Upper critical field in dirty two-band superconductors: breakdown of the anisotropic Ginzburg-Landau theory

TL;DR

This paper studies the upper critical magnetic field in dirty two-band superconductors, revealing the breakdown of Ginzburg-Landau theory due to strong anisotropies and disparities between bands, with implications for MgB₂.

Contribution

It demonstrates how large anisotropies and band disparities affect $H_{c2}$ and its angular dependence, showing limits of Ginzburg-Landau theory in such systems.

Findings

Temperature-dependent $H_{c2}$ anisotropy matches experimental data in MgB₂.

GL theory is valid only in a narrow temperature range near $T_c$.

Angular dependence of $H_{c2}$ deviates from effective-mass law even close to $T_c$.

Abstract

We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for MgB$_{2}$, is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies for two bands influence the in-plane $H_{c2}$ in a different way at high and low temperatures. This causes temperature-dependent $H_{c2}$ anisotropy, in accordance with recent experimental data in MgB$_{2}$. The three-dimensional band most strongly influences the in-plane $H_{c2}$ near $T_{c}$, in the Ginzburg-Landau (GL) region. However, due to a very large difference between the c-axis coherence lengths in the two bands, the GL theory is applicable only in an extremely narrow temperature range near $T_c$. The angular dependence of $H_{c2}$ deviates from a simple effective-mass law even near $T_c$.