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

TL;DR

This paper derives equations for the upper critical magnetic field in two-band superconductors across all temperatures, revealing how electron velocity ratios influence the field's temperature dependence, with results aligning with experimental data for MgB₂.

Contribution

It provides a comprehensive analytical framework for calculating $H_{c_2}$ in two-band superconductors valid for all temperatures, including the effects of electron velocity ratios.

Findings

Derived equations for $H_{c_2}$ valid for all T

Identified how electron velocity ratios affect $H_{c_2}(T)$ curvature

Qualitative agreement with experimental data for MgB₂

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 $MgB_2$.