Fully-gapped superconductivity with preserved time-reversal symmetry in NiBi$_3$ single crystals

Abstract

We report a study of NiBi$_3$ single crystals by means of electrical-resistivity-, magnetization-, and muon-spin rotation and relaxation ($\mu$SR) measurements. As a single crystal, NiBi$_3$ adopts a needle-like shape and exhibits bulk superconductivity with $T_c \approx 4.1$ K. By applying magnetic fields parallel and perpendicular to the $b$-axis of NiBi$_3$, we establish that its lower- and upper critical fields, as well as the magnetic penetration depths show slightly different values, suggesting a weakly anisotropic superconductivity. In both cases, the zero-temperature upper critical fields are much smaller than the Pauli-limit value, indicating that the superconducting state is constrained by the orbital pair breaking. The temperature evolution of the superfluid density, obtained from transverse-field $\mu$SR, reveals a fully-gapped superconductivity in NiBi$_3$, with a shared superconducting gap $\Delta_0$ = 2.1 $k_\mathrm{B}$$T_c$ and magnetic penetration depths $\lambda_0$ = 223 and 210 nm for $H \parallel b$- and $H \perp b$, respectively. The lack of spontaneous fields below $T_c$ indicates that time-reversal symmetry is preserved in NiBi$_3$. The absence of a fast muon-spin relaxation and/or precession in the zero-field $\mu$SR spectra definitely rules out any type of magnetic ordering in NiBi$_3$ single crystals. Overall, our investigation suggests that NiBi$_3$ behaves as a conventional $s$-type superconductor.