Gate-controlled Supercurrent in Ballistic InSb Nanoflag Josephson Junctions

High-quality III-V narrow band gap semiconductor materials with strong spin-orbit coupling and large Lande g-factor provide a promising platform for next-generation applications in the field of high-speed electronics, spintronics, and quantum computing. Indium Antimonide (InSb) offers a narrow band gap, high carrier mobility, and a small effective mass, and thus is very appealing in this context. In fact, this material has attracted tremendous attention in recent years for the implementation of topological superconducting states supporting Majorana zero modes. However, high-quality heteroepitaxial two-dimensional (2D) InSb layers are very diffcult to realize owing to the large lattice mismatch with all commonly available semiconductor substrates. An alternative pathway is the growth of free-standing single-crystalline 2D InSb nanostructures, the so-called nanoflags. Here we demonstrate fabrication of ballistic Josephson-junction devices based on InSb nanoflags with Ti/Nb contacts that show gate-tunable proximity-induced supercurrent up to 50 nA at 250 mK and a sizable excess current. The devices show clear signatures of subharmonic gap structures, indicating phase-coherent transport in the junction and a high transparency of the interfaces. This places InSb nanoflags in the spotlight as a versatile and convenient 2D platform for advanced quantum technologies.


Nanotechnology, Krakow, Poland
High-quality III-V narrow band gap semiconductor materials with strong spin-orbit coupling and large Landé g-factor provide a promising platform for next-generation applications in the field of high-speed electronics, spintronics, and quantum computing. Indium Antimonide (InSb) offers a narrow band gap, high carrier mobility, and a small effective mass, and thus is very appealing in this context. In fact, this material has attracted tremendous attention in recent years for the implementation of Today a great interest revolves around the possibility to create and manipulate new states of matter with topological properties. This stems mostly from the intrinsic robustness of topological states against local perturbation and the ensuing relevance for quantum computing architectures. 1,2 Hybrid superconductor/semiconductor heterostructures represent a promising platform in which topological properties can emerge. [3][4][5][6] In this context, Indium Antimonide (InSb) has attracted much attention recently. InSb has a narrow band gap (∼ 0.23 eV). 6-8 It also has a very high bulk electron mobility (7.7 × 10 4 cm 2 /(Vs)) 9,10 and a small effective mass (m * = 0.018 m e ), 8,9,[11][12][13][14] which are both important requirements for high-speed and low-power electronic devices. 10,15 Finally, it also exhibits a strong spin-orbit interaction and a large Landé g-factor (|g * | ∼ 50, 9,14 ) and thus it is useful for spintronics applications 8,15 and for the creation of hybrid structures hosting topological states, like Majorana zero-modes. Indeed, the first signatures compatible with Majorana bound states were reported in InSb nanowires coupled to a superconductor, 3,16 which has triggered strong efforts to improve the quality of hybrid systems based on InSb nanowires. [17][18][19][20][21][22][23][24] Besides one-dimensional nanowires, two-dimensional (2D) InSb structures also attract great attention, owing to their inherent design flexibility. 6,8,14 Indeed, InSb 2D electron gases 12 and the related ternary compound InSbAs 6 have recently been proposed as a platform for topological superconductivity, 25 and ballistic superconductivity was demonstrated in InSb quantum wells. 12 However, the growth of high-quality heteroepitaxial 2D InSb layers is still a challenge owing to their large lattice mismatch with common semiconductor substrates. Besides, such quantum wells are reported to suffer from instabilities due to the Si dopants. 14 A possible strategy to circumvent these problems consists in growing free-standing 2D InSb nanostructures on nanowire stems, because nanowires yield efficient relaxation of elastic strain along the nanowire sidewalls, when lattice-mismatched semiconductor systems are integrated. To emphasize their free-standing 2D shape, such nanostructures are often referred to as nanosails, nanosheets, nanoflakes, or nanoflags. However, until today only a few studies were reported on the growth and the electrical transport properties of such InSb nanoflags (NF). 7,9,13,19,[26][27][28][29][30] InSb NFs were first reported in 2016 by M. de la Mata et al. 9 their growth being based on molecular beam epitaxy (MBE). There, the authors attributed the 2D geometry of the NFs to a single twinning event in the otherwise pure zinc blende structure of the InSb sam-ple, and four-terminal electrical measurements revealed an electron mobility greater than 12000 cm 2 /(Vs). D. Pan et al. used Ag-assisted MBE to grow free-standing 2D singlecrystalline InSb NFs. 26 Hall-bar devices were then fabricated that showed ambipolar behavior and electron mobility of 18000 cm 2 /(Vs). The same group also demonstrated functional Also our group demonstrated the growth of single-crystal, free-standing InSb NFs, initially on InAs nanowires, using a directional growth technique based on chemical beam epitaxy (CBE). 29 There, NF size was limited by the flexibility of the InAs nanowires, which led to a bending of the stem and the resulting loss of the orientation for the asymmetric 2D growth. In order to overcome this issue, we recently optimized the growth of InSb NFs. 30 In particular, the InSb NFs were grown on sturdy tapered InP nanowires, which did not bend and allowed to grow larger NF with the same directional-growth approach. This strategy allowed to obtain InSb NFs of (2.8 ± 0.2) µm length, (470 ± 80) nm width, and (105 ± 20) nm thickness. 30 The resulting NFs are large enough to fabricate Hall bars with length-to-width ratios enabling precise electrical characterization. An electron mobility of 29500 cm 2 /(V s) was measured at a carrier concentration n = 8.5×10 11 cm −2 at 4.2 K. 30 The electron elastic mean free path e reached values of 500 nm, which favorably compares with present literature. 9,13,34 Here, we report on the fabrication and characterization of JJ devices based on these InSb NFs and provide evidence of ballistic superconductivity. We employ Ti/Nb contacts in InSb JJ devices and show gate-tunable proximity-induced supercurrent at 250 mK and a sizable excess current. The devices also show clear signatures of subharmonic gap structures, indicating phase-coherent transport in the junction and highly transparent interfaces. Our results indicate InSb NF as a promising platform for the study of topological superconductivity.  and V bg = 30 V. The device displays well-developed dissipationless transport thus demonstrating proximity-induced superconductivity in the InSb NF. As the bias current exceeds the critical value of ∼ 50 nA, a sudden jump in the measured voltage to a dissipative quasiparticle branch is observed, indicating that the JJ switches from the superconducting to the normal state, with a resistance of ∼ 330 Ω. Current sweeps in opposite directions show negligible hysteresis, i.e., switching and retrapping current are the same, so that in the following, we shall use switching current and critical current as synonyms. Consistently, the switching current is larger than the intrinsic thermal current noise δI th of the junction 27,45 δI th = 2ek B T /h; here δI th = 10.5 nA. The lower right inset to Fig. 1 shows the differential resistance dV /dI measured using a lock-in amplifier together with the V − I curve. Data clearly show that the differential resistance is zero in the supercurrent branch of the device.
Zhi et al. report a supercurrent of 20 nA at 10 mK in Nb/InSb nanoflag SNS junctions. 27 We attribute the improved numbers reported here mainly to a higher mobility of the nanoflags and progress in device fabrication.
Superconducting quantum interference was observed in the dependence of the supercurrent on a magnetic field applied perpendicularly to the sample plane (Fig. 2). Supercurrent maximum is obtained for B 0 = 6 mT instead of the expected maximum at zero B field.
This small offset can be attributed to a residual magnetization in the cryostat. Applying higher or lower magnetic fields, the suppercurrent symmetrically decreases, until for   Next, we characterize the dissipative regime. Figure 4(a) shows subharmonic gap structures in the differential conductance that can be attributed to multiple Andreev reflections (MARs). The peak present at V sd = 0 V corresponds to the superconductive state. On the other hand, above V sd ∼ ±0.8 mV, the differential conductance becomes constant and is equal to the inverse of the normal resistance, R −1 n . Between these two extrema, the differential conductance dI/dV displays characteristic singularities (minima and maxima), which represent the subharmonic gap structures. [60][61][62][63] Their presence is a signature of the high transparency of the interfaces between S and N regions. The positions of these MAR singularities follow the equation eV n = 2∆ * /n, with n = 1, 2, 3, ... and ∆ * the induced gap in the N region. Most commonly, the position of the maxima in the differential conductance has been analyzed, 6,12,13,18,27,28,36,41,64,65 but recently it was pointed out that for highly transparent junctions, the MAR resonances appear as minima in the differential conductance. 66 In order to estimate the junction transparency and the induced gap, we used a simple scattering model that assumes fully-coherent transport across a multimode JJ (see Ref. 67 and the Supplementary Material) and that has been applied to reproduce MAR traces of nanowire junctions. 68 Thus, the experimental curves were compared to optimized theoretical MAR conductance traces. One example is shown in Fig. 4(b). The best agreement between experiment and theory is obtained for a junction model with 40 modes of transparency T r = 0.94 and an induced gap of ∆ * = 160 µeV 69 . The dashed vertical lines in Fig. 4 highlight the series from n = ±1 to n = ±5, showing an excellent agreement with the predicted behavior for the minima in differential conductance in a highly transparent junction. 66  obtained value of the induced gap, ∆ * = 160 µeV, is smaller than the value extracted from the measurement of the critical temperature. We note that similar values for the induced gap ∆ * have been reported for InSb nanowires proximitized by Nb 64 and by NbTiN. 16 Besides differential conductance data, we recorded also DC traces (I −V curves). Figure 5 shows representative example obtained with V bg = 40 V. From a linear fit of the part of the curve at high bias, with |V sd | ≥ 2∆ * , where Andreev reflections are completely suppressed, we obtain an excess current of I e = 265 ± 12 nA and a normal resistance of R n = 481 ± 3 Ω.
We add that the results do not change significantly if we consider only the voltage range We should like to analyse the superconducting-gap values as obtained from the critical temperature of the superconductor and the observed multiple Andreev-reflection features.

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The measured critical temperature T c = 8.44 K is close to the reported value for bulk Nb and the resulting value of the gap ∆ = 1.28 meV is in good agreement with values reported for JJs with Nb contacts. 28,[36][37][38][39][40][41]65 Thus, we attribute the observed critical temperature to a switching of the Nb film from the superconducting to the normal state.
On the other hand, several groups reported gap values extracted from an analysis of MAR features that were smaller than the BCS-like gap of the superconducting leads. 12 Theory predicts for JJ at T = 0 that the product I c · R n is a constant proportional to the gap, I c · R n = α∆ * /e, with the prefactor α a constant of order unity. 45,[76][77][78][79][80] Here I c ·R n = 15 µV is only about 10% of ∆ * /e = 160 µV. Such a reduction is frequently observed in experiment 18,27,81 and has been attributed to a premature switching of the junction due to thermal activation. 76,82 On the other hand, excess current is due to Andreev reflections and thus depends primarily on the transparency of the (vertical) interface between the covered and uncovered parts of the semiconductor, 80 which is high. Consequently, a large product I e R n ≈ ∆ * /e is observed, close to the theoretical value of 8/3 ∆ * /e for ballistic junctions. 63,80 In summary, we have fabricated JJ devices with InSb NFs as normal region and Ti/Nb as superconducting contacts. The high electron mobility and large mean free path of the InSb NFs yielded ballistic transport across the normal region of the junction. We showed Josephson coupling between superconductor and semiconductor, as demonstrated by the zero-resistance supercurrent of ∼ 50 nA and the observation of MARs. Analysis of the MAR traces indicates a very high transparency of the interfaces. We also observe a sizable excess current. Our results show that free-standing 2D InSb NF on InP stems, thanks to their defect-free zinc blende crystal structure, 30 are a suitable material platform for fabrication of quantum devices. Considering also their strong spin-orbit interaction and their large Landé g-factor, we envision the use of these structures in future studies towards topological superconductivity.

SUPPLEMENTARY MATERIAL
See the Supplementary Material for Extended Methods and Additional Data.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.

CONFLICTS OF INTEREST
The authors have no conflicts to disclose.