Fully-gapped superconductivity in single crystals of noncentrosymmetric Re${}_6$Zr with broken time-reversal symmetry

The noncentrosymmetric superconductor Re${}_6$Zr has attracted much interest due to the observation of broken time-reversal symmetry in the superconducting state. Here we report an investigation of the superconducting gap structure of Re${}_6$Zr single crystals by measuring the magnetic penetration depth shift $\mathrm{\Delta }\lambda (T)$ and electronic specific heat $C_e(T)$. $\mathrm{\Delta }\lambda (T)$ exhibits an exponential temperature dependence behavior for $T\ll T_c$, which indicates a fully-open superconducting gap. Our analysis shows that a single gap $s$-wave model is sufficient to describe both the superfluid density ${\rho }_s(T)$ and $C_e(T)$ results, with a fitted gap magnitude larger than the weak coupling BCS value, providing evidence for fully-gapped superconductivity in Re${}_6$Zr with moderate coupling.