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We study a two-dimensional electron system in the presence of both Rashba andDresselhaus spin-orbit interactions in a perpendicular magnetic field. Definingtwo suitable boson operators and using the unitary transformations we are ableto obtain the exact Landau levels in the range of all the parameters. When thestrengths of the Rashba and Dresselhaus spin-orbit interactions are equal, anew analytical solution for the vanishing Zeeman energy is found, where theorbital and spin wave functions of electron are separated. It is also shownthat in this case the Zeeman and spin-orbit splittings are independent of theLandau level index $n$. Due to the Zeeman energy, new crossing between theeigenstates $|n, k, s=1, \sigma>$ and $|n+1, k, s^\prime =-1, \sigma^\prime>$is produced at certain magnetic field for larger Rashba spin-orbit coupling.This degeneracy leads to a resonant spin Hall conductance if it happens at theFermi level.Comment: 4 pages, 1 figur

Exact Landau levels in two-dimensional electron systems with Rashba and Dresselhaus spin–orbit interactions in a perpendicular magnetic field