Theory of Higgs modes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductors
Fan Yang, Meng Wu
Abstract
By applying a microscopic gauge-invariant kinetic theory in $d$-wave superconductors, we analytically derive the energy spectra of the breathing Higgs mode and, in particular, rotating Higgs mode that is unique for the $d$-wave order parameter. An analytical investigation on their dynamic properties is also revealed. We show that the breathing Higgs mode is optically visible in the second-order regime. Whereas the rotating Higgs mode is optically inactive, we show that this mode can be detected in the pseudogap phase by a magnetic resonance experiment. It is interesting to find that with a longitudinal temperature gradient, the charge-neutral rotating Higgs mode generates a thermal Hall current by a magnetic field in the pseudogap phase, providing a unique scheme for its detection. This finding is likely to capture a very recent experimental observation of negative thermal Hall signal in cuprate superconductors [G. Grissonnanche et al., Nature (London) 571, 376 (2019)] for the overdoped pseudogap phase.