BCS-like superconductivity in the noncentrosymmetric compounds Nb$_x$Re$_{1-x}$

We present research on the superconducting properties of Nb$_{x}$Re$_{1-x}$ ($x$ = 0.13-0.38) obtained by measuring the electrical resistivity $\rho(T)$, magnetic susceptibility $\chi(T)$, specific heat $C_P(T)$, and London penetration depth $\Delta\lambda(T)$. It is found that the superconducting transition temperature $T_c$ decreases monotonically with an increase of $x$. The upper critical field $B_{c2}(T)$ for various $x$ can be nicely scaled by its corresponding $T_c$. The electronic specific heat $C_e(T)/T$, penetration depth $\Delta\lambda(T)$, and superfluid density $\rho_{s}(T)$ demonstrate exponential behavior at low temperatures and can be well fitted by a one-gap BCS model. The residual Sommerfeld coefficient $\gamma_0(B)$ in the superconducting state follows a linear field dependence. All these properties suggest an \emph{s}-wave BCS-type of superconductivity with a very large $B_{c2}(0)$ for Nb$_{x}$Re$_{1-x}$ (0.13 $\leq x \leq$ 0.38).