Optical Response in Semiconductor Quantum Wells in proximity to Chiral p-wave Supercon- ductor

By using gauge-invariant optical Bloch equation, we investigate the optical response to
the linearly polarized THz pulses in semiconductor quantum wells in proximity to chiral p-wave superconductor, in which time-reversal symmetry is spontaneously broken.
We show that during the optical process, the Higgs mode and quasiparticle charge imbalance
are excited, leading to oscillations of the p-wave gap and effective chemical potential, respectively. Moreover, we study the nonlinear optical conductivity tensor including usual (diagonal) part similar to conventional superconductivity, as well as magneto-optical (off-diagonal) one present in superconductors with spontaneous time-reversal breaking. Finally, we extend the gauge-invariant optical Bloch equation into non-Abelian gauge-invariant one with spatially dependent magnetization. As an application, we also investigate the optical response to linearly polarized THz pulses in chiral p-wave superconducting semiconductor quantum wells in proximity to transverse conical ferromagnets. Besides the Higgs mode,
quasiparticle charge imbalance and nonlinear optical conductivity tensor, the properties of
triplet vector during the optical process are also revealed.