Higgs-mode signature in ultrafast electron dynamics in superconducting graphene

Abstract

We theoretically investigate the effect of superconductivity on the ultrafast electron dynamics in graphene interacting with an ultrashort linearly polarized optical pulse. The optical pulse, with frequency greater than 1 THz, quadratically couples to the Higgs (amplitude) mode and therefore can excite the Higgs-mode oscillations in superconductors, leading to quenching superconducting excitation energy, even in $s$-wave pairing symmetry. Since the duration of the used pulse is less than the electron scattering time in graphene (10--100 fs), the electron dynamics driven by the electric field of pulse remains coherent and is described within the tight-binding model of graphene. We show that the electron-electron and hole-hole transitions from valence to conduction bands are substantially irreversible, with a large residual population of the conduction band, which implies quantum electron dynamics being highly nonadiabatic. Such a feature of the system allows us to clearly project the effect of Higgs oscillations on the electric dipole moment created by the electric field of the pulse between the conduction and valence bands. In particular, we study the impact of the superconducting pair potential on the conduction band population, where the strong pulse causes electronlike and holelike quasiparticles transitions between the conduction and valence bands. The conduction band electron redistribution in honeycomb Dirac points results in almost asymmetric hot spots in two different $K$ and ${K}^{\ensuremath{'}}$ valleys after the pulse ends, which may be interpreted as the valley polarization effect due to the presence of superconductivity. The redistribution of hot spots around Dirac points is in good agreement with the Higgs-mode oscillations (corresponding to the electric dipole moment pattern), and the number of spots weakly depends on the superconducting gap, whereas it has a strong dependence on the ultrashort-pulse intensity.