Amplitude Higgs mode and admittance in superconductors with a moving condensate

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 $\delta \mathrm{\mid }\mathrm{\Delta }{\mathrm{\mid }}_{\mathrm{\Omega }}\exp (i\mathrm{\Omega }t)$ of the superconducting gap is excited by an external ac electric field ${\mathbf{E}}_{\mathrm{\Omega }}\exp (i\mathrm{\Omega }t)$ already in the first order in $\mathrm{\mid }{\mathbf{E}}_{\mathrm{\Omega }}\mathrm{\mid }$, 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 $\delta \mathrm{\mid }\mathrm{\Delta }{\mathrm{\mid }}_{\mathrm{\Omega }}$ has a resonance shape with a maximum at $\mathrm{\Omega }=2\mathrm{\Delta }$. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude $\delta \mathrm{\mid }\mathrm{\Delta }(t)\mathrm{\mid }$ contribute to the admittance $Y_{\mathrm{\Omega }}$. 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.