A gauge-invariant formulation of optical responses in superconductors
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929557135687680 |
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| author | Watanabe, Sena Watanabe, Haruki |
| author_facet | Watanabe, Sena Watanabe, Haruki |
| contents | Superconductors are often discussed in the mean-field approximation that breaks $U(1)$ symmetry. Since the $U(1)$ symmetry underlies the charge conservation, naive application of response theory sometimes gives results that are not gauge-invariant. We study the effect of vertex corrections on the electromagnetic responses of superconductors by employing the gauge-invariant formulation, called consistent fluctuations of order parameters, that manifestly satisfy the Ward identity. For inversion broken two-band superconductors, we find that the linear and second-order optical responses are significantly affected by vertex corrections and the conductivities near the gap energy almost completely disappear. We also investigate the linear optical responses in $d$-wave superconductors and obtained qualitatively different results compared to the result using the solution to the Bethe-Salpeter equation. The full photon vertex used in our study, manifestly satisfies the Ward identity. Our results demonstrate the fundamental importance of vertex corrections in exploring optical responses in superconductors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18679 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gauge-invariant formulation of optical responses in superconductors Watanabe, Sena Watanabe, Haruki Superconductivity Statistical Mechanics Strongly Correlated Electrons Superconductors are often discussed in the mean-field approximation that breaks $U(1)$ symmetry. Since the $U(1)$ symmetry underlies the charge conservation, naive application of response theory sometimes gives results that are not gauge-invariant. We study the effect of vertex corrections on the electromagnetic responses of superconductors by employing the gauge-invariant formulation, called consistent fluctuations of order parameters, that manifestly satisfy the Ward identity. For inversion broken two-band superconductors, we find that the linear and second-order optical responses are significantly affected by vertex corrections and the conductivities near the gap energy almost completely disappear. We also investigate the linear optical responses in $d$-wave superconductors and obtained qualitatively different results compared to the result using the solution to the Bethe-Salpeter equation. The full photon vertex used in our study, manifestly satisfies the Ward identity. Our results demonstrate the fundamental importance of vertex corrections in exploring optical responses in superconductors. |
| title | A gauge-invariant formulation of optical responses in superconductors |
| topic | Superconductivity Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2410.18679 |