Proximity-induced supercurrent through topological insulator based nanowires for quantum computation studies

Proximity-induced superconducting energy gap in the surface states of topological insulators has been predicted to host the much wanted Majorana fermions for fault-tolerant quantum computation. Recent theoretically proposed architectures for topological quantum computation via Majoranas are based on large networks of Kitaev’s one-dimensional quantum wires, which pose a huge experimental challenge in terms of scalability of the current single nanowire based devices. Here, we address this problem by realizing robust superconductivity in junctions of fabricated topological insulator (Bi2Se3) nanowires proximity-coupled to conventional s-wave superconducting (W) electrodes. Milling technique possesses great potential in fabrication of any desired shapes and structures at nanoscale level, and therefore can be effectively utilized to scale-up the existing single nanowire based design into nanowire based network architectures. We demonstrate the dominant role of ballistic topological surface states in propagating the long-range proximity induced superconducting order with high IcRN product in long Bi2Se3 junctions. Large upper critical magnetic fields exceeding the Chandrasekhar-Clogston limit suggests the existence of robust superconducting order with spin-triplet cooper pairing. An unconventional inverse dependence of IcRN product on the width of the nanowire junction was also observed.

. Various Majorana braiding architectures such as 1D wire networks forming a T-junction 2 , hexon architecture 5 , tri-junction geometry 4 , etc. have been proposed in the recent past. Ion-milling technique provides an excellent way to experimentally realize such architectures in comparison to other nanowire synthesis routes like chemical vapour deposition (CVD), VLS or electro-deposition, where fabricating such braiding networks is not possible. The observation of proximity-induced superconductivity in long Bi 2 Se 3 junction lengths with high I c R N products indicates the preferred coupling of proximity effect with the ballistic TSS channels, which is an essential requirement for a TSC to host MZMs. An unconventional inverse dependence of the I c R N product on the width of the nanowire, suggests the possibility of 1D-confined quantum states at the superconductor-TI (S-TI) interface. Also, the estimated large upper critical field B (0) c 2 (greater than the Chandrasekhar-Clogston limit) demonstrates the existence of proximity-induced robust superconducting order in TIs with a possible spin-triplet cooper pairing that is crucial for hosting MZMs.

Results
False colored FESEM images of the weak links of Bi 2 Se 3 nanowires (devices N4 and N5) with four-probe measurement geometry are depicted in insets of Fig. 1a. The estimated length (i.e. junction length) and width of the weak links (Bi 2 Se 3 nanowires) is about 368 nm and 226 nm for N4, and 286 nm and 121 nm for N5, respectively. Figure 1a shows the resistance vs. temperature (RT) characteristics (10 K to 2 K) of the samples N4 and N5. A small resistance increase of 47.08 Ω (N4) and 30.62 Ω (N5) is observed while cooling the system from room temperature to 15 K, followed by a sudden superconducting transition (T c onset ) at 5.357 K (N4) and 5.706 K (N5). This is consistent with the previously reported T c values of ~5 K for FIB-deposited W 22,23 . The transition width, i.e. Δ = − T T T c c onset c zero , is smaller for N5 (0.65 K) than N4 (2.81 K), which is evident from the shorter junction length of N5. Figure 1b  characteristics include both superconductivity and TSS properties, with zero resistance around zero B-field, above which MR increases with B-field. MR is symmetric with applied B-field direction. MR curve has been divided into three regimes with increasing B-field. Regime 1 represents the state of complete superconductivity in the nanowire due to proximity effect. Resistance starts to increase linearly with B-field in regime 2. The linear MR has been reported in various TI materials and is attributed to the linear Dirac energy spectrum of the TSS 9,18 . Also, it is well known that TIs exhibit Shubnikov-de Haas oscillations at higher perpendicular B-fields due to the presence of metallic TSS 9,18 . Similar oscillatory features can be observed in regime 3 of the MR curve. Thus, the MR at 2 K reveals the characteristics of TSC arising from the proximity-induced superconductivity in TSS of the Bi 2 Se 3 nanowire. Figure 2 depicts the broadening in RT curves with increasing perpendicular magnetic field (B) up to 14 T. The shifting of T c onset towards lower temperatures with increasing B-field is clearly visible for the samples. Zero resistance state is lost above 4 T for both N4 and N5 in the available temperature range till 2 K. Interestingly, for device N4, we observe a small resistance increase (kink-type feature) at 4.9 K (0 T). This resistance kink disappears above 0.5 T (upper inset in Fig. 2a), which suggests its dependence on the applied perpendicular B-field. In order to calculate the upper critical field (B c 2 ), we define T c at 90% of the resistance transition, i.e. R = 90%R N , where R N stands for the normal state resistance with values around 445 Ω for N4 and 556 Ω for N5. We incorporate the three standard approaches to calculate B c 2 : i) normal state paramagnetism leading to a Pauli limited transition field due to the competing Zeeman energy of external magnetic field and cooper pair condensation energy, given by the Chandrasekhar-Clogston limit 24 , type-II superconductor in dirty limit is given by the single-band Werthamer-Helfand-Hohenberg (WHH) theory 29 , reflects the robustness of this proximity-induced topological superconducting state towards high magnetic fields, which is necessary to sustain and manipulate MZMs via magnetic field. The superconducting coherence length ξ(0) can be estimated from the B (0) c 2 value using the GL formula 23 L T T where length of the nanowire is 2 L (centre at x = 0) and Δ L is the superconducting gap at the N-S interface. This equation clearly suggests that the proximity-induced superconductivity in the nanowire will weaken with increasing length. At the centre of the nanowire, Δ(x = 0)~[cosh(L/L T )] −1 indicates that smaller values of L T will destroy the superconducting state. In case of clean and highly transparent N-S interfaces, long range proximity effects up to 1 µm can be observed 22,32,33 . Previously, formation of spin-triplet cooper pairs in ferromagnetic Co nanowires was shown to possess long range proximity-induced superconductivity (~1 µm) 32 . Similar kind of phenomenon is possible in TIs, where the spin-polarized surface current can lead to a spin-triplet superconducting pairing of the SS. Theoretically, unconventional superconducting order is predicted to exist in the TSS though proximity effects, which has the potential to host MZMs 10 . Kasumov et al. 33 reported the first evidence of an anomalous proximity effect in a TI material BiSb, where the critical current (I c ) was shown to increase with increasing junction length, unlike Eq. (5). The reason for this anomaly was attributed to the very low effective mass of electrons in such materials (now called TIs), that accounts for high de-Broglie wavelengths comparable to the junction lengths 33 . Also, recent reports have shown the existence of long-range proximity-induced superconductivity in TI-based weak links, even for junction lengths much longer than the barrier coherence length (L T ) in diffusive channels and electron phase breaking length (L φ ) 14,26 . This inconsistency with the existing theory of superconducting proximity effect in normal metals can be explained by considering two different transport channels in TIs, ballistic TSS and diffusive bulk. Although, it is difficult to separate the diffusive bulk transport channels, but it was shown that the proximity-induced superconducting order prefers the ballistic TSS channel 26 . A similar kind of explanation is valid for the TI devices studied in this work. If a ballistic TSS channel is considered, then L T = ℏv F /2πk B T ~ 304 nm at 2 K for v F ~ 5 × 10 5 ms −1 (Fermi velocity in TSS for Bi 2 Se 3 ) 18,26 is comparable to the junction length of the devices, where ℏ = reduced Planck's constant and k B = Boltzmann constant = 8.62 × 10 −5 eV/K. This indicates towards the possibility of proximity-induced superconducting order parameter Δ(x) to survive throughout the long junction lengths due to the preferred coupling with the TSS, which is very crucial for hosting the MZMs that are predicted to occur when proximity effect induces superconductivity in the TSS. In order to understand the supercurrent behaviour in our samples, we hereby present the current-voltage (IV) characteristics, i.e. voltage versus the applied current. Figure 3a depicts the IV curves (device N4) for temperatures ranging from 2 K to 5.8 K at B = 0. Supercurrent vanishes with increasing temperature and the curves follow typical linear ohmic behaviour above 4.6 K. At 2 K, I c is 1.641 µA, above which there appears a finite voltage, as the system is driven to a resistive state. The IV curves for N4 depict low voltage foot-like features (shown by pink arrow in Fig. 3a), which was first observed by Octavio, Skocpol and Tinkham 34 in tin-microbridges and was attributed to the non-equilibrium quasiparticles created by the breaking of cooper pairs during the Josephson cycle. Figure 3b shows the IV curves for device N5 at different temperatures. A very sharp transition from superconducting to resistive regime can be observed for N5 at lower temperatures, which is obvious from the sharp  8), which gives information about the characteristic energy scale of the system. (b) IV curves for N5 depicting a sharp supercurrent transition till 3.6 K, above which foot-like transition (pink coloured arrow) starts to appear. At temperatures above T c , a linear ohmic IV is observed. Upper and lower inset shows the fits to Eqs (6) and (8), respectively, where the fit starts to deviate from experimental data near T c . (c) Hysteresis in device N5 at 2 K during up and down sweeps of current. Upper inset shows the small hysteresis persisting till 3.4 K, above which I r and I c merge. Lower inset highlights (dotted purple circle) the observed phase slip voltage step for 2 K < T < 3.2 K in device N5. (d) I c~( 1−T/T c ) n fits at two temperature regimes, T < 3.4 K and T > 3.4 K, for N5. Upper inset shows similar fit for I r . Lower inset depicts the decrease in I c with increasing B-field for N5. superconducting RT transition in this sample as shown above in Fig. 2b. For temperatures above 3.4 K, foot-like transition starts to appear (shown by pink arrow in Fig. 3b). The I c R N product (I c = critical current and R N = normal state resistance), which provides information about the superconducting gap (Δ), is equal to 0.73 mV for N4 at 2 K. Previously, it was reported that the maximum I c R N product at low temperature in a SNS junction is πΔ/e, where e is the electronic charge 25 . If we assume that BCS relation is followed by the superconducting contacts in this case, then Δ(T = 0) = 1.76k B T c provides a gap of 0.8127 meV for N4 at T c corresponding to 90% of resistance transition = 5.357 K (k B = Boltzmann constant = 8.62 × 10 −5 eV/K). Thus, the expected maximum I c R N product for N4 is 2.55 mV, which is about 3 times higher than the value at 2 K. A high I c R N product of 4.6 mV is obtained for N5 at 2 K (I c = 8.32 µA). The superconducting gap (Δ) of 0.866 meV is estimated for N5, and maximum I c R N product of 2.72 mV, which is about 1.5 times smaller than the value at 2 K. The expected maximum I c R N product at 0 K is slightly less for N4 due to the longer junction length than N5. Since N4 has longer junction length than both the ballistic TSS L T and diffusive bulk L T at 2 K, therefore, the I c R N product for N4 is very less at 2 K. Whereas, N5 has a shorter junction length than the estimated ballistic TSS L T (~304 nm at 2 K) that leads to high I c R N product at 2 K. This again hints towards the preferable coupling of proximity effect to the TSS channels, which is the basic need for the detection of Majorana fermions. An alternative explanation for the suppressed I c R N product in N4 can be the insufficiently transparent S-TI interfaces due to the presence of tiny superconducting islands near the electrode edges from FIB-deposition of W electrodes. Previously, anomalous small I c R N products were observed for TI flake or thin film based Josephson junctions 13,14,16 . Also, it is well known that this value is independent of the junction geometry 27 . But, Williams et al. 13 reported an inverse dependence of I c R N with the width of the TI weak link. We observe a similar dependence, where I c R N product (at 2 K) is larger for device N5 (width = 121 nm) than N4 (width = 226 nm). Since the minimum temperature accessible to us in this experiment is 2 K, therefore, we can assume a higher I c R N product at further lower temperatures. Upper insets in Fig. 3a,b depict the clean and dirty limit fits using the de Gennes I c equation for SNS junctions 31 :  6) is based on the GL theory; therefore ideally it should be valid only near T c . But, reports have shown its validity even at very low temperatures 35 . For our case, we found the best I c vs. T fit to Eq. (6) for 2 K ≤ T ≤ 3.4 K. For N5, it can be seen that the experimental data diverges from the fits for T > 3.4 K. Due to lack of experimental data below 2 K, we are unable to distinguish whether the system is in clean or dirty limit from the fit, as both the limits fit to the data in 2 K ≤ T ≤ 3.4 K. As explained in the Methods section, the presence of small superconducting islands nearby the S-TI interface due to FIB-deposited W may introduce disorder in the system. Thus, the transport in our junctions can be assumed to be slightly in the dirty/diffusive regime, where bulk transport channels might interfere with the surface transport. In that case, the value of D from the dirty limit fit is estimated to be 0.0137 m 2 /s and 0.059 m 2 /s for N4 and N5, respectively. The values are in agreement with the previously reported D values in Bi 2 Se 3 material 13 . In a dirty/diffusive SNS junction, the Usadel equation (which gives information about the quantum transport in a dirty/diffusive superconductor, i.e. where junction length is longer than the electron mean free path) 14,15,25 can be written in terms of junction length as 36 : . Ω = Δ + ω n 2 n 2 is energy related to the superconducting gap and thermally excited states at finite temperature. Dubos et al. 36 performed the numerical analysis of Eq. (7) and came up with an approximate solution for low temperature regime, given by: where a and b are unitless coefficients. Lower insets in Fig. 3a,b shows the fit to Eq. (8) for device N4 and N5, respectively. The fit for N5 deviates from experimental data when close to T c as Eq. (8) is valid in the low temperature regime. Transport in diffusive conductors is governed by a characteristic energy scale, E c = ℏD/L 2 , called the Thouless energy, which provides the diffusion rate through the system 16,36,37 . For our case, E c is estimated to be 0.0667 meV and 0.476 meV for N4 and N5, respectively. Since E c < Δ (Δ = 0.8127 meV for N4 and 0.866 meV for N5) for both the devices, therefore, the systems are in the long junction limit 36,37 , where diffusive L T is smaller than the junction length of the devices. The existence of long-range superconducting proximity effect even with small diffusive L T , clearly indicates the co-existence of two different types of transport channels (bulk and TSS) in the Bi 2 Se 3 junction. As discussed earlier, TSS is expected to carry this long-range proximity-induced superconducting order parameter through the long TI junction.  Figure 3c depicts the hysteresis present in the IV characteristics of device N5 at 2 K. The critical current observed while switching from resistive to supercurrent regime (downward current sweep), i.e. the retrapping current I r , is slightly less than the critical current (I c ) for supercurrent to resistive state transition (upward current sweep). Upper inset in Fig. 3c shows the variation in I r and I c with temperature, where small hysteretic behaviour disappears completely above 3.4 K. According to the RCSJ (resistively and capacitively shunted junction) model 25,27 , a Josephson junction can be described by resistance and capacitance connected in parallel to each other. In our case, the effective capacitance (C eff ) of the lateral junction can be written as eff 0 1 sc sc 0 2 nw nw where ε 0 is the vacuum permittivity, K 1 and K 2 are the dielectric constants of vacuum and Bi 2 Se 3 , t sc,nw and W sc,nw are the thickness and width of superconducting electrode and Bi 2 Se 3 nanowire, respectively. For device N5, C eff is estimated to be 95.83 aF. Thus, the Stewart-Mc Cumber parameter (β c ) is estimated to be 0.747 at 2 K from Eq. (10) 16,25,27 .
Usually, hysteresis is observed in under-damped junctions (β c ≫ 1) 16,25,27 . But in this case the junction is almost critically or intermediately damped (β c ≈ 1); therefore, the width of hysteresis loop is quite small. Since large hysteresis is related to large values of shunt resistance and capacitance that ultimately leads to decrease of I c (and superconductivity), therefore, presence of small hysteresis in superconducting TI junctions (similar to N5) provides favorable platform to host MZMs. Previously, Courtois et al. 37 demonstrated that the hysteresis in SNS junctions is a direct consequence of electron heating in the normal metal during the supercurrent to resistive regime transition. According to the Skocpol, Beasley and Tinkham (SBT) hotspot model 38 , the Joule heating in the weak link may induce an increase in the local temperature, where − 1 T/T c dependence of I r is predicted with temperature 38,39 . Upper inset in Fig. 3d depicts the (1−T/T c ) 0.33 dependence of I r on T, which suggests the possibility of self-heating induced hysteresis for N5. No hysteretic IV behaviour was observed for device N4 in the available temperature range. Figure 3d shows the (1−T/T c ) n dependence of I c on T for device N5. For clean superconductors, n = 1.5 represents the standard GL model, where I c is dependent on the cooper pair breaking mechanism in the weak links 39 . In case of dirty superconductors, n exceeds 1.5. Since the GL theory is valid near T c , therefore, we divide the data into two regimes, T < 3.5 K and T > 3.5 K. For T < 3.5 K, n equals 0.4, which does not follow the GL value. Near T c (T > 3.5 K), n = 1.6, which corresponds to the GL value in dirty limit. It must be noted that for all the graphs (including upper inset) in Fig. 3d, T c was taken at maximum value of dR/dT. Lower inset in Fig. 3d shows the decrease in I c with increasing B-field at 2 K. Supercurrent is strongly retained at 1 T, which is suggestive of the high critical field (B c ) of the system. Previous reports used small external B-field perpendicular to spin-orbit B-field to open a Zeeman gap in semiconducting nanowires to detect MZMs [6][7][8] . Since this is essential for a Majorana wire to be in topological phase 3,8 , therefore, presence of strong supercurrent even at high B-field of 1 T suggests the efficiency of TI-based nanowires for hosting MZMs. Interestingly, we also observed phase slip events in device N5 up to 3.2 K. Previously, coherent quantum phase slip (CQPS) was demonstrated in narrow segments of disordered superconductor, where local inhomogeneities can give rise to phase slip centres (PSC) 40 . The phase of the superconducting order parameter shifts by different rates on both side of PSC, and when the order parameter becomes zero at PSC, the phase difference slips by 2π 27 . This manifests itself as regular voltage steps in the IV curve, once the current is increased above I c . Lower inset in Fig. 3c highlights the voltage step due to phase slip. The FIB-induced disorder can account for the observed event in TI nanowire. Since phase slip event is exactly dual to the Josephson effect, therefore, phase slip mechanism can be used to realize the quantum current standard 39,40 . Although, the detailed study of phase slip events in TIs is not the prime motive of this work, but their observation in FIB-fabricated Bi 2 Se 3 nanowire triggers many future experiments intended to complete the quantum metrological triangle, i.e. resistance, voltage and current standard via TI-based quantum wires.

Discussion
Realization of supercurrent in FIB-fabricated nanowires of TIs is a significant step towards the hosting of MZMs for TQC. It is predicted that in the topological phase of Kitaev's superconducting quantum wire, Majorana fermions from the neighbouring lattice sites will form bound pairs, leaving two unpaired Majorana fermions at the ends of the nanowire 3 . This model of 1D p-wave TSC nanowire provides more efficiency in locating the MZMs than other 2D system based approaches like FQHE (ν = 5/2 state) or magnetic vortices, as in 2D system they can appear anywhere in the sample and at the same time could be masked by other low-energy 2D quasi-particle excitations, which increases the difficulty level of detecting MZMs. A major challenge to build a practical Majorana-based quantum computer is the scalability of these laboratory level hardware designs. Recent detection of Majorana fermions were performed in systems where scaling of the device geometry is very difficult. Along this line, the experts have recently proposed scalable designs for the realization of TQC with MZMs 2,4,5 . For the experimental realization of these designs, the fabrication of superconductor-TI nanowire junctions is of utmost priority. Presently, there is no single synthesis technique that can scale up the simple nanowire based devices of TI or other semiconducting material into complicated network geometries. To achieve high device scalability, one needs to grow or assemble 1D nanowires at specific locations, which surely is a very crucial step towards future quantum computing. Recently, we have shown and pioneered TI-based nanowire device fabrication by using milling method [18][19][20][21] , which has device fabrication potential for measuring two or more 1D nanowire based devices. We have already demonstrated the robust TSS properties in FIB fabricated nanowires of Bi 2 Se 3 through ½-shifted Shubnikov-de Haas (SdH) 18 and Aharonov-Bohm (AB) oscillations 19 in our previous reports, which further encourages the use of ion-milling for building TQC architectures. It is important to note that the alignment of two or four nanowires and making device geometry for manipulation of MZMs is a very difficult task, but our proposed approach will solve this engineering problem and will give an access to perform experiments by braiding these quasi-particles, which is a milestone step that has never been accomplished before. Further, the direct FIB deposition or e-beam based masked design of superconducting contacts on these milled nanostructures will enable the proximity-induced superconductivity, a perfect hardware for the creation, detection and braiding of MZMs. Figure 4 depicts the fabrication approach proposed by us for building the TQC hardware. Figure 4a shows the recently proposed TQC architectures like one-sided hexon 5 , tri-junction geometry 4 and hexagon 10 . False colored FESEM images in Fig. 4b show the patterning of the recently proposed TQC architectures (shown in Fig. 4a) through FIB milling on exfoliated Bi 2 Se 3 flakes. Figure 4b clearly demonstrates the superiority of milling technique, in arrangement of nanowires in a prescribed manner, over other nanowire synthesis methods. It must be noted that, higher quality thin films of TI via CVD or molecular-beam-epitaxy (MBE) can also be used for ion-milling of nanostructures. Figure 4c depicts the schematic of twelve FIB-milled TI nanowires (false colored FESEM image from Fig. 4b) with superconducting electrodes to host twenty-four bound pairs of Majorana fermions, which will serve as twelve qubits (2n MZMs = n-qubits). Braiding and reading the states of qubits with the proposed twelve nanowire array has the potential to compute much more data at a faster rate than the present day classical computer with millions of transistors. Realization of supercurrent in single nanowire of Bi 2 Se 3 indicates that such FIB-fabricated architectures coupled with superconducting electrodes and proper gate voltages can be used to probe and braid MZMs. Proximity-induced superconductivity in the TSS is predicted to lead to exotic phenomenon of Majorana fermions 10 . The Hamiltonian describing the proximity induced superconducting order parameter in TSS was earlier studied by Fu and Kane and can be written as 10

Conclusion
To conclude, we have studied the proximity-induced superconductivity in FIB-fabricated Bi 2 Se 3 nanowire junctions with W electrodes. A sharp superconducting transition was observed for shorter junction length. The high B c 2 values exceeding the Chandrasekhar-Clogston limit demonstrates the robust superconducting properties of proximity-coupled TIs with possible spin-triplet pairing of cooper pairs. The presence of long-range proximity effect with high I c R N product in the junctions suggests the dominant role of ballistic TSS in propagating the supercurrent, even in the presence of diffusive bulk transport channels with barrier coherence length much smaller than the junction length of the devices. Also, the unconventional inverse dependence of I c R N product on the width of the nanowire indicates the presence of quantum confined transport channel at the S-TI interface, which was previously predicted to arise from 1D Majorana modes at the interface. MR data also confirms the co-existence of both superconducting and TSS properties in the Bi 2 Se 3 junctions, which is essential for hosting robust MZMs. Overall, our work on the fabrication of nanowires of TI, demonstration of the robust nature of 2D TSS transport 18,19 and supercurrent through TI-junction have huge potential to scale-up these nanodevices in any proposed geometry for building the fault-tolerant quantum computer and hence, stands as a breakthrough at the level of fundamental device physics and nano-engineering. The next step would be to observe the Majorana particles in similar kind of fabricated superconductor-TI nanowire junctions. Manipulation of non-Abelian MZMs are useful for encoding the quantum information, but movement or braiding of these particles has not been achieved yet, which is an essential ingredient for routine quantum computing operation. Supercurrent studies on nanowires of topological insulator and their synthesis reported by us establish a solid platform towards the study of superconductivity through topological surface states and the detection of Majorana fermions to perform braiding experiments. We believe that similar future experimental efforts and results will further enhance the expertise in qubit creation, detection and measurement capabilities for TQC.

Methods
Device fabrication and characterization. We have incorporated the FIB-based Ga + ion milling technique to fabricate the Bi 2 Se 3 nanowire from exfoliated thin flakes of Bi 2 Se 3 . The standard Scotch-tape method was used to perform micro-mechanical cleavage of bulk crystals of Bi 2 Se 3 . The exfoliated flakes obtained were deposited on SiO 2 /Si substrates with pre-defined gold contacts, which were already cleaned chemically (via acetone, iso-propanol, methanol and de-ionized water) and with oxygen plasma for 10 min. The thin flakes were localized under optical microscope (Olympus) and field emission scanning electron microscope (FESEM, Zeiss Auriga). FIB milling using Ga + ion (Zeiss Auriga) was further used to shape the flake in the form of a nanowire. The FIB-based gas injection system (GIS) was used to deposit the metal electrodes of tungsten (W) on the fabricated nanowire. To prevent any damages to the Bi 2 Se 3 nanowire, a very low ion-beam-current was used (~50 pA) to deposit the superconducting electrode (W). Superconducting properties of W were optimized (thickness and T c ~ 5 K) before deposition and the same parameters were used for fabricating the devices. The release of precursor gas, tungsten hexa-carbonyl (W(CO) 6 ), was checked by monitoring the chamber vacuum. The FIB chamber vacuum was set to 5 × 10 −6 mbar before releasing the gas from needle nozzle and 2 × 10 −5 mbar during the deposition of W. This FIB induced metal deposition technique was further used to connect the W electrodes to pre-defined gold contacts, which serve as the functioning electrodes for the four terminal electrical measurements in the physical property measurement system (PPMS). In accordance with previous reports, where the FIB-deposited W material was shown to diffuse into the nanowire length close to the electrode edges 22 , it is visible in the high magnification FESEM images (See Fig. S1 in Supplementary Materials) that some of the superconducting (W) material has diffused along the length of Bi 2 Se 3 nanowire up to a maximum of 40 nm from W electrode edge on either side. This diffusion length was also verified using the high-resolution transmission electron microscope (HRTEM) characterization of the FIB-deposited W electrode on Bi 2 Se 3 flake (See Figs S3 and S4 in Supplementary Materials). Therefore, the estimated length is calculated by subtracting this diffusion length from the actual junction length.

Data Availability
All experimental data required to evaluate and interpret the conclusions are present in the main manuscript or supplementary materials file.