Berry connection from many-body wave functions and superconductivity: Calculations by the particle number conserving Bogoliubov-de Gennes equations

TL;DR

This paper introduces a revised superconductivity theory based on Berry connection from many-body wave functions, enabling particle number conserving calculations with the Bogoliubov-de Gennes equations, applicable to cuprates.

Contribution

The authors develop a novel particle number conserving formalism for superconductivity that incorporates Berry connection, addressing limitations of the BCS theory.

Findings

Successfully calculated superconducting states using the new formalism.

Demonstrated applicability to cuprate superconductor models.

Revealed insights into the phase variable origin in superconductivity.

Abstract

A fundamentally revised version of superconductivity theory has been put forward by the present authors since the standard theory of superconductivity based on the BCS theory cannot explain superconductivity in cuprates discovered in 1986, and reexaminations on several experimental results on the conventional superconductors indicate the necessity for a fundamental revision. The revision is made on the origin of the superconducting phase variable, which is attributed to a Berry connection arising from many-body wave functions. With this revision, the theory can be cast into a particle number conserving formalism. We have developed a method to calculate superconducting states with the Berry connection using the particle number conserving version of the Bogoliubov-de Gennes equations. An example calculation is made for a model originally built for cuprate superconductors.