Superheating fields of semi-infinite superconductors and layered superconductors in the diffusive limit: structural optimization based on the microscopic theory

The superheating field $H_{sh}$ of the Meissner state is thought to determine the theoretical field-limit of superconducting accelerator cavities. We investigate $H_{sh}$ of semi-infinite superconductors and layered structures in the diffusive limit using the well-established quasiclassical Green's function formalism of the BCS theory. The coupled Maxwell–Usadel equations are self-consistently solved to obtain the spatial distributions of the magnetic field, screening current density, penetration depth, pair potential, and $H_{sh}$. For a semi-infinite superconductor in the diffusive limit, we obtain $H_{sh}=0.795H_{c0}$ at the temperature $T\to 0$. Here, $H_{c0}$ is the thermodynamic critical-field at the zero temperature. By laminating a superconducting film (S) with the thickness $d$ on a semi-infinite superconductor (Σ), we can engineer $H_{sh}\left(d\right)$ of the layered structure. When $d$ is the optimum thickness $d_m$, $H_{sh}$ can be larger than that of the simple semi-infinite superconductors made from the S and Σ materials: $H_{sh}\left(d_m\right)>max\{H_{sh}^{\text{(S)}},H_{sh}^{\left(\Sigma \right)}\}$. The present study addresses the calculation of $H_{sh}$ of the dirty heterostructure using the microscopic theory from beginning to end for the first time, which contributes to the microscopic understanding of the surface engineering for pushing up the accelerating gradient of superconducting cavities for particle accelerators. (paper)