{\em Ab Initio} Calculations of $\bm H_{c2}$ in Type-II Superconductors: Basic Formalism and Model Calculations

TL;DR

This paper derives an $H_{c2}$ equation for type-II superconductors that accounts for anisotropic Fermi surfaces and energy gaps, enabling more accurate predictions of critical fields using ab initio calculations.

Contribution

It introduces a formalism for calculating $H_{c2}$ in anisotropic superconductors using ab initio Fermi surface data, improving quantitative understanding.

Findings

Fermi surface anisotropy significantly affects $H_{c2}$ near $T_c$.

Enhanced $h^{*}(T/T_{c})$ near Brillouin zone boundary.

Upward curvature of $H_{c2}$ curve explained by Fermi surface shape.

Abstract

Detailed Fermi-surface structures are essential to describe the upper critical field $H_{c2}$ in type-II superconductors, as first noticed by Hohenberg and Werthamer [Phys. Rev. {\bf 153}, 493 (1967)] and shown explicitly by Butler for high-purity cubic Niobium [Phys. Rev. Lett. {\bf 44}, 1516 (1980)]. We derive an $H_{c2}$ equation for classic type-II superconductors which is applicable to systems with anisotropic Fermi surfaces and/or energy gaps under arbitrary field directions. It can be solved efficiently by using Fermi surfaces from {\em ab initio} electronic-structure calculations. Thus, it is expected to enhance our quantitative understanding on $H_{c2}$. Based on the formalism, we calculate $H_{c2}$ curves for Fermi surfaces of a three-dimensional tight-binding model with cubic symmetry, an isotropic gap, and no impurity scatterings. It is found that, as the Fermi surface approaches to the Brillouin zone boundary, the reduced critical field $h^{*}(T/T_{c})$, which is normalized by the initial slope at $T_{c}$, is enhanced significantly over the curve for the spherical Fermi surface with a marked upward curvature. Thus, the Fermi-surface anisotropy can be a main source of the upward curvature in $H_{c2}$ near $T_c$.