Robust odd-parity superconductivity in the doped topological insulator ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$

We present resistivity and magnetization measurements on proton-irradiated crystals demonstrating that the superconducting state in the doped topological insulator ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($x=0.25$) is surprisingly robust against disorder-induced electron scattering. The superconducting transition temperature $T_c$ decreases without indication of saturation with increasing defect concentration, and the corresponding scattering rates far surpass expectations based on conventional theory. The low-temperature variation of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ follows a power law $[\mathrm{\Delta }\lambda \left(T\right)\sim T^2]$ indicating the presence of symmetry-protected point nodes. Our results are consistent with the proposed robust nematic $E_u$ pairing state in this material.

Figure 1

(a) The crystal structure of ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ derived from an ABC stacking of hexagonal sheets of Bi (green) and Se (red) atoms. The Nb ions (blue) sit in the van der Waals gap between quintuple layers of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ [21]. (b) View down the $c$ axis; the $y$ axis is chosen to lie in the mirror plane. (c) and (d) Schematic presentations of the effect of defect scattering on an $s$-wave gap with deep minima (c) and with symmetry-protected point nodes (d). Dark and light blue represent the gap amplitude before and after introduction of scattering, respectively.

Figure 2

Low-temperature resistivity of a single crystal of ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ showing suppression of $T_c$ and increase in the residual resistivity ${\rho }_0$ following multiple irradiations. The inset shows the resistivity up to room temperature with little change in curvature following repeated doses.

Figure 3

Normalized magnetic susceptibility of a single crystal of ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ as a function of temperature for various values of cumulative p-irradiation dose. The transition temperature $T_c$ is clearly suppressed with each dose given in p/${\mathrm{cm}}^2$.

Figure 4

Low-temperature variation of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ in a single crystal of ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ for multiple values of cumulative irradiation dose vs reduced temperature squared ${(T/T_c)}^2$. The linear fits (red, black lines) indicate quadratic behavior. As the dose increases, the temperature dependence remains quadratic, indicative of point nodes in the superconducting gap. Data are offset vertically for clarity of presentation. The top axis shows the corresponding $T/T_c$ values.

Figure 5

Evolution of $T_c$ with proton irradiation for several crystals of ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, as measured via transport (diamonds) and magnetic susceptibility (circles). The mustard diamonds and red circles are derived from the samples shown in Figs. 2 and 3, respectively. The inset shows $T_c/T_{c0}$ versus proton dose, whereas the main panel displays the same data as function of increase in residual resistivity, $\mathrm{\Delta }{\rho }_0$ (lower $x$ axis) and normalized scattering rate, $g^{\lambda }$ (top $x$ axis). For comparison, the $T_c/T_{c0}$ data versus $g^{\lambda }$ of p-irradiated ${\mathrm{BaFe}}_2$(${\mathrm{As}}_{1-x}{\mathrm{P}}_x$)${}_2$ (dashed line), ${\mathrm{He}}^{+}$-irradiated YBCO (red line), and the Abrikosov-Gor'kov prediction for $T_c/T_{c0}$ versus $g$ on a $100\times$ expanded scale (green line) are included.