Exact Landau Levels in Two-Dimensional Electron Systems with Rashba and Dresselhaus Spin-Orbit Interactions in a Perpendicular Magnetic Field

Abstract

We study a two-dimensional electron system in the presence of both Rashba and Dresselhaus spin-orbit interactions in a perpendicular magnetic field. Defining two suitable boson operators and using the unitary transformations we are able to obtain the exact Landau levels in the range of all the parameters. When the strengths of the Rashba and Dresselhaus spin-orbit interactions are equal, a new analytical solution for the vanishing Zeeman energy is found, where the orbital and spin wave functions of electron are separated. It is also shown that in this case the Zeeman and spin-orbit splittings are independent of the Landau level index $n$. Due to the Zeeman energy, new crossing between the eigenstates $|n,k,s=1,\sigma >$ 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 the Fermi level.

arXiv comment4 pages, 1 figure

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• Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling
• Quantum oscillations in 2D electron gases with spin-orbit and Zeeman interactions
• The Geometry of (non-Abelian) Landau levels
• Resonant Spin Polarization and Hall Effects in a Two-Dimensional Electron Gas
• Theory of resonant spin Hall effect
• Drift velocity of edge magnetoplasmons due to magnetic edge channels
• Semiclassical Landau quantization of spin-orbit coupled systems
• Oscillation of spin polarization in a two-dimensional hole gas under a perpendicular magnetic field
• Magnetotransport properties of an unconventional Rashba spin-orbit coupled two-dimensional electronic system
• Parameter-dependent unitary transformation approach for quantum Rabi model
• Analytically solvable model to the spin Hall effect with Rashba and Dresselhaus spin-orbit couplings