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

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 $h^{\ast }(T/T_c)$, 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 $T_c$.

arXiv comment16 pages, 4 figures, results from model calculations included

References in corpus (8)

• First-Principles Calculation of the Superconducting Transition in MgB2 within the Anisotropic Eliashberg Formalism
• Crossing lattices, vortex chains, and angular dependence of melting line in layered superconductors
• Fermi surface topology and the upper critical field in two-band superconductors - application to MgB2
• Anisotropy of the upper critical field in superconductors with anisotropic gaps. Anisotropy parameters of MgB2
• Magnetic Oscillations and Quasiparticle Band Structure in the Mixed State of Type-II Superconductors
• Theory of de Haas-van Alphen Effect in Type-II Superconductors
• Revised Calculation of ${\mathbf{\kappa }}_2(T)$ for s-wave Type-II Superconductors
• Entropy and Spin Susceptibility of s-wave Type-II Superconductors near $H_{c2}$

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