Energy spectra for quantum wires and 2DEGs in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

Abstract

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

13 pages, 11 figures

References in corpus (7)

• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Intersubband-induced spin-orbit interaction in quantum wells
• Ballistic Spin Resonance
• Rashba quantum wire: exact solution and ballistic transport
• Magnetic focusing of charge carriers from spin-split bands: Semiclassics of a Zitterbewegung effect
• Exact Landau Levels in Two-Dimensional Electron Systems with Rashba and Dresselhaus Spin-Orbit Interactions in a Perpendicular Magnetic Field
• Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells

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