Energy levels repulsion by spin-orbit coupling in two-dimensional Rydberg excitons

TL;DR

This paper investigates how Rashba spin-orbit coupling influences two-dimensional Rydberg excitons, revealing wave function modifications, level repulsion, and a transition towards quantum chaos, contrasting classical chaotic trajectories.

Contribution

It provides analytical and numerical evidence that spin-orbit coupling induces non-integrability and quantum chaos in 2D Rydberg excitons, a novel insight into their spectral properties.

Findings

Level repulsion modifies energy spectra.

Transition to non-Poissonian level statistics.

Randomization in transition strengths between states.

Abstract

We study the effects of Rashba spin-orbit coupling on two-dimensional Rydberg exciton systems. Using analytical and numerical arguments we demonstrate that this coupling considerably modifies the wave functions and leads to a level repulsion that results in a deviation from the Poissonian statistics of the adjacent level distance distribution. This signifies the crossover to non-integrability of the system and hints on the possibility of quantum chaos emerging. Such a behavior strongly differs from the classical realization, where spin-orbit coupling produces highly entangled, chaotic electron trajectories in an exciton. We also calculate the oscillator strengths and show that randomization appears in the transitions between states with different total momenta.