Geometric origin of supercurrents in Berry phase: Formula for computing currents from wavefunctions with correlation and particle number variation

TL;DR

This paper introduces a phase-based formula to compute supercurrents directly from microscopic wavefunctions, incorporating correlation and particle number variations, and unifies understanding of charge transport in superconductors and insulators.

Contribution

It provides a novel, wavefunction-based method for calculating supercurrents that accounts for correlations and particle number changes, bridging superconductors and insulators.

Findings

Derived a group velocity current from Berry phase independent of wave packet dynamics.

Identified a correlation-driven current component related to pairing correlations.

Formulated a unified framework for charge transport in conductors and insulators.

Abstract

The complexity of itinerant and many-body nature in Bardeen-Cooper-Schrieffer (BCS) wavefunctions has traditionally led to the use of coarse-grained order parameters for describing currents in superconductors (SC), rather than directly utilizing wavefunctions. In this work, we introduce a phase-based formula that enables the direct computation of currents from microscopic wavefunctions, accounting for correlation and particle number variations. Interestingly, the formulation draws parallels with insulators, suggesting a unified framework for understanding (intra-band) charge transport across two extremes of conductivity. A group velocity current $J_{band}{\propto}\frac{1}{\hbar}{\partial}_kE(k)$ is derived from Berry phase, independent of wave package dynamics, robust against correlation. Additionally, we identify a correlation-driven contribution, $J_{corr}$, which reveals that the pairing correlations ${\langle}c_kc_{-k}{\rangle}$ among dancing partners provide a current component beyond the velocity operator.