Energy levels of a two-dimensional hydrogen atom with spin-orbit Rashba interaction

TL;DR

This paper investigates how Rashba spin-orbit interaction influences the energy levels of a two-dimensional hydrogen atom, revealing that strong spin-orbit coupling results in lower energy levels and tighter electron binding.

Contribution

It provides numerical and analytical analysis of energy levels in a 2D hydrogen atom with Rashba interaction, highlighting the effects of varying spin-orbit coupling strength.

Findings

Energy levels decrease with increasing spin-orbit coupling.

Analytic expressions match numerical results in weak and strong coupling limits.

Electron binding becomes stronger as spin-orbit interaction intensifies.

Abstract

Electronic bound states around charged impurities in two-dimensional systems with structural inversion asymmetry can be described in terms of a two-dimensional hydrogen atom in the presence of a Rashba spin-orbit interaction. Here, the energy levels of the bound electron are evaluated numerically as a function of the spin-orbit interaction, and analytic expressions for the weak and strong spin-orbit coupling limits are compared with the numerical results. It is found that, besides the level splitting due to the lack of inversion symmetry, the energy levels are lowered for sufficiently strong spin-orbit coupling, indicating that the electron gets more tightly bound to the ion as the spin-orbit interaction increases. Similarities and differences with respect to the two-dimensional Fr\"ohlich polaron with Rashba coupling are discussed.