Amplitude Higgs mode and admittance in superconductors with a moving condensate

Abstract

We consider the amplitude (Higgs) mode in a superconductor with a condensate flow (supercurrent). We demonstrate that, in this case, the amplitude mode corresponding to oscillations $\delta |\Delta {|}_{\Omega }\exp (i\Omega t)$ of the superconducting gap is excited by an external ac electric field ${\mathbf{E}}_{\Omega }\exp (i\Omega t)$ already in the first order in $|{\mathbf{E}}_{\Omega }|$, so that $\delta |\Delta {|}_{\Omega }\propto ({\mathbf{v}}_0{\mathbf{E}}_{\Omega })$, where ${\mathbf{v}}_0$ is the velocity of the condensate. The frequency dependence $\delta |\Delta {|}_{\Omega }$ has a resonance shape with a maximum at $\Omega =2\Delta$. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude $\delta |\Delta (t)|$ contribute to the admittance $Y_{\Omega }$. We provide a formula for admittance of a superconductor with a supercurrent. The predicted effect opens new ways of experimental investigation of the amplitude mode in superconductors and materials with superconductivity competing with other states.

accepted for publication in PRL

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