Proximity-effect-induced Superconducting Gap in Topological Surface States – A Point Contact Spectroscopy Study of NbSe2/Bi2Se3 Superconductor-Topological Insulator Heterostructures

Proximity-effect-induced superconductivity was studied in epitaxial topological insulator Bi2Se3 thin films grown on superconducting NbSe2 single crystals. A point contact spectroscopy (PCS) method was used at low temperatures down to 40 mK. An induced superconducting gap in Bi2Se3 was observed in the spectra, which decreased with increasing Bi2Se3 layer thickness, consistent with the proximity effect in the bulk states of Bi2Se3 induced by NbSe2. At very low temperatures, an extra point contact feature which may correspond to a second energy gap appeared in the spectrum. For a 16 quintuple layer Bi2Se3 on NbSe2 sample, the bulk state gap value near the top surface is ~159 μeV, while the second gap value is ~120 μeV at 40 mK. The second gap value decreased with increasing Bi2Se3 layer thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi2Se3 thicknesses. It is plausible that this is due to superconductivity in Bi2Se3 topological surface states induced through the bulk states. The two induced gaps in the PCS measurement are consistent with the three-dimensional bulk state and the two-dimensional surface state superconducting gaps observed in the angle-resolved photoemission spectroscopy (ARPES) measurement.

Since the first experimentally accessible proposal of topological superconductors (TSCs) by Fu and Kane 1 , the search for TSCs and Majorana zero modes has generated significant interest in condensed matter physics. Majorana zero modes exist at the boundary of TSCs and have potential applications in quantum computing. TSCs may exist intrinsically in superconducting doped topological insulators (TI) [2][3][4][5][6][7][8][9] , however there is a lack of experimental evidence of this due to the lack of intrinsic TSCs. Alternatively, TSCs can also occur in proximity-induced superconductors, such as in a TI in contact with an s-wave superconductor [10][11][12][13][14][15][16][17][18][19][20][21][22] . For this reason, significant efforts have been devoted to proximity-induced topological superconductivity. Electron tunneling and point contact spectroscopy (PCS), which probe the density of states (DOS) of superconductors, have been widely used in studies of topological superconductor systems and in the search for Majorana fermions. Some studies reported zero-bias conductance peak (ZBCP) features in the transport spectra of S/TI junctions and point contact spectra on S/TI bilayers 15,[23][24][25][26][27] , which were proposed as a signature of TSCs. On the other hand, scanning tunneling spectroscopy (STS) measurements on epitaxial TI thin films on superconducting NbSe 2 substrates showed no ZBCP 13,19 . In the core of a magnetic vortex inside a topological insulator-superconductor bilayer, a ZBCP was observed by STS and attributed to Majorana fermions 21,22 . Recently, an angle-resolved photoemission spectroscopy (ARPES) study revealed two dimensional topological superconductivity in proximity coupled NbSe 2 /Bi 2 Se 3 heterostructures 20 . The topological nature of this superconducting state was demonstrated by the observation of spin-momentum locking. Since there is no clear conclusive observation of the topological superconducting states in transport studies, it is very important to know how the proximity-induced topological superconducting states in the same NbSe 2 /Bi 2 Se 3 samples will be reflected in the transport measurements.
In this work, we present point contact spectroscopy studies of epitaxial Bi 2 Se 3 thin films with different thicknesses grown on NbSe 2 single crystals at low temperatures down to 40 mK. The samples were grown in identical conditions as those measured by ARPES 20 . While the ARPES measurements are only sensitive to the surface layer of the order of nm, the PCS measurements are sensitive to the depth within the proximity coherence length range or the mean free path whichever is smaller, which is around 16 nm for the bulk Bi 2 Se 3 . Our results showed that a finite superconducting energy gap was successfully induced in the Bi 2 Se 3 from the superconducting NbSe 2 substrate through the proximity effect. No ZBCP features were present in the point contact spectra. The induced gap decreased with increasing Bi 2 Se 3 thickness. More importantly, a second gap-like feature appeared besides the main gap at temperatures below 0.45 K in the point contact spectra of a16 QL Bi 2 Se 3 on NbSe 2 sample, suggesting a possible signature of an induced superconducting gap in topological surface states through the bulk states. The second gap also decreased with increasing Bi 2 Se 3 thickness, but the ratio between the second gap and the bulk state gap remained about the same for different Bi 2 Se 3 thicknesses. The two induced gaps from our point contact spectroscopy measurements are consistent with the ARPES results that superconducting gaps are induced by proximity effect in both the Bi 2 Se 3 bulk states and the surface states.

Results
Soft point contact technique. We studied the point contact spectroscopy of NbSe 2 single crystal and NbSe 2 /Bi 2 Se 3 heterostructure samples by using the "soft" point contact technique 28 . The contacts were made by applying a small drop of silver paint between the top surface of the sample and a gold wire of 25 μm diameter (Fig. 1). The other electrical contacts were made on the NbSe 2 superconducting substrate for four-probe electrical measurements, as show schematically in the inset of Fig. 1. Unlike conventional Needle-Anvil point contacts, silver paint "soft" point contacts utilize nanometer-scale Ag particles to form parallel contact channels to the samples in which there is no pressure applied to the sample. Thus it is preferred in studying properties on the surfaces in thin and soft Bi 2 Se 3 films.
Depending on the ratio of the electron mean free path to the radius of contact channels, point contacts can be categorized into ballistic, diffusive, or thermal regimes 28 . It is very important to verify that the point contact is in the ballistic regime. Non-ideal features, such as dips at voltage values larger than the superconducting gap, can appear in the conductance curves when the contact is not ballistic. If the radius of a point contact is much larger than the mean free path, the contact is in the thermal regime and no spectroscopic information can be obtained. In addition, the thermal contact region temperature is higher than the bath temperature from local Joule heating. We carefully examined our point contact spectra to ensure all data reported were from ballistic contacts.
Proximity-effect-induced gap in Bi 2 Se 3 . The conductance spectra of point contacts on samples of different Bi 2 Se 3 film thicknesses at low temperatures are shown in Fig. 2a. For samples with thin Bi 2 Se 3 layers (<7 QL), the NbSe 2 gap feature (~1.0 mV) dominates the spectrum. With increasing Bi 2 Se 3 film thickness, another conductance peak feature appears at low voltage bias (~0.3 mV) and becomes more and more pronounced. Eventually, only this peak feature is present in the 16 QL sample. For the samples with multiple peaks in the spectra, we fitted the experimental data using an extended Blonder-Tinkham-Klapwijk (BTK) model 29 which assumes a linear combination of two different gaps and independent fitting parameters Δ, Γ, and Z for each gap. The BTK theory is widely used to describe the transport between a normal metal and a superconductor with a finite transparency of the interface. The parameter Γ was included to describe the broadening effect, which is associated with the lifetime of the quasiparticles 30 . The fitted gap values Δ from PCS measurements of all samples are plotted in Fig. 2b together with Bi 2 Se 3 bulk gaps at the top surface from the ARPES measurement 20 . The PCS gaps are clearly separated into two groups. The NbSe 2 gap value decreases slightly in the Bi 2 Se 3 /NbSe 2 heterostructures from the gap of pure NbSe 2 (~1.2 meV) with the increasing Bi 2 Se 3 layer thickness. Meanwhile, a smaller gap feature appears in the PCS spectra when the Bi 2 Se 3 film thickness is above 10 QL and follows the same thickness dependence trend as the induced Bi 2 Se 3 bulk band gaps from ARPES measurements on the same type of NbSe 2 /Bi 2 Se 3 heterostructures. Therefore, this gap feature is the proximity-induced bulk state gap in Bi 2 Se 3 near the surface. The NbSe 2 gap and induced bulk state gap show very different magnetic field dependences. The conductance spectrum peaks from the induced gap (~0.3 mV) are quickly suppressed in small magnetic fields. On the other hand, the NbSe 2 gap feature at ~1.0 mV disappears under ~4 T magnetic field, which is consistent with the H c2 of NbSe 2 (See Supplementary Information A and B for more details).
Unlike ARPES, which is only sensitive to a few monolayers from the top surface, PCS probes the top surface with a deeper depth into the sample with a length of the order of the mean free path l e in dirty limit 28  2 is estimated to be ~16 nm for the bulk Bi 2 Se 3 . This is very close to the Bi 2 Se 3 thickness threshold when no NbSe 2 gap is observed. When the Bi 2 Se 3 film thickness is much smaller than l e , the signal is mainly from the interface of NbSe 2 substrate. With increasing Bi 2 Se 3 film thickness, the gap from the Bi 2 Se 3 film starts to gain more weight in the total spectra. Eventually, when the Bi 2 Se 3 film thickness is beyond l e , the gap in Bi 2 Se 3 dominates the spectra and the signal from the interface vanishes. Therefore, this also supports that the gap values from 0.30 to 0.16 meV in 10 to 16 QL samples in Fig. 2b are the proximity-effect-induced superconducting energy gap in the bulk states of the Bi 2 Se 3 thin film. It should be noted that the above spectra are obtained on samples with medium contact transparency so that the spectrum is close to tunneling regime. When the point contact is very clean (low barrier strength), we observed Andreev reflection spectra which were from the NbSe 2 / Bi 2 Se 3 interface, as shown in Fig. 5a of ref. 20. We did not observe ZBCP features in the spectra, consistent with STS measurement results 13,19 , but different from some PCS measurement results 15,[23][24][25] . Our results, similar to the STS results, also call for a careful re-examination of the interpretation of ZBCP in the PCS as the signature of unconventional superconductivity or Majorana fermions. Now we focus on the samples with only proximity-effect-induced gap feature. Figure 3a shows the conductance spectra of a point contact junction on a NbSe 2 /16 QL Bi 2 Se 3 sample at low temperatures down to 40 mK. Only the proximity-induced gap is present in the spectra, without a signal from the NbSe 2 substrate contribution. Spectra at temperatures from 1.8 K to 7.5 K are plotted in Fig. 3b. As the temperature increases, the induced gap peaks in the conductance spectra start to smear into a single broad peak at zero bias likely due to the thermal broadening. The zero bias conductance then decreases gradually till 7 K, T c of NbSe 2 , confirming that this gap is due to the proximity effect from the superconductor NbSe 2 . Figure 3c plots the conductance spectra to high voltage bias at temperatures up to 15 K. The spectra shows a linear background, which is often attributed to inelastic tunneling at the point contact-sample interface [35][36][37][38] . The conductance spectra at ~60 mK under different magnetic fields are plotted in Fig. 3d. The gap feature is suppressed by a field less than 0.3 T, which is much smaller than the Additional gap-like feature at low temperatures. We fitted the conductance spectra with the BTK model. Figure 4a plots the normalized conductance spectra of the point contact junction on the NbSe 2 /16 QL Bi 2 Se 3 at low temperatures down to 40 mK. The barrier strength parameter Z from the fittings is ~1 for all temperatures, indicating high tunneling barrier strength. The fitted gap value Δ and broadening parameter Γ versus  temperature T are shown in Fig. 4b. We find that at very low temperatures below 0.45 K, the fitting curves using the standard BTK model deviate from the experimental conductance spectra as shown in Fig. 4a. If we force to use a single gap fitting, the gap value from the fittings shows an abnormal decrease at low temperatures (circled in Fig. 4b), which cannot be true as the superconductivity and the proximity-coupling enhance with decreasing temperatures. The conductance curves can be fitted nicely using the BTK model above 0.45 K, indicating the point contact is in the ballistic regime and the anomaly at low temperature is not from diffusive or thermal contacts. Using the same Δ, Γ, and Z parameters as in the last good fitting curve at 0.45 K, a conductance curve is calculated for T = 40 mK and plotted together with the experimental data in Fig. 5. While the outside edges of peaks agree well for the two curves, the inner gap edge is narrower for the experimental data. The calculated curve is then subtracted from the experimental data and the difference is plotted in the top right inset of Fig. 5. The excess spectrum shows a clear peak feature at ~120 μV. The peak position remains unchanged as the temperature is increased from 40 mK to 260 mK. Figure 6a plots the low magnetic field dependence of the PCS spectra on the NbSe 2 /16 QL Bi 2 Se 3 heterostructure at T ~ 43 mK. Deviations of fittings using the BTK model from experimental data are also visible below 0.02 T. In PCS studies under magnetic field, Γ is often used to simulate the pair-breaking effect of a magnetic field in a first-order approximation 28 . We fitted the PCS data under magnetic field at both 60 mK and 1.8 K with the BTK model and observed a Γ/H ratio of ~3 meV/T at low magnetic field for both temperatures (Supplementary Information C). Using the Γ/H ratio and the BTK parameters listed in Fig. 5 and assuming that  the main gap at 159 μeV doesn't change in small magnetic fields, we employed a similar method to calculate the conductance difference between the experimental data and simulated curves. The results are plotted in Fig. 6b. Although the peak position does not change much, the peak magnitude at ~120 μV is suppressed by a small magnetic field ~0.03 T. From the temperature dependence and magnetic field dependence of the PCS data, an additional gap feature ~120 μeV at 40 mK seems to appear besides the induced bulk band gap ~159 μeV. This second gap feature is not observable in the spectra above 0.45 K, likely because that the thermal broadening (kT ~ 86 μeV/K) at high temperatures smears the difference between the two gaps (the two gap energy difference ~39 μeV at 40 mK) in the point contact spectra. Similarly, the second gap feature in the spectra is smeared in a small magnetic field ~0.03 T likely due to the broadening effect from the pair-breaking in magnetic fields. Spectroscopic measurement with much higher energy resolution is desired to resolve more accurately at what temperature and the magnetic field the second gap disappears. A similar second gap feature is also present in a 13 QL Bi 2 Se 3 sample at low temperatures (see Supplementary Information D). The second gap feature is ~210 μeV with a bulk gap ~0.3 meV at 0.4 K. The ratio of the second gap value to the bulk gap value is ~0.7, close to the two gap ratio in the16 QL Bi 2 Se 3 sample at similar temperatures. This indicates that the second gap feature in 16 QL and 13 QL samples are from the same origin. The second gap value decreases with increasing Bi 2 Se 3 thickness, but the ratio between the second gap and the bulk state gap stays constant, independent of the Bi 2 Se 3 thickness.

Discussions
There are several possible origins of multiple proximity-effect-induced gap values. First, in "soft" point contact measurement, the silver paint contact area is much larger than the real electrical contact size, parallel conductance channels may form in the contact area. In this case, a second gap measured from another contact will be present in the spectra. However, in our data, the second gap feature is observed in both 13 QL and 16 QL samples with a ratio ~0.7 to the main induced gap at 0.2 to 0.4 K. Therefore, it is not likely from the parallel contact channels to a non-uniform sample surface. Secondly, NbSe 2 is a multiband superconductor. High resolution scanning tunneling microscopy (STM) measurements on pure NbSe 2 single crystal reveals a main tunneling peak at 1.2 meV with a shoulder at 0.75 meV [39][40][41][42] . In our data, only one gap ~1.2 meV is visible down to low temperatures in the PCS spectra on pure NbSe 2 and NbSe 2 /Bi 2 Se 3 heterostructure with very thin Bi 2 Se 3 (see Fig. S1b in supplementary information). Therefore, the second gap feature is not from the multiple superconducting gaps in NbSe 2 . Thirdly, proximity effect is greatly affected by the boundary conditions 43 . In the case of S/N bilayer samples, multiple Andreev bound states may exist when the N layer thickness is larger than the proximity coherence length 44 . In our samples, the Bi 2 Se 3 film thickness is much smaller than the Bi 2 Se 3 proximity coherence length at low temperatures. Therefore, the two induced gap features are not from the multiple bound states in proximity coupled Bi 2 Se 3 bulk states.
In the previous ARPES studies on the NbSe 2 /Bi 2 Se 3 samples 20 , S.Y. Xu et al. showed that both the Bi 2 Se 3 bulk states and the topological surface states become superconducting due to the proximity effect from the superconducting NbSe 2 . Here our result on the same NbSe 2 /Bi 2 Se 3 heterostructures suggests that there is clearly a proximity-induced bulk state gap, but there is also a second gap at low temperatures which could be the topological surface state gap as observed in the ARPES measurements. While the gap ~159 μeV in the16 QL Bi 2 Se 3 sample is from the superconducting bulk states, the gap feature ~120 μeV at 40 mK could be a signature of the proximity-induced superconductivity in the Bi 2 Se 3 surface states on the top surface. In the ARPES measurements, it was reported that the surface-to-surface (interface) hybridization may enhance the helical pairing in the surface states on the top surface when the Bi 2 Se 3 layer thickness is below 6 QL. As Bi 2 Se 3 thickness increases (≥6 QL), the surface state wave function from the top surface and the interface become spatially separated. Therefore, in thick Bi 2 Se 3 samples (13 QL and 16 QL), NbSe 2 does not directly induce superconductivity in the top surface states through surface hybridization; the superconducting surface state gap at top surface is induced through the bulk bands of Bi 2 Se 3 . In our results, The ratio of the superconducting surface state gap to bulk state gap value is ~0.7 in both 13 QL and 16 QL samples between 0.2 K to 0.4 K, indicating a similar coupling strength from the bulk to the surface bands in different thickness samples. The second gap feature is only observed at ultra-low temperatures for all samples. This is largely due to that the energy gap of the surface states is very close to the bulk gap. Decreasing temperature improves the spectrum energy resolution by reducing the thermal broadening (kT ~ 86 μeV/K) in the PCS measurements. Our results suggest that cooling to ultra-low temperature is desired to resolve the superconducting surface states from the superconducting bulk states in electron spectroscopic measurements, which is consistent with other reports that the signatures from the TI surface states were only observed at very low temperatures 15,16 .
The ARPES measurements showed that the induced superconductivity in the surface states has a unique spin-momentum locking and Dirac-dispersion nature, different from the induced superconductivity in the bulk states. The standard BTK model employed in our PCS data fitting is based on the s-wave superconductivity. While it could describe the induced superconducting gap in the bulk states satisfactorily, it does not apply to the induced gap in the topological surface states due to its unique two dimensional helical-Cooper pairing phase. Indeed, we were not able to fit the point contact spectra of the 16 QL sample below 0.45 K using an extended BTK model with a linear combination of two different gaps. A model developed for helical pairing is desired to characterize the superconductivity in the topological surface states in the future.
In summary, we conducted point contact spectroscopy measurements on NbSe 2 /Bi 2 Se 3 heterostructures down to 40 mK. We observed a proximity-effect-induced superconductivity gap in the bulk of the TI Bi 2 Se 3 thin film, which is consistent with the bulk state gap values reported by the ARPES measurements on similar samples. The induced bulk gap value is ~159 μeV at 0.45 K for a 16 QL Bi 2 Se 3 on NbSe 2 sample. Below 0.45 K, excess conductance spectra appeared which may correspond to a second gap feature. This could be due to the topological superconductivity gap as observed by ARPES. The induced second gap value is ~120 μeV at 40 mK for a 16 QL Bi 2 Se 3 sample. The second gap spectra peaks were suppressed at temperatures above 0.45 K or in a magnetic field of ~0.03 T, likely due to thermal or field-induced broadening effect in the spectra. The second gap feature was also observed in a NbSe 2 /13 QL Bi 2 Se 3 sample with a similar two gap value ratio ~0.7 at around 0.4 K. As the ARPES measurements confirmed both the Bi 2 Se 3 bulk state and topological surface state become superconducting from the proximity effect, it is plausible that the second induced gap feature in the point contact spectra is due to the induced superconductivity in the topological surface states. The PCS result suggests that ultra-low temperature is desirable to separate the superconducting surface states from the bulk states in electron spectroscopic measurements.

Methods
Single phase epitaxial Bi 2 Se 3 /NbSe 2 heterostructure samples were fabricated using molecular beam epitaxy (MBE) method, which has been described in detail elsewhere 20 . The contacts were made by applying a small drop of silver paint between the top surface of the sample and a gold wire of 25 μm diameter. Immediately after point contacts were made on fresh NbSe 2 /Bi 2 Se 3 heterostructures, samples were cooled in a Quantum Design Physical Property Measurement System (PPMS) for four probe electrical measurements at temperatures down to 1.8 K. A Quantum Design dilution refrigerator system was used for measurements down to 40 mK. The differential conductance spectra were obtained by a lock-in technique in which a 262 Hz AC modulation of less than 50 μV was applied to the sample in addition to a DC current bias. Mathematical derivatives of the I-V data were also used to confirm the measurement, but with lower resolutions. The AC modulation amplitude was reduced to be less than k T B 1 2 for measurements below 1 K.
Data availability. The data generated during the current study are available from the corresponding author on request.