London moment, London's superpotential, Nambu-Goldstone mode, and Berry connection from many-body wave functions

TL;DR

This paper proposes a revised theory of superconductivity incorporating London's superpotential and Berry phase, resolving the discrepancy in the London moment's mass and replacing the Nambu-Goldstone mode with a Berry connection-induced collective mode.

Contribution

It introduces a new framework that integrates Berry phase effects into superconductivity theory, explaining the free electron mass in the London moment and altering the understanding of collective excitations.

Findings

The free electron mass appears in the London moment when Berry phase is included.

The induced current is stable and derived from free energy, not linear response.

The Nambu-Goldstone mode is replaced by a Berry connection-induced collective mode.

Abstract

Although the standard theory of superconductivity based on the BCS theory is a successful one, there are several experimental results that indicate the necessity for fundamental revisions. One of them is the mass in the London moment. Experiments indicate the mass in the London moment is the free electron mass although the BCS theory and its extension predict it to be an effective mass. We show that this discrepancy is lifted if we install the London's superpotential in the theory, and identify it as the Berry phase arising from the many-body wave functions. Then, the induced current by the applied magnetic field becomes a stable current calculated using the free energy in contrast to the linear response current assumed in the standard theory which yields the Nambu-Goldstone mode. The Nambu-Goldstone mode arising from the breakdown of the global $U(1)$ gauge invariance in the standard theory is replaced by the collective mode arising from the Berry connection. Then, the free electron mass appears in the London moment.