The pressure-enhanced superconducting phase of Sr$_x$-Bi$_2$Se$_3$ probed by hard point contact spectroscopy

The superconducting systems emerging from topological insulators upon metal ion intercalation or application of high pressure are ideal for investigation of possible topological superconductivity. In this context, Sr-intercalated Bi$_2$Se$_3$ is specially interesting because it displays pressure induced re-entrant superconductivity where the high pressure phase shows almost two times higher $T_c$ than the ambient superconducting phase ( $T_C\sim$ 2.9 K). Interestingly, unlike the ambient phase, the pressure-induced superconducting phase shows strong indication of unconventional superconductivity. However, since the pressure-induced phase remains inaccessible to spectroscopic techniques, the detailed study of the phase remained an unattained goal. Here we show that the high-pressure phase can be realized under a mesoscopic point contact, where transport spectroscopy can be used to probe the spectroscopic properties of the pressure-induced phase. We find that the point contact junctions on the high-pressure phase show unusual response to magnetic field supporting the possibility of unconventional superconductivity.

In superconductors, due to particle-hole symmetry, the positive and negative energy eigenstates of the Bogoliubov-DeGennes Hamiltonian come in pairs [1,2]. In the superconducting ground state, the negative-energy eigenstates are fully occupied. Therefore, as in case of insulators, depending on the dimension and the symmetries of the system, various topological numbers (e.g., the Chern number) for the occupied states can be defined [3][4][5][6]. If non-zero topological numbers exist for a superconductor, that can be classified as a "topological" superconductor [7][8][9][10]. By this definition, when certain unconventional superconductors display nodes in the order parameter symmetry, the node themselves might have non-zero topological numbers thereby making the superconductors "weakly" topological.
On the other hand, in strong topological superconductors, the non-zero topological numbers can exist along with a fully gapped bulk superconducting gap. Hence, characterizing the topological nature of strong topological superconductors is a challenging task. However, due to topological restrictions, the surface of such superconductors host gap-less modes which can be detected by surface sensitive spectroscopic techniques [11][12][13][14][15]. Potentially, point-contact Andreev reflection can be a powerful technique to probe transport through such topological surface states in a topological superconductor [13,[16][17][18]. One popular route to possibly achieving topological superconductivity is doping charge carriers through metal intercalation in topological insulators like Bi 2 Se 3 [19][20][21][22]. ARPES experiments have confirmed that at the required doping level for superconductivity (∼ 2 × 10 20 cm −3 ) in charge doped Bi 2 Se 3 systems, there is still significant separation in the momentum space between the topological surface states and the bulk states [22]. Hence, it is expected that when the bulk superconducting phase leads to proximity-induced superconductivity on the surface, due to the inherent topological nature of the surface states, the proximity induced phase should become a 2D topological superconductor [10,14,15,23]. Another potentially interesting way of inducing superconductivity in a topological insulator is through applying pressure [24][25][26][27]. A pressure-induced superconducting phase was indeed found in undoped Bi 2 Se 3 [27]. A more interesting pressure-induced superconducting phase was seen to appear in Sr-intercalated Bi 2 Se 3 which shows ambient superconductivity below T c = 2.9 K [28]. In this case, superconductivity was first seen to disappear with applying pressure and re-emerge at higher pressure [26]. The high-pressure re-entrant superconducting phase was found to be interesting owing to a significantly higher T c compared to the T c of the ambient superconducting phase of Sr-Bi 2 Se 3 . More importantly, the pressure-induced re-emerged phase showed strong signatures of unconventional superconductivity indicating a high possibility of the pressure-induced superconducting phase of Sr-Bi 2 Se 3 being topological in nature. However, because technologically it is extremely challenging to perform spectroscopic investigation of the re-entrant phase, the exact nature of superconductivity in this phase remained poorly understood. In this paper, we discuss a unique way of realizing such a superconducting phase by applying uniaxial pressure under a point contact, where the superconducting phase can be investigated through mesoscopic transport spectroscopy.
We have performed experiments on high quality single crystals of Sr 0.1 Bi 2 Se 3 . The bulk magnetization (Figure 1(a)) and transport measurements (Figure 1(b)) revealed a critical temperature T c ∼ 2.9 K below which the system superconducts. The high quality of the crystals were further confirmed by atomic resolution scanning tunnelling microscopy and spectroscopy. As shown in Figure 1(c), the atomic lattice is seen with very low defect density. Tunnelling spectroscopy revealed a fully formed superconducting gap that evolves systematically with increasing temperature and near 2 K the spectra become too broad for the gap to be clearly seen. The gap also evolves systematically with magnetic field before being almost completely suppressed at 15 kG ( Figure 1 After that, we continued pressing the tip harder onto the crystal surface. During the process, we found signature of superconductivity at a temperature higher than the T c of pristine Sr-Bi 2 Se 3 . As it is seen in Figure 3(a), upon applying large pressure under the point contact, superconductivity at a higher temperature is achieved, but now due to large force   8 K which corresponds to the known pressure-induced re-entrant superconducting phase of Sr-Bi 2 Se 3 [26]. As it is seen in the point contact R − T data, the transition is broad and at a relatively lower temperature (around 6 K), another transition like feature is seen.
These could be attributed to multiple electrical contacts with different contact geometries formed. Each contact may experience different pressure due to the difference in their effective contact area. Comparing the measured T c with the published literature [26], we estimate the approximate pressure experienced by the superconducting region under the point contact to be 9 GPa.
In order to gain further understanding on the pressure-enhanced superconducting phase, we carried out detailed temperature and magnetic field dependent experiments. As seen in   (Figure 3(f)). For all the micro-constrictions, the critical current is seen to decrease at a slow rate. For the constriction with highest critical current (red dots in Figure   3(f)), the critical current shows slight increase at lower fields and then starts decreasing slowly. At a field of 6 kG, the critical current has become only half of the zero field value.
The over-all superconductivity-related spectral features completely disappear at 7.5 kG.
In order to find out whether the unusual magnetic field dependence is also seen in the transport experiments, we have analyzed the R vs. T data of the thermal limit point contact obtained at different magnetic fields. The field-dependent R − T curves are shown in Figure 4(a). We have tracked the shift in transition at higher temperature with magnetic field to construct the H − T phase diagram. As shown in Figure 4 phase [26].
It should be noted that despite multiple attempts, a ballistic point contact could not be realized in this phase as during our efforts to reduce the contact diameter through controlled withdrawal of the tip, the effective pressure also decreased thereby causing a sudden disappearance of the pressure-induced phase.