Fully anisotropic superconductivity with few Helmholtz Fermi-surface harmonics

TL;DR

This paper introduces a new efficient method for solving anisotropic Eliashberg equations in superconductivity, significantly reducing computational costs and enabling high-throughput material exploration.

Contribution

The authors develop a Helmholtz Fermi-surface harmonic representation that simplifies anisotropic superconductivity calculations, improving efficiency and accuracy over traditional methods.

Findings

Reproduced MgB₂ gap anisotropy with less computational effort.

Accurately determined transition temperature of YH₆ hydride in agreement with experiments.

Enabled high-throughput exploration of superconducting materials.

Abstract

We present an alternative representation for the anisotropic Eliashberg equations of superconductivity, whose numerical solution yields an efficiency gain of several orders of magnitude with respect to the conventional representation in momentum space. Our method is a practical realization of a long-sought approach, whose essence is a linear transformation from regular ${\bf k}$ space to a set of orthonormal functions defined as the solutions of the Helmholtz equation on the Fermi surface. In this way, all the anisotropy of the problem can be described by a handful of coefficients with built-in symmetry. We perform benchmark calculations on the gap anisotropy of MgB$_2$, and reproduce previous results at a remarkably reduced computational cost. Furthermore, we apply our methodology to efficiently determine the transition temperature of the compressed YH$_6$ hydride, obtaining very good agreement with recent experimental measurements. The simplification introduced by our method enables the high-throughput exploration of superconducting materials without having to resort to the isotropic approximation, and opens up possibilities towards first principles calculations of more advanced theories of superconductivity.