Ab initio methods for superconductivity

A Technical Review in Nature Reviews Physics

A Technical Review to introduce non-specialists to the simulation of superconducting materials from first principles has been published in Nature Reviews Physics.

Researchers from the Max Planck Institute of Microstructure Physics have recently published a Technical Review on modern theories and computational methods to predict the properties of conventional superconductors from first principles, i.e., directly from basic physical quantities of the material, such as the Coulomb force between the electrons and phonon frequencies, based on the principles of quantum mechanics. The work is published in Nature Reviews Physics.

Ab initio (= from first principles) theories of superconductivity allow computing material-specific properties such as the critical temperature and the superconducting gap of conventional (phonon-driven) superconductors with very high accuracy without any experimental input, which makes them a valuable tool to accelerate the pace at which new superconducting materials are discovered.

Although the fundamentals of the theory were laid down in the 1960s, it is only in the past 25 years that ab initio approaches have matured into standard tools for the prediction of superconducting properties. Importantly, the past decade has witnessed a new wave of theoretical and computational developments among which are GW calculations of the electron–phonon matrix elements, the inclusion of anisotropy effects in the Eliashberg equations and extensions to include dynamical Coulomb interactions (plasmonic pairing) and Coulomb vertex corrections (towards the description of spin-fluctuation pairing).

The Technical Review recently published on the 29^th of July in Nature Reviews Physics aims at giving an overview of the most recent technical developments in the field of ab initio superconductivity from the theory to code implementation in terms accessible to the non-expert reader.

 

Abstract

Modern ab initio theories of superconductivity allow characterizing and predicting phonon-mediated superconductors. In this Technical Review, we analyse Eliashberg theory, density functional theory for superconductors as well as McMillan and Allen–Dynes equations, providing a summary of the underlying approximations and capabilities. We highlight in simple terms and with examples the many sources of error, which may lead to inaccurate predictions, including limitations on the applicability of the methods, subtle convergence aspects and improper practices often adopted to simplify the treatment of Coulomb interactions. Additionally, we compare the accuracy of the various methods by computing the critical temperature (T_c) for a broad range of superconductors and benchmarking against experimental results. We find that even the simple McMillan and Allen–Dynes formulas give T_c distributions centred on the experimental values. The Eliashberg theory and density functional theory for superconductors yield more peaked distributions, strongly reducing the possibility of incorrect predictions.