Charge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices
A.O. Denisov, A.V. Bubis, S.U. Piatrusha, N.A. Titova, A.G. Nasibulin, J. Becker, J. Treu, D. Ruhstorfer, G. Koblmueller, E.S. Tikhonov, V.S. Khrapai
CCharge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices
A.O. Denisov,
1, 2
A.V. Bubis,
3, 1
S.U. Piatrusha, N.A. Titova, A.G. Nasibulin,
3, 5
J. Becker, J. Treu, D. Ruhstorfer, G. Koblm¨uller, E.S. Tikhonov, and V.S. Khrapai Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Russian Federation Department of Physics, Princeton University, Princeton, New Jersey 08544, USA Skolkovo Institute of Science and Technology, Nobel street 3, 121205 Moscow, Russian Federation Moscow State University of Education, 29 Malaya Pirogovskaya St, Moscow, 119435, Russia Aalto University, P. O. Box 16100, 00076 Aalto, Finland Walter Schottky Institut, Physik Department, and Center for Nanotechnology and Nanomaterials,Technische Universit¨at M¨unchen, Am Coulombwall 4, Garching 85748, Germany
Nonlocal quasiparticle transport in normal-superconductor-normal (NSN) hybrid structuresprobes sub-gap states in the proximity region and is especially attractive in the context of Ma-jorana research. Conductance measurement provides only partial information about nonlocal re-sponse composed from both electron-like and hole-like quasiparticle excitations. In this work, weshow how a nonlocal shot noise measurement delivers a missing puzzle piece in NSN InAs nanowire-based devices. We demonstrate that in a trivial superconducting phase quasiparticle response ispractically charge-neutral, dominated by the heat transport component with a thermal conductancebeing on the order of conductance quantum. This is qualitatively explained by numerous Andreevreflections of a diffusing quasiparticle, that makes its charge completely uncertain. Consistently,strong fluctuations and sign reversal are observed in the sub-gap nonlocal conductance, includingoccasional Andreev rectification signals. Our results prove conductance and noise as complementarymeasurements to characterize quasiparticle transport in superconducting proximity devices.
Nonlocal conductance measurements [1] insemiconductor-superconductor proximity structuresgain renewed interest in the context of Majorana re-search [2–8]. The key underlying idea is that the nonlocalsignals can probe global sub-gap states characteristicof a true topological phase transition [9–11]. This is incontrast to a standard two-terminal conductance [12–14]sensitive to the states near the point where the currentinflows in the proximity region. Recent experimentsin three-terminal NSN nanowire-based (NW-based)hybrid devices confirm conceptual power of the nonlocalconductance approach [15, 16].Conductance measurement provides only partial infor-mation about quasiparticle non-equilibrium in proximitystructures. A sub-gap quasiparticle entering the proxim-ity region carries the electric charge, q < q > ε = | E | >
0, where E is the kinetic energyrelative to the chemical potential of the superconduc-tor. On its way, apart from possible normal scattering, aquasiparticle experiences a few Andreev reflections (ARs)from the superconducting lead [17, 18], each time invert-ing the q but preserving the ε . Thereby the AR mediatesa coupling of the charge and heat (energy) transport com-ponents that is unique to proximity structures and doesnot occur in bulk superconductors [19, 20]. Thus, a fullcharacterization of the non-equilibrium can be achievedby measurement of both the electric and heat nonlocalconductances.In this article, we investigate the nonlocal response inNSN InAs NW-based devices. We show that a quasipar-ticle non-equilibrium can be understood if the nonlocalconductance is accompanied by a shot noise measure-ment substituting the heat conductance measurement, that allows to separate the contributions of transmissionprocesses involving even and odd number of the ARs. Ex-periments performed in a trivial superconducting phasedemonstrate that quasiparticle transport is practicallycharge-neutral, so that the heat transport componentdominates the nonlocal response in our devices. Our re-sults prove shot noise as a valuable, complementary toconductance, tool to probe the sub-gap states in proxim-ity structures.We start the discussion from the energy diagram of theNSN NW-based hybrid structure in a nonlocal experi-ment sketched in Fig. 1a. Consider the case of zero tem-perature T = 0 and negative bias voltage V < . The superconductor andthe right normal terminal N are grounded, position oftheir chemical potential shown by the dashed line. Trans-mitted quasiparticles are distinguished by their energyrelative to this chemical potential, ε > − ε for holes. Inside the NW quasiparticles experi-ence ARs from the S-lead and elastic normal scatteringfrom disorder and possibly from the S/NW interface, in-elastic scattering is absent [21]. The charge current I and the heat current J in the right lead read [22, 23]: I = − e h V Σ T − ; J = e h V Σ T + ; T ± ≡ T ± A (1)where the positive direction for the electric current isfrom the lead into the scattering region and oppositefor the heat current. T and A are the probabilitiesof transmission, respectively, preserving and changinga quasiparticle type, sometimes also called normal andcrossed-Andreev transmission [6] and the sum over theeigenchannels is performed. Generally, the two transmis-sion processes involve both the normal and Andreev scat- a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n N S N eV T A N N S NW NW
FIG. 1. (a) Energy diagram of the NSN NW-based device.In this illustration, the left normal terminal N is biased withvoltage V <
0, while the central S-terminal and the right N terminal are grounded, their chemical potential shown by thedashed line. Depending on the number of Andreev reflections,the electron incident from N can be transmitted towards N as an electron ( e ) or hole ( h ) with probability T or A cor-respondingly. (b) Scanning electron microscope image of theNSN-II device (false color) and the shot-noise measurementscheme used in actual experiment. Voltages V and V thatbuild up in response to the current bias I are measured in aquasi-four-terminal configuration. tering and are distinguished by the parity of the numberof ARs involved. Processes with an even and odd numberof ARs contribute, respectively, to T and A . Eqs. (1)imply that a simultaneous measurement of the chargeand heat response permits an independent characteriza-tion of T and A . Measurement of the heat transportis not an easy task [24–27] and we choose a different pathin present experiment. We perform a shot noise measure-ment in a nonlocal configuration [21, 28, 29], based on thefindings of Ref. [11] briefly mentioned below.The average charge Q (in units of e ) transmitted inone eigenchannel in an individual scattering event equals h Q i = T − . Its fluctuation is h ( δQ ) i = h Q i − h Q i ,where h Q i = T + . Thus, in spirit of Ref. [30], we obtainfor the spectral density of the current noise in the rightlead: S = 2 e h | V | Σ (cid:0) T + − T − (cid:1) , (2)that contains T + and can substitute J in a nonlocal mea-surement. In the limit of suppressed AR A → F nl ≡ S / e | I | is bounded by unity F nl = 1 − T ≤
1. In the oppositelimit of T = A the shot noise and the heat current re-main finite, S ∝ J , whereas I = 0. Here, the nonlocal quasiparticle response is charge-neutral and F nl → ∞ .Eqs. (1-2) illustrate our main idea that nonlocal con-ductance G ≡ ∂I /∂V and shot noise S can serveas two complementary electrical measurements requiredto fully characterize quasiparticle transport. We applythis paradigm to explore the nonlocal response in InAsNW-based NSN devices. The outline of the experiment isdepicted in Fig. 1b. A semiconducting InAs nanowire isequipped with an S terminal, made of Al, in the mid-dle and two N terminals, made of Ti/Au bilayer, onthe sides. In essence, this device represents two back-to-back N-NW-S junctions sharing the same S terminal.We study two similar devices NSN-I and NSN-II whichhave the width of S terminal equal to w = 200 nmand w = 300 nm, respectively. Note the absence ofthe quantum dots [32–34] or tunnel barriers [35] adja-cent to the S-terminal, that enables better coupling ofthe sub-gap states to the normal conducting regions. Inaddition, for all contacts in-situ Ar milling was appliedbefore the evaporation in order to improve the semicon-ductor/metal interface quality. Throughout the exper-iments the S terminal is grounded, terminal N is cur-rent biased. The terminal N is DC floating through-out the experiment, which allows to access the differen-tial resistances R ij ≡ ∂V i /∂I j in a quasi-four-terminalconfiguration excluding the wiring contributions. Thedifferential conductances are obtained by inverting themeasured resistance matrix. In present experiment thenon-diagonal elements are much smaller than the diago-nal ones, so that approximate relations G ii ≈ R − ii and G ij ≈ − R ij ( R R ) − hold within a few percent accu-racy. Experiments are performed at bath temperaturesof T = 120-150 mK unless stated otherwise.Back-gate voltage ( V g ) dependencies of the linear re-sponse diagonal conductances are shown in Fig. 2a. G ii fall in the range of a few conductance quanta and ex-hibit a usual sublinear increase with V g accompaniedby universal mesoscopic fluctuations. Standard proce-dure [36] gives a field-effect mobility of ∼
300 cm / Vsunderestimated because of the field screening by con-tacts. Impact of a superconducting proximity effect on G ii is similar for both devices and all V g used, typicaldata shown in Fig. 2b. In zero magnetic field B a mod-erate zero-bias minimum is seen surrounded by maximaat V = ± ∆ /e , where ∆ = 180 µ eV is the Al supercon-ducting gap determined independently from the criticaltemperature, see Supplemental Material. In a perpen-dicular field B = 50 mT high enough to suppress the su-perconductivity the minimum weakens and the maximadisappear, whereas the above-gap conductance remainsunchanged. Overall, this is a standard for coherent dif-fusive NS junctions re-entrant behaviour [37, 38], with aminor effect of the interface reflectivity and/or Coulombeffects [39].The non-diagonal conductance probes quasiparticletransport via InAs-NW section underneath the S-terminal [4, 6, 7, 15, 16] and its bias dependence turnsout much less universal. In Figs. 2c and 2d we plot G ( V ) G ( V ) V g = 10 V . .
50 mT0 mT50 mT0 mT V g = 40 V32 V26 V22 V19 V17 V V g = 15 V10 V5 V0 V-5 V-10 V FIG. 2. (a) Zero-bias diagonal conductances versus V g forboth devices in zero magnetic field. (b) Diagonal differentialconductance as a function of bias voltage in zero and highenough to suppress superconductivity magnetic fields. Dottedlines show position of the superconducting gap. (c, d) B =0 nonlocal differential conductance as a function of V forseveral V g values. The curves are vertically offset for claritywith zero level shown by the dashed lines. Bars indicate theordinate scale common for all V g . − G , having in mind that the negative sign correspondsto normal transmission. At sub-gap biases very differ-ent behaviour of − G can be observed depending on V g , from almost symmetric with zero-bias maximum,see V g = 40 V data in device NSN-I, to strongly anti-symmetric with sign inversion, see V g ≤ G is neg-ative, featureless and consistent with a current transferlength of ∼
100 nm determined by a residual interface re-flectivity, see the Supplemental Material. Figs. 2c and 2dshow that at sub-gap biases in the superconducting state | G | strongly increases compared to its above-gap val-ues, which is expected since quasiparticles are forbiddento enter the superconductor. The G is much smallerthan e /h and occasionally changes sign, implying that | Σ T − | (cid:28) inresponse to the current between the biased terminal N and the grounded S-terminal. Plotted as a function of V F n l = F n l = 100 F n l = F n l = FIG. 3. (a, b) Measured current noise spectral density in theright lead as a function of bias voltage on the left one. Dottedlines show positions of the superconducting gap. (c, d) Mea-sured current noise spectral density in the right lead as a func-tion of the nonlocal current I . Symbols have the same colouras the lines in panels (a, b) for the respective V g . Guide lineswith Fano-factor F nl = 1 and F nl (cid:29) all the data in both devices feature the same qualitativebehaviour shown in Figs. 3a and 3b. The shot noise spec-tral density S starts from the Johnson-Nyquist equilib-rium value 4 k B T G at zero bias [23] and increases almostsymmetrically and linear with V showing a pronounceddownward kink at the gap edges | V | = ∆ /e marked byvertical dashed lines. Above the gap the slope dropsdown consistent with the fact that transmission probabil-ity diminishes as soon as the quasiparticles can sink in thesuperconductor. Nonlocal noise is more informative thanthe usual two-terminal noise in NS structures [33, 40–42],which exhibits only a minor reduction in the presence ofsub-gap density of states [43]. According to the Eq. (2),neglecting the contributions of T − the slope dS /dV isdetermined by T + and allows to evaluate the linear re-sponse thermal conductance G th ≡ G Σ T + . We have0 . < G th /G < .
6, where G = L T e /h is the ther-mal conductance quantum and L is the Lorenz number.This estimate of G th is legitimate provided |T − | (cid:28)
1, i.e.if ballistic transmission is suppressed by disorder scat-tering [18, 44], as in our devices, or by structure geome-try [45].Next we analyse the same data in terms of the non-local Fano factor where the nonlocal current is obtained T = 0.5 K F n l = F n l = (a) (b) FIG. 4. (a) Evolution of the nonlocal noise spectral density S ( V ) in magnetic field and T = 0 . S ( I ) in magnetic field. Sym-bols have the same colour as the lines in panel (a) for the re-spective B . Guide lines with Fano-factor F nl = 1 and F nl (cid:29) via I = − G V . Here we use that the electric currentcaused by non-equilibrium quasiparticles is compensatedby an extra current flowing in the opposite direction, sothat the net current is zero in the floating configuration.This extra current flows near the Fermi level and is noise-less, since the junction N -NW-S remains essentially un-biased throughout the experiment, | V | < k B T /e , see theSupplemental Material. Figs. 3c and 3d plot S vs I for both devices. Two main features are evident. First,the symmetry inherent to S vs V data is in many caseslost here, since I is not an anti-symmetric function of V . Second, the noise slope corresponds to nonlocal Fanofactor values in the range 30 . F nl . F nl ruleout a heretical interpretation that normal quasiparticlescattering from a poor quality Al/InAs interface is themain source of nonlocal signals, that would correspondto F nl ≤
1, see the dashed guide line.It is convenient to define the average charge of trans-mitted quasiparticles as the ratio between the transmit-ted charge and total number of transmitted quasiparticles h q T i = Σ T − / Σ T + . The value of h q T i = 1 corresponds tothe case when quasiparticles conserve their charge duringthe transmission process, whereas in the case h q T i = − |h q T i| < /F nl , i.e. the observation of a giant Fano fac-tor implies nearly charge-neutral nonlocal quasiparticletransport with |h q T i| (cid:28)
1. This can be easily understoodin case of a metallic diffusive NW covered by a supercon-ductor with a transparent interface. Traversing the prox-imity region a quasiparticle experiences a number of ARsgiven on the average by h N AR i = ( w/d ) , where w is thewidth of the S-terminal and d ≈
100 nm is the diameterof the NW. Given the randomness of diffusion the mean-square fluctuation is p h δN i = p h N AR i ≥
2, so thatis the parity of N AR and thus the sign of the transmit- ted charge are completely uncertain. More rigorously, forthe device NSN-II we find |h q T i| < .
01, meaning that ittakes at least a hundred quasiparticles to transmit a unitof elementary charge.Our observations in a trivial superconducting phasehave common features with the predicted nonlocal re-sponse at the topological phase transition in MajoranaNWs. Here, even in presence of a moderate disorder, afinite transmission occurs in just one eigenchannel with T = A = 1 / G th = G / G th in the present experiment demonstratesa monotonic dependence on V g . The nonlocal charge re-sponse at the topological transition restores at a finitebias, G ∝ V , owing to the energy-dependence of thetransmission probabilities, known as the Andreev rectifi-cation [4]. Similar transport features are occasionally ob-servable in Figs. 2c and 2d, originating from mesoscopicfluctuations of G around zero. This suggests that, un-like the peak in G th , Andreev rectification is not a uniquesignature of the topological transition, see also Ref. [16].As a final step, we demonstrate a crossover from nearlycharge-neutral to normal nonlocal quasiparticle transportin a magnetic field in the device NSN-I. Fig. 4a showsthe evolution of S vs V , taken at a bath temperature of0.5 K. The shot noise gradually diminishes at increasing B -field and the kink at the gap edge disappears concur-rently with a transition of the Al to the normal state,see the B = 50 mT trace. Plotted as a function of I in Fig. 4b this data reveals a transition from the giantnoise at sub-gap energies in the B = 0 superconduct-ing state to the Poissonian noise in the normal state, seethe dashed guide line. In B = 0 we find F nl ∼
10, con-siderably diminished compared to Fig. 3c as a result ofthermal smearing. The Poissonian noise F nl ≈ A = 0 and T (cid:28)
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Nonlocal I-Vs and differential conductance.
12 2 . V g = 35 V NSN-I T = 0.5 K NSN-I NSN-II V g =
40 V32 V26 V22 V19 V17 V V g =
15 V10 V5 V0 V-5 V-10 V T = 0.15 K T = 0.15 K Supplemental Material Fig. 1. (a, b)Measured nonlocal I-V characteristics versus V g for both devices in zero magnetic field.Different curves are vertically spaced with zero level shown as the dashed lines. (c) Non-diagonal conductance is plotted as afunction of the bias voltage at different magnetic fields. Dotted lines show position of the superconducting gap. Measured V ( I ) curves in the nonlocal configurations show similar non-universal behavior for both devices asevident from Fig. 2a, b. First, the nonlocal voltage signal is small | V | < k B T /e ≈ µV and we can suppose thejunction N -NW-S to be essentially unbiased. Second, some of the I-V curves are highly non-anti-symmetric as aresults we observe finite odd contribution to the non-diagonal conductance G as shown in Fig. 2c. At increasingmagnetic field all the sub-gap features are smeared and eventually remain featureless in sufficiently high B = 55 mT,where the superconductivity of Al is already suppressed. Device fabrication
InAs nanowires grown by molecular beam epitaxy on Si substrate [S1] are ultrasonicated in isopropyl alcohol.Nanowires are drop casted on Si/SiO2 (300 nm) substrates [S2] with preliminary defined alignment marks. Forsuperconducting contacts conventional electron beam lithography (EBL) followed by e-beam deposition of Al (150 nm)is utilized. To obtain the ohmic contacts, in-situ Ar ion milling is performed before Al deposition in a chamber with abase pressure below 10 − mbar. Normal metal contacts are fabricated in two different ways (different device batches):magnetron sputtering or e-beam deposition. For sputtering (NS and NSN - I devices) in-situ Ar plasma etching isfollowed by sputtering of Ti/Au (5 nm/200 nm). Normal metal contacts Ti/Au (5 nm/150 nm) in device NSN - II aredeposited in the same way as superconducting ones. a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n Current transfer length estimation
Supplemental Material Fig. 2.
Effective resistance model for nanowire/superconductor interface.
To estimate the characteristic length of charge overflow within grounded S terminal l T we use circuit shown in fig. 2.Here ρ wire and g int are resistance of the nanowire (NW) and conductivity of interface per unit length respectively. Inthe continuous limit we can write current conservation for each point along NW/S interface: V ( x + dx ) − V ( x ) ρ wire dx + V ( x − dx ) − V ( x ) ρ wire dx = V ( x ) dx /g int d V ( x ) dx = V ( x ) l , l T = 1 √ ρ wire g int Boundary conditions including one that normal terminal N2 is floating and no current flow into it. dV ( x ) dx (cid:12)(cid:12)(cid:12)(cid:12) x =0 = − ρ wire I, dV ( x ) dx (cid:12)(cid:12)(cid:12)(cid:12) x = L = 0Solving elementary Neumann problem we can find non-local rsistance r : R = V ( L ) I = l T ρ wire sinh( Ll T )At high biases | V | (cid:29) ∆ /e for two measured devices (NSN-I, NSN-II) we have R ≈ ,
10 Ω and L ≈ ,
300 nmrespectively, thus l T ≈
75 nm.
Critical Temperature of Al contacts T (K) R () Supplemental Material Fig. 3. The resistance of a four-terminal Al strip, deposited via the same process, as the one used inthe fabrication of the samples, featured in the main text.
The temperature dependence of superconducting Al, deposited via the same process as described in ”Device Fabri-cation” was performed separately on the four-terminal Al strips, incorporated in the samples studied in [S3]. Here wepresent raw data (see Fig. 3), which leads to the estimate T c = 1 . ± .
03 K, corresponding to the superconductingenergy gap of ∆ = 183 ± µV in Al leads. [S1] S. Hertenberger, D. Rudolph, M. Bichler, J. J. Finley, G. Abstreiter, and G. Koblm¨uller, Growth kinetics in position-controlled and catalyst-free InAs nanowire arrays on si(111) grown by selective area molecular beam epitaxy, Journal ofApplied Physics , 114316 (2010).[S2] J. Becker, S. Mork¨otter, J. Treu, M. Sonner, M. Speckbacher, M. D¨oblinger, G. Abstreiter, J. J. Finley, and G. Koblm¨uller,Carrier trapping and activation at short-period wurtzite/zinc-blende stacking sequences in polytypic inas nanowires, Phys.Rev. B , 115306 (2018).[S3] A. V. Bubis, A. O. Denisov, S. U. Piatrusha, I. E. Batov, V. S. Khrapai, J. Becker, J. Treu, D. Ruhstorfer, andG. Koblm¨uller, Proximity effect and interface transparency in al/InAs-nanowire/al diffusive junctions, SemiconductorScience and Technology32