Superconductivity by Berry connection from many-body wave functions: revisit to Andreev$-$Saint-James reflection and Josephson effect

TL;DR

This paper proposes a revised theory of superconductivity where the phase originates from a Berry connection in many-body wave functions, explaining phenomena like Andreev reflection and Josephson effect through this new framework.

Contribution

It introduces a Berry connection-based origin of the superconducting phase, challenging the traditional electron-pairing explanation and providing a new perspective on superconducting phenomena.

Findings

Superconductivity arises from a non-trivial Berry connection in many-body wave functions.

The phase variable is linked to a Berry connection, not solely to electron-pairing.

Reinterpretation of Andreev reflection and Josephson effect as consequences of Berry connection.

Abstract

Although the standard theory of superconductivity based on the BCS theory is a successful one, several experimental results indicate the necessity for a fundamental revision. We argue that the revision is on the origin of the phase variable for superconductivity; this phase appears as a consequence of the electron-pairing in the standard theory, but its origin is a Berry connection arising from many-body wave functions. When this Berry connection is non-trivial, it gives rise to a collective mode that generates supercurrent; this collective mode creates number-changing operators for particles participating in this mode, and these number-changing operators stabilize the superconducting state by exploiting the Cooper instability. In the new theory, the role of the electron-pairing is to stabilize the nontrivial Berry connection; it is not the cause of superconductivity. In BCS superconductors, however, the simultaneous appearance of the nontrivial Berry connection and the electron-pairing occurs. Therefore, the electron-pairing amplitude can be used as an order parameter for the superconducting state. We revisit the Andreev$-$Saint-James reflection and the Josephson effect. They are explained as consequence of the presence of the Berry connection. Bogoliubov quasiparticles are replaced by the particle-number conserving Bogoliubov excitations that describe the transfer of electrons between the collective mod and single particle mode.