# High Landau levels of 2D electrons near the topological transition caused by interplay of spin-orbit and Zeeman energy shifts

## TL;DR

This paper investigates the complex Landau level behavior of 2D electrons influenced by spin-orbit coupling and Zeeman effects near a topological transition, revealing asymmetric and oscillatory coupling phenomena.

## Contribution

It provides a detailed analysis of Landau quantization near a topological transition, highlighting asymmetric and oscillatory coupling effects due to trajectory behavior.

## Key findings

- Coupling strength varies asymmetrically near the transition.
- Oscillations in coupling are explained by St{"u}ckelberg interference.
- Unusual scaling of detuning with magnetic length.

## Abstract

In the presence of spin-orbit coupling two branches of the energy spectrum of 2D electrons get shifted in the momentum space. Application of in-plane magnetic field causes the splitting of the branches in energy. When both, spin-orbit coupling and Zeeman splitting are present, the branches of energy spectrum cross at certain energy. Near this energy, the Landau quantization becomes peculiar since semiclassical trajectories, corresponding to individual branches, get coupled. We study this coupling as a function of proximity to the topological transition. Remarkably, the dependence on the proximity is strongly asymmetric reflecting the specifics of the behavior of the trajectories near the crossing. Equally remarkable, on one side of the transition, the magnitude of coupling is an oscillating function of this proximity. These oscillations can be interpreted in terms of the St{\"u}ckelberg interference. Scaling of characteristic detuning with magnetic length is also unusual. This unusual behavior cannot be captured by simply linearizing the Fermi contours near the crossing point.