Optical response of Higgs mode in superconductors at clean limit

F. Yang; M. W. Wu

doi:10.1016/j.aop.2023.169312

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arXiv · 2111.06128

Optical response of Higgs mode in superconductors at clean limit

F. Yang·M. W. Wu

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Abstract

The phenomenological Ginzburg-Landau theory and the charge conservation directly lead to the finite Higgs-mode generation and vanishing charge-density fluctuation in the second-order optical response of superconductors at clean limit. Nevertheless, recent microscopic theoretical studies of the second-order optical response, apart from the one through the gauge-invariant kinetic equation [Yang and Wu, Phys. Rev. B {\bf 100}, 104513 (2019)], have derived a vanishing Higgs-mode generation but finite charge-density fluctuation at clean limit. We resolve this controversy by re-examining the previous derivations with the vector potential alone within the path-integral and Eilenberger-equation approaches, and show that both previous derivations contain mathematical flaws. After fixing these flaws, a finite Higgs-mode generation through the drive effect of vector potential is derived at clean limit, exactly recovering the previous result from the gauge-invariant kinetic equation as well as Ginzburg-Landau theory. By further extending the path-integral approach to include electromagnetic effects from the scalar potential and phase mode, in the second-order response, a finite contribution from the drive effect of scalar potential to the Higgs-mode generation at clean limit as well as the vanishing charge-density fluctuation are derived, also recovering the results from the gauge-invariant kinetic equation. Particularly, we show that the phase mode is excited in the second-order response, and exactly cancels the previously reported unphysical excitation of the charge-density fluctuation, guaranteeing the charge conservation.

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F. Yang, M. W. Wu. 2021-11-11. Optical response of Higgs mode in superconductors at clean limit. https://doi.org/10.1016/j.aop.2023.169312

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