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

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 $J_{band}\propto \frac{1}{\hslash }{\partial }_{k}E(k)$ 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 $⟨c_k{c}_{-k}⟩$ among dancing partners provide a current component beyond the velocity operator.

11 pages, 2 figures

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