Kavli Affiliate: Ke Wang
| First 5 Authors: Ke Wang, Rufus Boyack, K. Levin, ,
| Summary:
Observing the “Higgs" or amplitude mode in superconductors has been a
central challenge in condensed matter physics. Moreover, arriving at a
theoretical understanding of this mode and how it is accessible in, say,
conductivity experiments presents an additional challenge as here one needs to
satisfy gauge invariance in the presence of disorder. In this paper, we
characterize the Higgs contribution within a fully gauge-invariant treatment of
the linear optical conductivity, $sigma(omega)$, for a disordered
superconductor carrying a uniform supercurrent. As a consequence of gauge
invariance, there are two distinct charge conservation laws underlying the
linear electromagnetic response with two associated sets of $f$-sum rules. An
interesting finding from the Higgs-related sum rule is that the imaginary part
of $sigma(omega)$ yields an anisotropic, textit{negative} $1/omega$
contribution in the THz regime. This is relevant to device applications and
appears to be consistent with recent experiments. The work presented here
emphasizes how difficult it is to disentangle the neutral amplitude mode
contributions from those of the charged quasi-particles and we demonstrate why
this is the case.
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