Schroedinger representation of quantum mechanics, Berry connection, and superconductivity

TL;DR

This paper links the Berry phase arising from many-electron interactions in the Schrödinger representation to superconductivity, providing a new perspective on the superconducting ground state and its relation to BCS theory.

Contribution

It introduces a novel interpretation of the Berry phase as a source of superconductivity within the Schrödinger framework, connecting geometric phases to physical ground states.

Findings

Berry phase from many-electron interactions can induce superconductivity.

Superconducting ground state corresponds to a non-trivial Berry connection.

Connection established between this approach and traditional BCS theory.

Abstract

The standard quantum mechanical electronic state calculations for molecules and solids uses the Schroedinger representation where the momentum conjugate to the coordinate $q_r$ is given by $-hbar {partial over {partial q_r}}$. This formalism contains an extra $U(1)$ phase degree-of-freedom. We show that it can be regarded as a Berry phase arising from many-electron interaction, and when it is non-trivial, it gives rise to a current carrying ground state identified as the superconducting ground state. The connection between this superconducting state and the BCS one is presented.