Higgs mode in electric-field-induced superconductors

We develop a theory for the Higgs (gap-amplitude) mode excitation in electric-field-induced (EFI) superconductors. The Higgs mode can be excited directly by an oscillating electric field in EFI superconductors since the gap value depends sensitively on the external electric field that induces superconducting carriers. The mass of the Higgs mode in EFI superconductors does not coincide with the threshold energy of pair-breaking two-particle excitations.

Figure 1

Multiband structure in electric-field-induced superconductors. Two electrons with momentum ${\mathbf{k}}_{Fn}$ and $-{\mathbf{k}}_{Fn}$ and with opposite spin in the same band form a Cooper pair.

Figure 2

Frequency dependence of real and imaginary parts of the pair-amplitude susceptibility $\mathrm{Re}{\chi }_1^R(\mathbf{0},\omega )$ and $\mathrm{Im}{\chi }_1^R(\mathbf{0},\omega )$.

Figure 3

Response of the gap function to a pump electric field. The solid line represents the time dependence of $\delta {\Delta }_1\left(t\right)$. The asymptotic behavior of $\delta {\Delta }_1\left(t\right)$ is well fitted by the function proportional to $cos({\omega }_{H}t-\delta )/t^2$ (dashed line).

Figure 4

Frequency dependence of the phase shift appearing in the response of the gap function to a steady electromagnetic wave.