Gauge-invariant theory of optical response to THz pulses in s-wave and ($s$+$p$)-wave superconducting semiconductor quantum wells

Abstract

We investigate the optical response to the THz pulses in the s-wave and ($s$+$p$)-wave superconducting semiconductor quantum wells by using the gauge-invariant optical Bloch equations, in which the gauge structure in the superconductivity is explicitly retained. By using the gauge transformation, not only can the microscopic description for the quasiparticle dynamics be realized, but also the dynamics of the condensate is included, with the superfluid velocity and the effective chemical potential naturally incorporated. We reveal that the superfluid velocity itself can contribute to the pump of quasiparticles (pump effect), with its rate of change acting as the drive field to drive the quasiparticles (drive effect). Specifically, the drive effect can contribute to the formation of the blocking region for the quasiparticle, which directly suppresses the anomalous correlation of the Cooper pairs. We find that both the pump and drive effects contribute to the oscillations of the Higgs mode with twice the frequency of the optical field. However, it is shown that the contribution from the drive effect to the excitation of Higgs mode is dominant as long as the driven superconducting momentum is less than the Fermi momentum. This is in contrast to the conclusion from the Liouville or Bloch equations in the literature, in which the drive effect on the anomalous correlation is overlooked with only the pump effect considered.Furthermore, in the gauge-invariant optical Bloch equations, the charge neutrality condition is {\em consistently} considered based on the two-component model for the charge, in which the charge imbalance of quasiparticles can cause the fluctuation of the effective chemical potential. ......