  When the Rashba and Dresslhaus spin-orbit coupling are both presented for a
two-dimensional electron in a perpendicular magnetic field, a striking
resemblance to anisotropic quantum Rabi model in quantum optics is found. We
perform a generalized Rashba coupling approximation to obtain a solvable
Hamiltonian by keeping the nearest-mixing terms of Laudau states, which is
reformulated in the similar form to that with only Rashba coupling. Each Landau
state becomes a new displaced-Fock state with a displacement shift instead of
the original Harmonic oscillator Fock state, yielding eigenstates in closed
form. Analytical energies are consistent with numerical ones in a wide range of
coupling strength even for a strong Zeeman splitting. In the presence of an
electric field, the spin conductance and the charge conductance obtained
analytically are in good agreements with the numerical results. As the
component of the Dresselhaus coupling increases, we find that the spin Hall
conductance exhibits a pronounced resonant peak at a larger value of the
inverse of the magnetic field. Meanwhile, the charge conductance exhibits a
series of plateaus as well as a jump at the resonant magnetic field. Our method
provides an easy-to-implement analytical treatment to two-dimensional electron
gas systems with both types of spin-orbit couplings.
