Superconductive superheating field for finiteκ

Abstract

We have calculated analytically the superheating fieldH _sh for bulk superconductors, correct to second order inκ. We find${{H_{sh} } \mathord{\left/ {\vphantom {{H_{sh} } {H_c }}} \right. \kern-\nulldelimiterspace} {H_c }} = (\kappa ^{ - \tfrac{1}{2}} 2^{ - \tfrac{1}{4}} ) \cdot ({{1 + 15\sqrt 2 \kappa } \mathord{\left/ {\vphantom {{1 + 15\sqrt 2 \kappa } {32}}} \right. \kern-\nulldelimiterspace} {32}})$, which agrees well with numerical computations forκ<0.5. The surface order parameter is$f_0 (H_{sh} ) = ({1 \mathord{\left/ {\vphantom {1 {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }})({{1 - 7\sqrt {2\kappa } } \mathord{\left/ {\vphantom {{1 - 7\sqrt {2\kappa } } {32}}} \right. \kern-\nulldelimiterspace} {32}})$, and the penetration depth is${{\lambda (H_{sh} )} \mathord{\left/ {\vphantom {{\lambda (H_{sh} )} {\lambda (0)}}} \right. \kern-\nulldelimiterspace} {\lambda (0)}} = \sqrt 2 ({{1 + 3\sqrt 2 \kappa } \mathord{\left/ {\vphantom {{1 + 3\sqrt 2 \kappa } {32}}} \right. \kern-\nulldelimiterspace} {32}})$.