Gate-Controlled Supercurrent in Epitaxial Al/InAs Nanowires

Gate-controlled supercurrent (GCS) in superconducting nanobridges has recently attracted attention as a means to create superconducting switches. Despite the clear advantages for applications, the microscopic mechanism of this effect is still under debate. In this work, we realize GCS for the first time in a highly crystalline superconductor epitaxially grown on an InAs nanowire. We show that the supercurrent in the epitaxial Al layer can be switched to the normal state by applying ≃±23 V on a bottom gate insulated from the nanowire by a crystalline hBN layer. Our extensive study of the temperature and magnetic field dependencies suggests that the electric field is unlikely to be the origin of GCS in our device. Though hot electron injection alone cannot explain our experimental findings, a very recent non-equilibrium phonons based picture is compatible with most of our results.


INTRODUCTION
Superconductor circuits have become promising building blocks in various architectures for quantum computing devices [1,2], single photon detectors [3,4], quantum-limited amplifiers (parametric amplifiers) [5], phase-coherent caloritronics [6,7], ultra-sensitive magnetometers [8,9] and fast classical supercomputers [10,11].In the latter, the superconducting electronics are integrated with semiconductor technology.In particular, rapid single flux quantum (RSFQ) devices become more desirable due to their fast switching speed and low power consumption [11].Since RSFQ consists of a superconducting loop with Josephson junctions along with onchip coils, its up-scaling remains a challenge.In order to realize a scalable network, electrical control via gate electrodes would be desirable.
Very recently a striking new effect was observed in metallic nanostructures.In superconductor nanobridges the supercurrent can be controlled by applying a voltage on a closely spaced gate electrode [12][13][14][15][16][17][18][19][20][21][22][23][24].By increasing the gate voltage beyond a certain threshold, the supercurrent is monotonically decreased until switching of the device from the superconducting to normal state.Previous works show GCS in thin metallic nanowires [12,18,22,23], in proximitized normal metal in superconductor-normal-superconductor (SNS) junction [13] and in Dayem nanobridges [15,17,19].In addition to high speed superconductor switches [23], observation of GCS in superconductor nanostructures led to realization of new superconductor nanodevices such as phase shifter [20] and gate-controlled superconductor half-wave nanorectifier [17].On the other hand, the inverse of this effect was observed in type II superconductors, where the supercurrent is enhanced by bipolar increase of the gate voltage [25].Since GCS is bipolar with gate voltage, the origin of the effect being unclear.Some works explained the suppression of supercurrent by electric field induced perturbation of the superconducting state [26][27][28], like the superconductor Swinger effect [29], others attributed the effect to injection of high energy quasiparticles tunneling from the gate electrodes [22][23][24].The injected high energy electrons create a large number of quasiparticles and suppress the superconducting state.Despite the physical origin of the effect is unclear, gate-controlled nanobridges can work at ultra low power and highly switching speed.In addition, their configuration can be easily scaled up which provides a promising building block for superconductor switches in modern architectures of supercomputers and on-chip circuits for quantum computers.
Recently InAs semiconductor nanowires with epitaxial Al superconducting shells [30], have become the primary platform for research on various potential quantum bit devices.Concepts have been developed for topologically protected qubits [31] and even their surface code [32] based on hybrid nanowires and they are also promising for realization of Gatemon or Andreev qubits [33,34].In all these quantum hardwares the gate tunable superconductivity would be highly desirable allowing an additional experimental control knob of the system.However, up to now, all gate tuning experiments were performed on polycrystalline materials and therefore it has not been clear if GCS exists for these highly crystalline materials.In this work, we studied for the first time the superconducting gating effect in single crystalline Al shells grown on InAs nanowires.We will show in the following that the superconducting state can be switched off by application of a gate voltage on an epitaxial Al/InAs nanowire and provide detailed characteristics for the gating behaviour.

EXPERIMENTS A. Device outline
We have used InAs nanowires grown by molecular beam epitaxy (MBE) with a length of 5.5 µm using gold nanoparticles as catalysts.After InAs nanowire growth, Al shell layer of thickness 20 nm was epitaxially grown by deposition within the MBE chamber at low temperature.By rotating the substrate during Al growth, the Al shell layer is grown in all InAs nanowire facets resulting in fully covered nanowires [30].
To investigate the gate-controlled supercurrent in the epitaxial Al layer, nanowire-based device was fabricated as shown in Fig. 1a-c.A metallic gate from Ti/Au (yellow colored) with thicknesses of 7/33 nm was fabricated on an intrinsic Si wafer with a 290 nm thick oxide layer.To insulate the gate from the wire, 20-30 nm thick hBN (pink colored) was stacked on the gate electrode with PDMSbased dry transfer technique.hBN provides an excellent single crystal insulator between gate and wire serving as a tunnel barrier [35][36][37][38].The nanowire (gray) with Al shell (green) was deposited by a micromanipulator on top of the hBN layer.Two pairs of Al contacts (blue colored) have been fabricated on the top of the nanowire with a distance of 1.5 µm to allow four-terminal measurements for the nanowire.More details about fabrication are given in Methods section.
The current-voltage (I-V) characteristics of the nanowire device measured at 40 mK clearly show a well developed zero resistance state (see red curve in Fig. 1d) corresponding to a supercurrent flowing through the Al shell of the wire.Two clear switches to a finite resistance state are observed at I C,NW = 1.94 µA and I C,C = 2.34 µA.Similar multiple transitions were observed in suspended Ti nanowire [18].The nanowire device shows a hysteretic behaviour and switches back at the retrapping current I r = 1.74 µA when the measurements were carried out in the opposite ramping direction.To identify the origin of both I C,NW and I C,C , we have separately measured (I-V) curves for each horizontal pairs of contacts (blue electrodes in Fig. 1a) using 2-probe method.The measurements for one of the pairs with grey curve have switching current value at I C,C value, while the other electrode switches at 7.5 µA (see supporting information).From this, we could attribute I C,NW to the switching current of the nanowire segment while I C,C to the switching current of the small metallic electrode segment (blue) above the nanowire marked by the red rectangle in Fig. 1a.

B. Gate voltage dependence
The dependence of the supercurrent on the gate voltage was investigated by measuring the (I-V) curve of the nanowire device as a function of the bottom gate voltage, V BG (see Fig. 2a).The white regions represent the zero resistance state.By increasing V BG with either negative or positive polarity, both I C,NW and I C,C remains constant until V BG ±12 V, then both are suppressed together up to full suppression at pinch-off gate voltage

V BG0
±23 V where the device is switched to normal state.The fine characteristics of the I-V curves are better visible in Fig. 2b, where the red and gray dashed lines trace the suppression of I C,NW and I C,C with increasing V BG , respectively.We should note that with increasing V BG , the difference between the retrapping current I r and I C,C is decreased and fully vanished at V BG ±22 V.
The leakage current I leak from the gate to the nanowire device was measured within ±V BG0 window by recording voltage across the preresistor on the gate (see Fig. 1a).The leakage current was then corrected by subtracting the leakage between lines of the cryostat (see supporting information) [23].The leakage current shows an exponential increase with V BG for both polarities (see Fig. 2c).

C. Temperature dependence
The critical temperature was determined by measuring the IV characteristics of the device at different elevated temperatures at V BG = 0 (see Fig. where, is the superconducting gap at temperature T [41,42]

D. Magnetic field dependence
The dependence of critical currents with magnetic field was investigated by measuring (I-V) characteristics of the nanowire device as a function of out of plane magnetic field B as shown in Fig. 4a.Both I C,NW and I C,C decreases in magnetic field, as expected.Moreover, it can be also seen that I C,NW and I C,C crosses each other at B = ± 24 mT and their corresponding critical fields are B C,NW = 64 mT and B C,C = 50 mT, respectively.This is clearly seen in Fig. 4b, which shows the magnetic field dependence of critical currents extracted from measurements in Fig. 4a.
Magnetic field dependence of GCS in nanowire device shows a similar dependence as its temperature dependence: that the gate dependence has the same general trend at all magnetic fields up to 46 mT as shown in Fig. 4c in case of I C,C .On the other hand, V BG0 decreases when B values approaches to B C,C .In the same way, I C,NW shows a similar magnetic field dependence (see supporting information).We have also measured both critical currents I C,NW and I C,C as a function of the magnetic field at different gate voltages up to values very close to V BG0 .A significant shift in B C,NW and B C,C to smaller values is observed by increasing the V BG higher than 15 V as illustrated in Fig. 4 d,e, respectively.Similar dependence with B field was observed in Ti-based superconductor nanostructures [12,19].

DISCUSSION
As we mentioned before, the origin of GCS was attributed in the previous studies to two different mechanisms, either to distortion of the superconducting state by induced electric field [12-20, 22, 23, 26-29] or to high energy quasiparticle injection via tunneling [22][23][24].We will compare our experimental findings with these explanations in the following.
GCS was reported in various device geometries of evaporated policrystaline metallic nanobridges from different superconductors [12-20, 22, 23] and explanation was proposed based on electric field induced distortion of the superconducitng wave function which could destroy the BCS state [26][27][28] like e.g. by Swinger effect [29].The observed B field and T dependencies of gating effect shows very similar characteristics to our epitaxial superconductor case.However, there is a finite leakage current of 100 pA at gate voltages where supercurrent gets reduced (see Fig. 2a and c).This leakage current is B-field and temperature independent, as expected (see supporting information).Assuming that the leakage takes place between the gate electrode and the nanowire, hot electrons are injected into the superconducting shell with energies several orders of magnitude higher than the SC gap.These electrons can heat up the superconducting bridge and drive it to the normal state, as it is proposed by Refs.22-24 as a microscopic origin of the gating effect.Our basic estimation (see supporting information) of induced heat transfer also suggests that hot electrons could bring the temperature of the epitaxial shell in the range of superconducting critical temperature.Instead of using silicon dioxide or other amorphous insulators, the gate electrode and the superconductor is connected by 20-30 nm thick single crystalline hBN layer in our device, which is a large bandgap insulator commonly used as a tunnel barrier in 2D electronics [35][36][37].Considering a tunnel barrier between the gate and superconductor, the heating effect resulted from hot electron injection should show a strong asymmetric dependence on the polarity of the gate voltage.For the polarity when electrons tunnel from the gate electrode to the superconductor (see Fig. 4f left) hot electrons relax their energy in the superconductor by inducing a large number of quasiparticles, which results in a significant heat load.On the other hand, for opposite polarity (see Fig. 4f right), hot electrons heat the metal block of a large gate electrode, which has a much smaller heating effect on the superconductor isolated by the gate insulator.Such gate voltage asymmetry was reported by Ref. 22, however, it does not appear in our measurements (see Fig. 2a) after the initial training period (see supplementary information), which contradicts with a simple explanation based on hot electron injection.Moreover, very recent studies based on suspended nanobridges [18], where the leakage current is suppressed by several orders of magnitude, superconducting gating is also present.This supports that besides leakage another origin of gating could also exist.Considering the magnetic field dependence on the gate voltage (Fig. 4d,e), it is consistent with the hot electron injection, since increasing the gate voltage results in an increase in the rate of injection of high energy electrons to the nanowire segment.This will heat up the device and decreases the critical field of the superconducting wire to smaller values.Moreover, switching of the superconductor at smaller V BG0 with increasing the magnetic field shown in Fig. 4c can be attributed to decreasing of the critical temperature of the superconductor with the external magnetic field.So, a smaller gate voltage would bring the electronic temperature of the device up to the critical temperature of the superconductor.Finally, let us focus on the T dependence of V BG0 .For temperatures larger than T C,NW the nanowire is in the normal state and only the contacts are superconducting.As shown by the red arrow on Fig. 3d, V BG0 decreases at elevated temperatures which is consistent with joule heating induced by hot electron injected into the nanowire.At elevated temperatures, less heat load is enough to drive the contacting segment to normal state.On the other hand, similar suppression of V BG0 with T is not observed either for I C,NW or for I C,C when the nanowire is superconducting (i.e.below T C,NW ), as seen on Fig. 3c and  d, which is in contradiction with the expectation for hot electron injection as an origin of GCS.

CONCLUSIONS
In summary, we have demonstrated the superconducting gating effect in an epitaxially grown superconducting layer for the first time.We developed a novel superconducting field effect transistor using high quality single crystalline hBN insulator layer and Al shell around an InAs nanowire as the active region, which shows a supercurrent suppression at 20 V. Detailed magnetic field and temperature dependent characterization allowed us to compare the experimental facts with existing scenarios of superconducting gating.Although leakage current between the gate and the nanowire was detected the sign independent gating effect suggests that simple hot electron injection does not provide a complete explanation of the observed gating.Besides the fundamental interest, our results open the way to integrate superconducting switches into novel Al/InAs-based hybrid quantum architectures.

METHODS
InAs nanowires with 20 nm thick Al shell and total diameter approximately 100 nm were grown by Au-assisted molecular beam epitaxy (MBE).After InAs nanowire growth with a total length of 5.5 µm, the Al shell layer was epitaxially grown around the nanowire by rotating the substrate and depositing at an angle within the MBE chamber at low temperature [30].
The device was fabricated by electron beam lithography (EBL) in two separate steps.In the first step, metallic gates of Ti/Au layers with thicknesses of 5/40 nm and width of 600 nm were fabricated on an intrinsic Si wafer with a 290 nm thick oxide layer.h-BN flakes were mechanically exfoliated from the bulk onto a clean 290 nm thick SiO 2 /Si wafer by using adhesive tape.A poly-dimethylsiloxane (PDMS) polymer stamp prepared with polycarbonate (PC) layer is used to pick up the h-BN flakes at 75 • C with a thickness of 20-30 nm which can be identified from their contrast on the Si wafer under an optical microscope.The flakes are then transferred and released on the top of the bottom gates by melting the PC layer at 120 • C. PC layer was then dissolved by left the substrate in chloroform for 20 minutes [43][44][45][46].After drying the substrate, Nanowires deposited on the top of the hBN layer and aligned perpendicular to the bottom gate by a thin glass needle with a microscopic tip controlled by a hydraulic micromanipulator along with a high magnification optical microscope.Finally, four contacts of Ti/Al with thicknesses of 10/80 nm were fabricated in the second lithography step.Before this last evaporation step, nanowires were exposed to Ar-ion plasma milling for 8 minutes at 50 W to remove any oxides on the top of Al shell [47,48].
All measurements have been done on Leiden Cryogenics CF-400 top loading cryo-free dilution refrigerator system with a base temperature of 30 mK.We have used a standard power supply with series 1 MΩ resistor to inject current through nanowire via pair of Al contacts on opposite sides of nanowire and measure the voltage across the other pair by voltage differential amplifier.Leakage current was recorded by measuring the voltage across 10 MΩ preresistor connected to the gate.

I. MEASUREMENTS OF THE OTHER PAIR OF CONNECTED AL CONTACTS
In the main text, we have shown the IV characteristics of one of the contacts, here, in

II. CORRECTION OF THE LEAKAGE CURRENT MEASUREMENTS
The leakage current measured by the preresistor connected to the gate during investigation of the device is shown in the red curve in Fig. 2 and contains two current components: a leakage current from the gate to the nanowire device plus other leakage components e.g. through the wiring of the measurement setup.To extract the exact leakage current of the investigated device, the later component should be subtracted from the measurements in the entire gate voltage range.For that purpose, we have connected one contact of the device to an I/V converter and let the other contacts on float.By sweeping the gate voltage up to ±V BG0 , the current measured through the I/V converter would give only the leakage current component to the nanowire device (green curve) 1 .As Fig. 2 shows there is a difference between the current leaking from the gate (preresistor) and the current drained by the superconducting nanowire (I/V conv).Since the later current can not be measured during supercurrent measurement we estimated the leakage current to the superconducting nanowire in the following way: from the leakage current measured by the preresistor the difference between the linear slope of the preresistor measurement (blue dotted line) and I/V converter measurement (black dotted line) was subtracted.These leakage current values are plotted in Fig. 2c in the main text.In this section, we will give a simple estimation for the increase of the electronic temperature of the nanowire segment resulting from the injection of hot electrons from the gate.
Suppose that a single electron tunnels from the gate electrode to the Al layer (that has a volume Ω) with energy eV BG , that is much higher than the superconducting gap of Al as illustrated in the schematic in Fig 5a.This electron will release its energy to the electron gas.
Assuming that the temperature of the Al shell is initially at temperature T i , the injection of an electron to the Al shell will result in a sharp increase on its electronic temperature derived from the heat equation: 2,3 where γ is the Sommerfeld coefficient.The temperature difference between the nanowire segment and the contacts which are at base temperature T b = 100 mK will result in a cool-down of the nanowire segment through heat diffusion by electrons to the contacts.The amount of heat transferred within time dt is given by: where the Wiedemann-Franz law is used: where K is the thermal conductivity of the Al shell, σ = R n L/A is its electrical conductivity, L is the half length of the nanowire segment from the injection point to the contacts, A is its cross-sectional area, R n is its normal state resistance, L is the Lorentz number and ∆T is the temperature difference between actual temperature of the middle of the nanowire, T i and the temperature of the contact T b : ∆T =T i -T b .Due to the heat loss to the contacts, the electronic temperature of the nanowire segment T i will be decreased to T i+1 given by the following heat loss equation: Assuming that at every time period of t inj = e/I leak a hot electron arrives and in the meantime the wire continuously cools, the time dependent temperature can be simulated by Eqs. 1 -4 in discretized points T i , i=1, 2, 3, ....

FIG. 1 .
FIG. 1. Device configuration.a False colored SEM image of the fabricated device with schematics of the device circuit.b Schematic of the device with 45 • angle view and side view in c. d (I-V) characteristics of the nanowire device (red curve) at 40 mK with two different switchings at IC,NW and IC,C in case of the bias current is ramped from negative to positive values (red arrow).In the opposite ramping direction (orange arrow), It switches back at the retrapping current Ir.The measurement of pair of Al contacts (grey curve) has switching at the same value of IC,C.

FIG. 2 .
FIG. 2. Gating of supercurrent a (I-V) characteristics of the nanowire device as a function of bipolar voltage applied to the bottom gate VBG as I was sweeping from negative to positive values.b High resolution (I-V) curves measured at selected gate voltages and separated on y-axis for better visibility.The red and gray dashed lines traces the suppression of IC,NW and IC,C with increasing VBG.c The measured and corrected leakage current from bottom gate to nanowire device as a function of VBG.
3a).Again both dashed red and grey lines traces the suppression of critical currents of nanowire segment I C,NW and contact segment I C,C , respectively with increasing bath temperature T , respectively.In case of I C,NW , it shows a transition to normal state at T C,NW = 1050 mK while for I C,C it switches at T C,C = 1400 mK with corresponding normal state resistances R n,NW = 135 Ω and R n,C = 191 Ω, respectively.By extracting the values of I C,NW and I C,C , the dependence of critical currents on temper-ature is plotted in Fig.3b.The red dashed-dotted and grey dotted curves are fits of the temperature dependence of I C,NW and I C,C , respectively by using Ambegaokar Baratoff relation:[39,40] , R n is the resistance of the normal metal, k B is Boltzmann constant.The temperature dependence of both I C,NW and I C,C is fitted using the coefficient a = 2 and 2.4, and R n = 130 and 143 Ω, respectively.The latter values of normal state resistances are in a good agreement with our experimental findings.The temperature dependence of GCS has been investigated by measuring the critical currents; I C,NW and I C,C as a function of bipolar gate voltage at elevated temperatures (see Fig. 3c and d, respectively).By increasing the bath temperature, GCS of both I C,NW and I C,C is observed for all values of T even when T reaches almost 98% of their critical temperature e.g. for I C,NW , T = 1000 mK (see pink curve in Fig. 3c) the gating characteristics remain the same.The pinch-off gate voltage V BG0 in case of I C,NW did not change with increasing T up to close to its critical temperature at T C,NW , while in case of I C,C , it shifts to lower values (indicated by red arrow) for measurements at temperatures higher than T C,NW .Similar shift of V BG0 in case of I C,C was observed in Ref. 18.

FIG. 3 .
FIG. 3. Temperature dependence a (I-V) characteristics of nanowire device at elevated temperatures up to 1400 mK.Red and grey dashed lines traces the suppression of both IC,NW and IC,C with increasing temperature,respectively.IC,NW switches to normal state at critical temperature TC,NW = 1050 mK, while IC,C switches at TC,C = 1400 mK.b Temperature dependence of IC,NW and IC,C estimated from Fig. 3a.IC,NW and IC,C extracted from panel a are fitted by using Ambegaokar Baratoff relation illustrated by red dasheddotted and grey dotted lines, respectively.c,d critical current as a function of bipolar gate voltage for both IC,NW and IC,C up to 98% of their critical temperatures, respectively.

FIG. 4 .
FIG. 4. Magnetic field dependence a (I-V) characteristics of nanowire device as a function of out of plane magnetic field b Critical currents of both nanowire device and contact interface region as a fuction of applied magnetic field extracted from measurements in panel a.IC,NW and IC,C crossing each others at B = ± 24 mT which results in corresponding critical magnetic fields BC,NW = 64 mT and BC,C = 50 mT, respectively.c IC,C as a function of bipolar gate voltage for at magnetic field values up to 46 mT.d,e IC,NW and IC,C as a function of magnetic field at gate voltage values up to very close to pinch-off voltage, respectively.f Schematic diagrams of electron injection from/to metallic gate to/from superconductor nanowire device in the left and right panel, respectively.Colored/uncolored parts represent occupied/unoccupied states, As the hot electron (red circle) tunnels it will relax to lowest unoccupied state releasing heat either in the N or in the S side, resulting different heating of the S for changing polarity of VBG.

Fig. 1
Fig. 1 the IV characteristics of the other pair of Al contacts measured by the 2-probe method is presented.The measurement shows switching of these contacts from the superconducting state to normal state at ± 7.5 µA which is larger than the value of both I C,NW and I C,C in the IV characteristics of the nanowire device in the main text.

FIG. 1 .
FIG. 1. IV characteristics of the other pair of connected Al contacts measured by 2-probe method.

FIG. 2 .
FIG. 2. Leakage current measurements by preresistor (red curve) and I/V converter (green curve).The two doted lines are linear fit to the I/V converter (black) and prepresistor (blue) based leakage currents for small gate voltage values.

FIG. 3 .
FIG. 3. Magnetic field dependence of critical current of nanowire segment I C,NW .

FIG. 4 .
FIG. 4. (a) The leakage current I leak as a function of the gate voltage V BG at elevated temperatures and (b) at different values of external magnetic field.

FIG. 5 .
FIG. 5. (a) Schematic of the thermal model for calculating the electronic temperature of nanowire device after injection of of electrons with energy eV g from the gate electrode.(b) Calculated electronic temperature of the nanowire segment within 30 successive electron injection cycles at different gate voltages, where t inj = e/I leak .(c)The average nanowire temperature over 20 injection cycles as a function of gate voltage.

Fig 5b shows the 8 V 2 K
Fig 5b shows the calculated temperature as a function of time, for a time period that contains 30 successive electron injection cycles (t inj ) at different gate voltages using Ω = 7.536 × 10 −21 m 3 ,γ = 135.1 Jm −3 K −2 , R n = 135 Ω, A= 5.024 × 10 −15 and L = 2.45 × 10 −8 V 2 K −2 .At smaller gate voltages, the leakage current is quite small and the corresponding electron injection time t inj is very long (see table inFig 5b), the nanowire segment will