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.

4 pages, 1 figure

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• Spin Hall effect and Berry phase in two dimensional electron gas
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry

Cited by in corpus (6)

• Spin Hall effect in a two-dimensional electron gas in the presence of a magnetic field
• Explicit Green functions for spin-orbit Hamiltonians
• Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling
• Theory of resonant spin Hall effect
• Resonant Spin Polarization and Hall Effects in a Two-Dimensional Electron Gas
• Oscillation of spin polarization in a two-dimensional hole gas under a perpendicular magnetic field