed out at 0.2 T.The dI/dV versus B shows a maximum at zero B which decreasesby increasing B up to 0.25 T (see Fig. 3). Above this point it reachesa constant value indicating that the junction turns into the normalstate. When decreasing B to below ±0.25 T, vortex pinning in theNb electrodes causes a hysteresis in dI/dV (B) plot. The dI/dV curvein Fig. 3 shows a symmetric shift of conductance close to zero Bfield for both positive and negative fields.Here, the applied B field and the vortex penetrating the elec-trodes are parallel. However, when the sign of the applied B fielderential resistance (dV/dI) versus bias voltage VSD at temperatures between 50 andview of a symmetric Nb-In0.75Ga0.25As-Nb Josephson junction. The superconductingen two Nb electrodes has a length L = 850 nm and a width w = 4 lm at the shortestferred to the web version of this article.)rconductivity in indium gallium arsenide quantum wells, Journal of Mag-0.0570.00 0.02 0.04 0.06 0.08 0.100.10.20.30.40.50.60.7VSD (mV)B (T) 2 e 2 e 2 e-0.8 -0.4 0.0 0.40.00.10.20.3dV/dI (k)VSD (mV)T= 50 mK, B= 1 mTFig. 2. Magnetic field dependence of the induced superconductivity in a ballisticJosephson junction: The blue, green and red circles (see their corresponding arrowsin inset) indicate the magnetic field evolution of the induced- and subharmonic-gapstructures. Inset is the dV/dI (V) measured at B = 1 mT and T = 50 mK. Arrowscorrespond to SGS: 2D/3e (blue), 2D/4e (green), and 2D/6e (red). (For interpretationof the references to color in this figure legend, the reader is referred to the webversion of this article.)-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.43.63.84.04.24.44.6T= 50 mK dI/dV (mS)B (T)Fig. 3. Magnetoconductance oscillations and hysteresis on the differentialconductance of the Nb-In0.75Ga0.25As-Nb Josephson junction: Differentialconductance (dI/dV) vs. applied magnetic field B perpendicular to the junction’splane at temperature 50 mK. Arrows indicate the B sweep directions.K. Delfanazari et al. / Journal of Magnetism and Magnetic Materials xxx (2017) xxx–xxx 3changes (e.g. B < 0 to B > 0), B and the pinned vortex becomes anti-parallel [16,17]. The pinned vortex may cause a phase change atthe interface, and causes the appearance of the dI/dV oscillationsand zero B shift.Please cite this article in press as: K. Delfanazari et al., Proximity induced supenetism and Magnetic Materials (2017), https://doi.org/10.1016/j.jmmm.2017.1Such oscillations have also been observed in different systemssuch as granular Sn wires [18], superconducting Pb nanobridges[19], and gold nanowires [20].4. ConclusionWe have experimentally studied the proximity inducedsuperconductivity in a hybrid Nb-In0.75Ga0.25As-Nb ballisticJosephson junction. We demonstrated the formation of highlytransparent interfaces between Nb and In0.75Ga0.25As quantumwells. The temperature and magnetic field dependences of theinduced superconducting gap and subharmonic gap structureswere discussed. The presented platform may be helpful for thedevelopment of integrated quantum circuitry.AcknowledgmentAuthors acknowledge financial support from EPSRC grantnumbers EP/M009505/1 and EP/J017671/1. K. Delfanazari is grate-ful to Dr. H. Asai for helpful discussions. The data presented in thispaper can be accessed at https://doi.org/10.17863/CAM.13774.References[1] A.F. Andreev, Thermal conductivity of the intermediate state ofsuperconductors, Sov. Phys. JETP 19 (1964) 1228.[2] Z. Wan et al., Induced superconductivity in high-mobility two-dimensionalelectron gas in gallium arsenide heterostructures, Nat. Commun. 6 (2015)7426, https://doi.org/10.1038/ncomms8426.[3] M. Kjaergaard et al., Quantized conductance doubling and hard gap in a two-dimensional semiconductor–superconductor heterostructure, Nat. Commun. 7(2016) 12841, https://doi.org/10.1038/ncomms12841.[4] T. Sand-Jespersen, J. Paaske, B.M. Andersen, K. Grove-Rasmussen, H.I.Jørgensen, M. Aagesen, C.B. Sørensen, P.E. Lindelof, K. Flensberg, J. Nygard,Kondo-enhanced Andreev tunneling in InAs nanowire quantum dots, Phys.Rev. Lett. 99 (2007) 126603.[5] J.A.V. Dam, Y.V. Nazarov, E.P.A.M. Bakkers, S.D. Franceschi, L.P. Kouwenhoven,Supercurrent reversal in quantum dots, Nature 442 (2006) 667–670.[6] F. Giazotto, P. Spathis, S. Roddaro, S. Biswas, F. Taddei, M. Governale, L. Sorba, AJosephson quantum electron pump, Nat. Phys. 7 (2011) 857–861.[7] V. Mourik et al., Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336 (2012) 1003–1007.[8] L.P. Rokhinson, X. Liu, J.K. Furdyna, The fractional a.c. Josephson effect in asemiconductor-superconductor nanowire as a signature of Majorana particles,Nat. Phys. 8 (2012) 795–799.[9] M.T. Deng et al., Majorana bound state in a coupled quantum-dot hybrid-nanowire system, Science 354 (2016) 1557–1562.[10] A.Yu. Kitaev, Fault-tolerant quantum computation by anyons, Ann Phys 303(2003) 2–30.[11] K. Delfanazari, R.K. Puddy, P. Ma, T. Yi, M. Cao, Y. Gul, I. Farrer, D.A. Ritchie, H.J.Joyce, M.J. Kelly, C.G. Mith, On chip Andreev devices: hard gap and quantumtransport in ballistic Nb-In0.75Ga0.25As quantum well-Nb Josephson junctions,Adv. Mater. 29 (2017) 1701836.[12] C. Chen, I. Farrer, S.N. Holmes, F. Sfigakis, M.P. Fletcher, H.E. Beere, D.A. Ritchie,Growth variations and scattering mechanisms in metamorphic In0.75Ga0.25As/In0.75Al0.25As quantum wells grown by molecular beam epitaxy, J. Cryst.Growth 425 (2015) 70–75.[13] G.E. Blonder, M. Tinkham, T.M. Klapwijk, Transition from metallic to tunnelingregimes in superconducting microconstrictions: excess current, chargeimbalance, and supercurrent conversion, Phys. Rev. B 25 (1982) 4515.[14] K. Flensberg, J.B. Hansen, M. Octavio, Subharmonic energy-gap structure insuperconducting weak links, Phys. Rev. B 38 (1988) 8707.[15] H.Y. Günel, N. Borgwardt, I.E. Batov, H. Hardtdegen, K. Sladek, G. Panaitov, D.Grützmacher, Th. Schäpers, Crossover from Josephson effect to single interfaceAndreev reflection in asymmetric superconductor/nanowire junctions, NanoLett. 14 (9) (2014) 4977–4981.[16] Y. Takagaki, Transport properties of semiconductor-superconductor junctionsin quantizing magnetic fields, Phy. Rev. B 57 (1998) 4009.[17] Y. Asano, Magnetoconductance oscillations in ballistic semiconductor-superconductor junctions, Phys. Rev. B 61 (2000) 1732.[18] A.V. Herzog, P. Xiong, R.C. Dynes, Magnetoresistance oscillations in granular Snwires near the superconductor-insulator transition, Phys. Rev. B 58 (1998) 21.[19] Jian Wang et al., Semiconductor-superconductor transition andmagnetoresistance terraces in an ultrathin superconducting Pb nanobridge, J.Vac. Sci. Technol. B 28 (2010), https://doi.org/10.1116/1.3437016.[20] J. Wang, C. Shi, M. Tian, Q. Zhang, N. Kumar, J. Jain, T. Mallouk, M.H.W. Chan,Proximity-induced superconductivity in nanowires: minigap state anddifferential magnetoresistance oscillations, Phys. Rev. Lett. 102 (2009) 247003.rconductivity in indium gallium arsenide quantum wells, Journal of Mag-0.057

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