Two-gap superconductivity and topological surface states in TaOsSi

The occurrence of superconductivity in topological materials is considered as a promising route for realizing topological superconductors, a platform able to host the long-sought Majorana fermions in condensed matter. In this work, by using electrical transport and heat-capacity measurements, as well as first-principles band-structure calculations, we investigate the physical properties of TaOsSi, a superconductor with $T_c\approx 5.8$ K. The behavior of both its upper critical field and low-temperature heat-capacity suggest the existence of two superconducting gaps. More strikingly, first-principles calculations reveal gapless topological surface states in the present material. The evolution of the electrical resistivity with pressure (up to 50 GPa) was also investigated, and a “V-shaped” diagram of $T_c$ vs $P$ was found. Overall, our data suggest that TaOsSi is a new system where multiband superconductivity and topological surface states coexist and, hence, it may serve as a possible candidate in the search for topological superconductivity.

Figure 1

Powder XRD pattern and Rietveld refinement for TaOsSi. The blue line at the bottom indicates the residuals. The inset shows the orthorhombic crystal structure of TaOsSi.

Figure 2

(a) Temperature dependence of resistivity. Inset: At low temperature (above $T_c$), $\rho \left(T\right)$ is proportional to $T^2$, a behavior compatible with Fermi-liquid theory. (b) Temperature dependence of magnetic susceptibility for a zero-field cooling (ZFC) and a field cooling (FC) process. (c) Temperature dependence of heat capacity, plotted as $C/T$ versus $T^2$. The red solid line is a fit based on $C/T={\gamma }_n+\beta T^2+\delta T^4$.

Figure 3

(a) Temperature dependence of resistivity in different applied magnetic fields. (b) Temperature dependence of the upper critical field, as obtained by the $90\%$ and the $50\%$ criteria (see main text). Solid lines represent fits based on a two-band model.

Figure 4

(a) $\mathrm{\Delta }C$ versus $T$. Here $\mathrm{\Delta }C=C-C_n$, with $C_n$ being the heat capacity in the normal state. (b) The lower panel shows an enlarged view of the low-$T$ region, where $\mathrm{\Delta }C\left(T\right)$ is fit by using different gap-symmetry functions.

Figure 5

Electronic band-structure calculations for TaOsSi (a) without accounting for SOC and (b) including SOC.

Figure 6

(a) Bulk and surface first Brillouin zone, illustrating the high-symmetry points. (b) 3D bulk Fermi surfaces and color-coded Fermi velocities (blue is low velocity). (c) Calculated Fermi surfaces at the $k_x=0$ plane. (d) Surface-state spectra at a (100) section; bright red lines denote surface states.

Figure 7

(a) Temperature-dependent resistivity for different applied pressures. The inset is an enlarged view near the superconducting transition. (b) Pressure dependence of the superconducting transition temperature. $T_c\left(\text{onset}\right)$ and $T_c\left(\text{zero}\right)$ refer to the onset of SC transition and to the zero-resistivity SC transition temperature, respectively. The inset shows the resistivity vs pressure, measured at 10 and 300 K.