Optical signatures of Rashba--Dresselhaus coupling across Franz--Keldysh and Landau regimes in two-dimensional semiconductors
We develop a unified theory of the interband optical response of a two-dimensional semiconductor with simultaneous Rashba and Dresselhaus spin-orbit couplings in electric and magnetic fields. In crossed fields, the in-plane electric field generates an effective spin-orbit drift field that modifies the Landau spectrum and spinor states, while at zero magnetic field the problem maps onto Landau--Zener spin dynamics.At zero external fields, the total joint density of states above the band gap remains unchanged, while characteristic subgap structures appear. Pure Rashba coupling produces an inverse square root singularity, whereas a finite Dresselhaus term gives a step and a logarithmic peak, allowing the two couplings to be distinguished optically. At zero magnetic field, the Franz--Keldysh response shows a crossover from diabatic to adiabatic spin dynamics as the electric field is reduced. In the weak-field Rashba regime, the field-free singularity becomes a finite peak whose height scales as $\mathcal E^{-1/3}$ and whose position approaches $E_g-E_{\rm SO}$, providing a direct measure of the Rashba energy. In a perpendicular magnetic field, spin-orbit coupling shifts and splits the Landau absorption lines and produces anticrossings without changing their total weights. The Rashba splitting changes from a $\sqrt{B}$ dependence at weak fields to a linear dependence at strong fields. Finally, in crossed electric and magnetic fields, the electric field broadens the Landau lines and drives a continuous crossover toward the Franz--Keldysh regime, while spin-orbit coupling produces opposite shifts and different widths for the two members of each doublet.