Upper critical field $H_{c_2}$ in two-band superconductor

Abstract

It was obtained the equation for the definition of upper critical field $% H_{c_2}$ in the system with two overlapping energetic bands on the Fermi surface, which is valid for the whole temperature interval $0 \leq T < T_c$. The analytic expressions for the value $H_{c_2}$ at $T \sim T_c$ and $T \ll T_c$ cases were defined. The possibility of changing the curvature $H_{c_2} (T)$ with changing of the electrons speed ratio $v_1 / v_2$ on different cavities on the Fermi surface was revealed. It was obtained the qualitative accordance with experimental data for the intermetallic compound $MgB_2$.