Gauge-invariant electromagnetic responses in superconductors

Sena Watanabe; Haruki Watanabe

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arXiv · 2501.13722

Gauge-invariant electromagnetic responses in superconductors

Sena Watanabe·Haruki Watanabe

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Abstract

Gauge invariance is essential for making physically meaningful predictions. In superconductors, mean-field Hamiltonians that explicitly break $U(1)$ symmetry often yield gauge-dependent results. While this issue has been resolved for linear responses in conventional superconductors, a unified framework that also covers unconventional superconductors and nonlinear responses has yet to be established. In this study, we present a comprehensive theoretical framework that enables gauge-invariant calculations of electromagnetic responses at arbitrary orders in external fields, applicable to both conventional and unconventional superconductors. Our construction generalizes the consistent-fluctuation-of-the-order-parameter (CFOP) approach to full photon vertices and admits a diagrammatic representation of the response kernel in terms of Feynman diagrams.

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Sena Watanabe, Haruki Watanabe. 2025-01-23. Gauge-invariant electromagnetic responses in superconductors. https://arxiv.org/abs/2501.13722

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