Divergent absorption from spin-orbit interaction in distorted Landau levels

• URL: http://arxiv.org/abs/2303.01286v1
• Date: Thu, 2 Mar 2023 14:09:38 GMT
• Title: Divergent absorption from spin-orbit interaction in distorted Landau levels
• Authors: Dominik Sidler, Michael Ruggenthaler and Angel Rubio
• Abstract summary: Effect of spin-orbit (and Darwin) interaction on a 2D electron gas subject to a radial, inhomogeneous $1/r$-magnetic field is discussed analytically. Numerical calculation 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. We show analytically the emergence of a discrete Rydberg-like band structure that obeys these symmetry properties.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 calculation 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 by induced radial spin-orbit currents, where the induced flow direction depends on the effective $g^*$-factor of the material. In more detail, the divergent currents show a critical behaviour at $g^*_c=2$, where it abruptly switches direction. The observed diverging spin-orbit 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 emergence of a discrete Rydberg-like band structure that obeys these symmetry properties. In a last step, we investigate the robustness of the spectra with respect to slow variations of the applied magnetic field, by solving analytically the Dirac equation expanded up to order $1/(mc)^2$. We find that the spin-orbit interaction from the time-dependent field variations cannot lift the static degeneracies, i.e., the degenerate states are protected with respect to slow changes of the $1/r$-magnetic field.

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