Superfluid flow in disordered superconductors with Dynes pair-breaking scattering: depairing current, kinetic inductance, and superheating field

We investigate the effects of Dynes pair-breaking scattering rate $\mathrm{\Gamma }$ on the superfluid flow in a narrow thin-film superconductor and a semi-infinite superconductor by self-consistently solving the coupled Maxwell and Usadel equations for the BCS theory in the diffusive limit for all temperature $T$, all $\mathrm{\Gamma }$, and all superfluid momentum. We obtain the depairing current density $j_d(\mathrm{\Gamma },T)$ and the current-dependent nonlinear kinetic inductance $L_k(j_s,\mathrm{\Gamma },T)$ in a narrow thin-film and the superheating field $H_{sh}(\mathrm{\Gamma },T)$ and the current distribution in a semi-infinite superconductor, taking the nonlinear Meissner effect into account. The analytical expressions for $j_d(\mathrm{\Gamma },T){\mathrm{\mid }}_{T=0}$, $L_k(j_s, \Gamma, T)|{T=0}$,and$H{sh}(\Gamma, T)|_{T=0}$ are also derived. The theory suggests $j_d$ and $H_{sh}$ can be ameliorated by reducing $\mathrm{\Gamma }$, and $L_k$ can be tuned by a combination of the bias current and $\mathrm{\Gamma }$. Tunneling spectroscopy can test the theory and also give insight into how to engineer $\mathrm{\Gamma }$ via materials processing. Implications of the theory would be useful to improve performances of various superconducting quantum devices.