Observation of the superconducting proximity effect in the surface state of SmB6 thin films

The proximity effect at the interface between a topological insulator (TI) and a superconductor is predicted to give rise to chiral topological superconductivity and Majorana fermion excitations. In most TIs studied to date, however, the conducting bulk states have overwhelmed the transport properties and precluded the investigation of the interplay of the topological surface state and Cooper pairs. Here, we demonstrate the superconducting proximity effect in the surface state of SmB6 thin films which display bulk insulation at low temperatures. The Fermi velocity in the surface state deduced from the proximity effect is found to be as large as 10^5 m/s, in good agreement with the value obtained from a separate transport measurement. We show that high transparency between the TI and a superconductor is crucial for the proximity effect. The finding here opens the door to investigation of exotic quantum phenomena using all-thin-film multilayers with high-transparency interfaces.

has been attributed to the transition from bulk state-dominated conduction to surface statedominated conduction at low temperatures.
To see if there is any thickness dependent effect in our samples, we plot G at 2 K and 300 K as a function of film thickness (Figure 1). G at 300 K clearly displays a linear thickness dependence, indicating bulk transport. However, if the resistance plateau at low temperatures arises from the surface conduction, G at 2 K should be independent of the thickness and become a constant. This is indeed the case, as seen in Fig. 1, strongly suggestive of the presence of the surface conduction channel. We also measured the Hall resistance (R xy ) as a function of magnetic field, and calculated the sheet carrier concentration and the mobility of the SmB 6 thin films at 2 K. Both were found to be constant and independent of the film thickness (Supplementary Info.).
To determine the thickness of the surface conduction channel, we adopt a simple parallel conductance model where the electronic conduction is through two channels: a surface channel including contributions from both the top and the bottom surfaces and a bulk channel [24,31,43]. This model is valid for the temperature region where the Kondo gap of SmB 6 opens, which is a sufficient condition for the emergence of the topological surface state.
Therefore, we apply this model to the transport results in a temperature range below 120 K, at which the Kondo gap starts to open in SmB 6 [23]. The conductance of the surface channel is assumed to be temperature independent, and that of the bulk channel is temperature dependent and it can be described by a bulk resistivity and exponential function (i.e., Arrhenius equation). The total conductance of the SmB 6 thin film can then be described as: The use of the bulk conductivity in the G bulk term allows us to add a thickness of bulk channel (t bulk ) as fitting parameters, and subsequently to estimate a thickness of surface channel (t surface ) because the total film thickness is 2t surface + t bulk . The bulk conductivity, σ bulk,300K , is 7.66×10 5 S m -1 which is the slope of G at 300 K obtained from the data shown in Fig. 1. G , 2K is the G at 2 K for each sample, and a and w are the length and the width of the Hall bar channel, respectively. Fitting parameters are t bulk and E a , where E a is an activation energy. We fit the data for all samples using the equation (1) and (2). A representative fitting result is shown in Fig. 2a. The values of fitting parameters E a and t surface for the different thickness samples are shown in Figure 2b, and t surface is the thickness of the surface conduction channel,  [19]. This value is also in agreement with an independent estimate of v F obtained from the proximity effect study as discussed below.

B. Proximity effect
The superconducting proximity effect describes a phenomenon at a superconductor-normal metal interface where Cooper pairs diffuse into the normal metal resulting in the suppression of the critical temperature (T c ) of the superconductor while inducing surface or local superconductivity in the normal metal. We fabricated Nb/SmB 6 bilayers and observed a change in T c depending on the thickness of Nb layer due to the proximity effect at the interface. To characterize the proximity effect of the bilayers, we treat the Nb/SmB 6 bilayer as a superconductor/metal bilayer system, where the metallic layer in SmB 6 is the surface conducting channel (Figure 3), and we calculate the normal coherence length (ξ) and v F of SmB 6 thin films using the Usadel equation [16,47,48]. Assuming that ξ of SmB 6 (ξ SmB6 ) is longer than the thickness of the surface conducting channel of SmB 6 (ξ SmB6 > t surface ), the fitting equation for evaluating ξ SmB6 can be obtained by linearizing the Usadel equation [16]: where T cb and T cs represent the T c of the Nb/SmB 6 bilayer and the T c of a single Nb layer, respectively. T cb is evaluated by the Ginzburg-Landau equation, and γ and p(γ) are approximated by the expressions above [16]. γ represents the strength of the proximity effect between layers [47]. ρ Nb and ρ SmB6 are the residual resistivities of the Nb layer and the SmB 6 layer, respectively. ξ Nb and ξ SmB6 are the coherence length of the Nb layer and the SmB 6 layer, respectively. d Nb is the thickness of the Nb layer. To check the validity of the model, a series of Nb/Au bilayers were also fabricated, and the extracted value of ξ Au was in good agreement with their known value (~ 1µm).
For Nb/SmB 6 bilayers, d Nb was varied from 20 to 100 nm, and the thickness of SmB 6 layer was fixed to be 50 nm. Figure 4a and  layers. Based on x-ray diffraction and cross-sectional SEM of the bilayers, we do not believe there is any significant diffusion at the interface. Figure 4c shows the T cb /T cs of the Nb/SmB 6 system as a function of d Nb . As a comparison, one bilayer was made with an ex-situ interface: following the deposition of SmB 6 , it was exposed to air before the Nb layer was deposited. As represented in Fig. 4c, this sample shows a much higher T cb /T cs (i.e., higher T c ) than the corresponding in-situ bilayer. The proximity effect is very sensitive to the nature of the top most layer of SmB 6 . Specifically, degradation of the top most surface layer (e.g., due to oxidation) may reduce the boundary transparency, resulting in reduction of the proximity effect. This result demonstrates that insitu formed multilayers with clean interfaces are critical for establishing such a proximity effect at the interface of SmB 6 .
To evaluate ξ SmB6 , we performed a fitting process based on the expression discussed above.
Using measured values of ρ Nb = 8.5×10 -6 Ω·cm, the mean free path (l) of Nb was estimated from ρ Nb l = 3.75 × 10 −6 µΩ·cm 2 [50] (i.e., l = 4.4 nm) and we obtain ξ Nb = 0.852(ξ Nb(bulk) l) 1/2 = 11 nm where ξ Nb(bulk) is the known value of coherence length of Nb bulk (ξ Nb(bulk) = 38 nm) [51]. The thickness of the surface conducting channel of SmB 6 has been evaluated from our transport result (t surface = 7 nm), and the resistivity of the surface state was calculated to be 8.96×10 -5 Ω·cm (= ρ SmB6 ) at 2 K based on the above measured sheet conductance (ρ=2t surface /G ). The only unknown parameter is ξ SmB6 . The fitting result is shown as a red solid line in Fig. 4c, and we arrive at ξ SmB6 of 9.6 nm.
, where l of the SmB 6 thin film was assumed to be the grain size of our SmB 6 film, ≈ 4 nm [37], and we obtain v F ≈ 10 5 m/s at 2 K for SmB 6 . This v F is comparable to the value obtained from the transport study above (v F = 1.8×10 5 m/s), which implies that the observed superconducting proximity effect is attributed to the surface state of SmB 6 thin film. As a comparison, we have also carried out a fit using entire bulk of the SmB 6 thin film (even though, we have shown above that the bulk of the film is insulating): in this case, the fit does not provide a v F value consistent with the v F value obtained from the transport study. Our bilayer fabrication method in ultra high vacuum process excludes any degradation or contamination as the origin of the metallic surface state.  [54]. We have examined the Sm valence state in the surface of our SmB 6 thin films using x-ray photoemission spectroscopy at room temperature and found that it is similar to that of SmB 6 single crystals, which is ~ 2.7 [55] (Supplementary Info.). Therefore, we exclude chemical extrinsic effects as the origin of the large v F value observed here. We believe our high v F value is also due to the Kondo breakdown effect [54]. We note that t surface of ≈ 7 nm found in this study is consistent with the thickness predicted with the Kondo breakdown effect [54]. It has been reported that SmB 6 has three Dirac cones, each with its own slightly different value of v F [32,39] The measured v F in this study is therefore expected to be the average v F of the three Dirac cones.
With the ξ SmB6 obtained from the fitting above, we are able to evaluate γ which is a measure affects the I C R N product. It is interesting to note that significantly reduced I C R N products, presumably due to lack of the pristine surface of the TI during the fabrication process, have been observed in various studies on chalcogenide-TI-based Josephson junctions [5,6].
Specifically, the observed I C R N products in such studies are typically around 20 µV, which is far below the theoretical value, i.e., I C R N ~ πΔ(0)/2e ≈ 4.7 mV, for junctions in the clean limit [56] , [57]. Higher I C R N product junctions (and in particular high I C junctions) are always

IV. CONCLUSIONS
In summary, thickness-independent behavior in the transport properties was observed in ultrathin SmB 6 films, and the thickness of the surface state was deduced to be ≈ 7 nm. We provide first direct evidence of the superconducting proximity effect in the surface state of   To further investigate the surface state, we measured the Hall resistance (R xy ) as a function of magnetic field, and calculated the carrier concentration and the mobility of the SmB 6 thin films. As shown in Figure S1a, the Hall resistivity R xy of the 50 nm film appears to follow a straight line at 2 K in the entire magnetic field range we studied, suggesting that only one type of carriers contributes the electrical conductivity at 2 K and that bulk contribution is well suppressed: if the bulk contribution persists at such low temperatures, we would expect there to be multiple types of carriers with different concentrations and mobility values, leading to a nonlinear field dependence of R xy as it has been previously observed in other TIs such as Bi 2 Se 3 [1,2]. In contrast, the linear field dependence we observed indicates a presence of a single carrier in SmB 6 thin films at 2 K and the insulating bulk state attributed to the Kondo insulating nature. A mobility, µ of carriers can be calculated from µ= G☐ /en. We obtain both n and µ for each thin film and plot them as a function of film thickness in Figure S1b. Both n and µ appear to be constant regardless of the variation in the film thickness. The average values of n and µ are 1.87×10 16 cm -2 and 4.27 cm 2 /Vs, respectively. As expected from the observed behavior of G☐, because the surface conduction is dominant at low temperatures, the transport parameters (n and µ) are also independent of the thickness as seen in Fig. S1b.
-Valence state of the Sm ion near surface Figure S2. Investigating the valence state of Sm ion in a SmB 6 thin film Comparison of xray photoelectron spectroscopy (XPS) Sm 4d spectra of a SmB 6 thin film, a single crystal SmB 6 (measured) and bulk [3] (reference) To investigate the valence state of Sm ions, we used x-ray photoelectron spectroscopy (XPS) to measure the Sm 4d spectrum of a SmB 6 thin film. We also measured the Sm 4d spectrum of a SmB 6 single crystal as a reference. Details on the single crystal growth and properties can be found elsewhere [4,5]. The Sm 4d spectra of the SmB 6 thin film and the single crystal are shown in Fig. S2: the Sm 4d spectrum consists of Sm 2+ and Sm 3+ related multiplet structures at lower and higher energies than the binding energy of ~ 130 eV, respectively, which partially overlap. As shown in Fig.   S2, the Sm 4d spectra of the single crystal and the thin film are almost identical, implying that the Sm valence state in the thin film and the single crystal is the same.
For comparison, we also included the reported Sm 4d spectrum [3] of a bulk SmB 6 sample showing the mixed valence state in the ratio Sm 2+ :Sm 3+ ≈ 1:3 in Fig. S2. This J.-N. Chazalviel et al. [3] Thin film (this study) Intensity (a.u.) Binding Energy (eV) Single crystal