Schroedinger representation of quantum mechanics, Berry connection, and superconductivity

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 $-hbarpartialoverpartial{q}_r$. 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.

References in corpus (2)

• Theory of Supercurrent in Superconductors
• London moment, London's superpotential, Nambu-Goldstone mode, and Berry connection from many-body wave functions

Cited by in corpus (4)

• Constrained Hamiltonian dynamics for electrons in magnetic field and additional forces besides the Lorentz force acting on electrons
• Supercurrent and Electromotive force generations by the Berry connection from many-body wave functions
• Toward the detection of spin-vortex-induced loop currents in a single bilayer Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ thin film and their possible use as qubits: Model calculations for three nano-island architecture
• Semi-classical understanding of flux quantization in superconductors