Kavli Affiliate: Ke Wang
| First 5 Authors: Ke Wang, Rufus Boyack, K. Levin, ,
| Summary:
Observing the amplitude-Higgs mode in superconductors has been a central
challenge in condensed matter physics. Unlike the phase mode in the
electromagnetic (EM) response, the amplitude mode is not needed to satisfy
gauge invariance. Indeed, it couples to linear EM response properties only in
special superconductors that are associated with a pairing vector $mathbf{Q}
neq 0$. In this paper we characterize the amplitude-mode contribution within a
gauge-invariant treatment of the linear optical conductivity for these
non-uniform superconductors, noting that they are by their very nature
particularly vulnerable to pair-breaking from non-magnetic impurities. This
leads to inevitable damping of the Higgs mode. Our gauge-invariant formulation
provides an in-depth understanding of two sets of $f$-sum rules which must be
obeyed. We illustrate how difficult it is to disentangle the neutral amplitude
mode contributions from those of the charged quasi-particles. These
observations are presented in the context of an applied supercurrent, where we
observe a new low-frequency feature that reflects the superfluid density and
appears consistent with recent experiments.
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