A protected spin-orbit induced absorption divergence in distorted Landau levels

Abstract

The effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial symmetric, inhomogeneous $1/r$-magnetic field is discussed analytically in a perturbative and non-perturbative manner. For this purpose, we investigate the radial Hall conductivity that emerges from an additional homogeneous electric field perturbation perpendicular to the 2D electron gas, which solely interacts via spin-orbit coupling. Numerical calculations of the absorptive spin-orbit spectra show for an ideal InSb electron gas a behaviour that is dominated by the localized (atomic) part of the distorted Landau levels. In contrast, however, we also find analytically that a (non-local) divergent static response emerges for Fermi energies close to the ionization energy in the thermodynamic limit. The divergent linear response implies that the external electric field is entirely absorbed outside the 2D electron gas by induced radial spin-orbit currents, as it would be the case inside a perfect conductor. This spin-orbit induced polarization mechanism depends on the effective $g^{\ast }$-factor of the material for which it shows a critical behaviour at $g_c^{\ast }=2$, where it abruptly switches direction. The diverging absorption relies on the presence of degenerate energies with allowed selection rules that are imposed by the radial symmetry of our inhomogeneous setup. We show analytically the presence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra by solving analytically the Dirac equation expanded up to order $1/(mc{)}^2$. We find that the distorted Landau-levels, and thus the divergent spin-orbit polarization, remain protected with respect to slow changes of the applied $1/r$-magnetic field.

References in corpus (15)

• Spintronics: Fundamentals and applications
• Anomalous Hall effect
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Ultrastrong coupling of the cyclotron transition of a two-dimensional electron gas to a THz metamaterial
• Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation
• Magneto-transport controlled by Landau polariton states
• Ultrastrong coupling between a cavity resonator and the cyclotron transition of a 2D electron gas in the case of integer filling factor
• Towards a quantum Hall effect for atoms using electric fields
• Landau Quantization of Neutral Particles in an External Field
• Light-matter interactions in synthetic magnetic fields: Landau-photon polaritons
• Polaritonic Hofstadter Butterfly and Cavity-Control of the Quantized Hall Conductance
• Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
• Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields
• Magnetic quantum dots and rings in two dimensions
• New degeneracies and modification of Landau levels in the presence of a parallel linear electric field