Gauge-invariant microscopic kinetic theory of superconductivity: Application to the optical response of Nambu-Goldstone and Higgs modes
F. Yang, M. W. Wu
DOI 10.1103/PhysRevB.100.104513 · Physical Review B
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Abstract
We show that the gauge-invariant kinetic equation of superconductivity provides an efficient approach to study the electromagnetic response of the gapless Nambu-Goldstone and gapful Higgs modes on an equal footing. We prove that the Fock energy in the kinetic equation is equivalent to the generalized Ward's identity. Hence, the gauge invariance directly leads to the charge conservation. Both linear and second-order optical responses are analytically investigated. The linear response of the Higgs mode vanishes in the long-wave limit, whereas the linear response of the Nambu-Goldstone mode interacts with the long-range Coulomb interaction, causing the original gapless energy spectrum effectively lifted up to the plasma frequency as a result of the Anderson-Higgs mechanism, consistent with previous work. The second-order response exhibits interesting physics. On the one hand, a finite second-order optical response of the Higgs mode is obtained in the long-wave limit. We reveal that this response, which has been experimentally observed, is attributed solely to the drive effect rather than the widely considered Anderson-pump effect. On the other hand, the second-order optical response of the Nambu-Goldstone mode, free from the influence of the long-range Coulomb interaction and hence the Anderson-Higgs mechanism, is predicted. We find that both Anderson-pump and drive effects play important role in this response. A tentative scheme to detect this second-order response is proposed.