Ab initiocalculations ofHc2in 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 and Hohenberg and Werthamer [Phys. Rev. 153, 493 (1967)] and shown explicitly by Butler for high-purity cubic Niobium [Phys. Rev. Lett. 44, 1516Lett. 44, (1980]. We derive an H c2 equation for classic type-II superconductors that 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 ab initio electronicstructure 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 .

Critical temperature and upper critical field of Li 2 Pd 3−x Cu x B (x=0.0, 0.1, 0.2) superconductors

“…The second unexpected behavior is an enhancement of the H C2 (T ) at low temperatures that deviates from the WHH theory. This enhancement has been related to different causes; strong electron-phonon coupling [28], anisotropic Fermi surface [29] and localization effects in highly disordered superconductors [30]. (T ).…”

Magnetic-Field Dependences of Thermodynamic Quantities in the Vortex State of Type-Ii Superconductors

“…This method has been powerful for (i) solving the Ginzburg-Landau equations 27 and the Bogoliubovde Gennes equations 28,29,30,31 and (ii) obtaining quantitative agreements on the upper critical field H c2 of Nb, NbSe 2 , and MgB 2 with Fermi surfaces from firstprinciples electronic-structure calculations. 25,26 Thus, the method may be more advantageous for the calculations of thermodynamic quantities in finite magnetic fields when realistic Fermi surfaces are used as inputs. It will also be convenient for microscopically calculating responses of the vortex-lattice state to external perturbations, 32 such as vortex-lattice oscillations.…”

“…Together with the equation to determine H c2 derived recently, 25 the above coupled equations form a basis for efficient numerical calculations of the Eilenberger equations for vortex-lattice states with arbitrary Fermisurface structures.…”

“…It should be noted, however, that those numerical studies all adopted simplified model Fermi surfaces instead of complicated Fermi surfaces for real materials. Indeed, recent theoretical studies 10,24,25,26 have clarified that detailed Fermi-surface structures are indispensable for the quantitative description of the vortex state.…”

“…We choose the gauge such that ∇·Ã = 0. The Eilenberger equation for the even-parity pairing without Pauli paramagnetism is given by 6,25 …”