# Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and g-Factor in Spin-Orbit Coupled Solids

## TL;DR

This paper introduces a non-perturbative quantum method based on matrix mechanics and k.p theory to accurately calculate spin-split Landau levels and g-factors in spin-orbit coupled solids, accounting for detailed band structures.

## Contribution

The paper presents a novel fully quantum approach that considers multiband effects and band structure details, improving the accuracy of spin-split Landau level calculations in spin-orbit coupled materials.

## Key findings

- The spin-splitting parameter M depends strongly on magnetic field strength.
- The field dependence of M explains discrepancies between experiments and theory.
- M derived from fan diagrams differs from the ratio of Zeeman to cyclotron energy.

## Abstract

We have proposed a fully quantum approach to non-perturbatively calculate the spin-split Landau levels and g-factor of various spin-orbit coupled solids, based on the k.p theory in the matrix mechanics representation. The new method considers the detailed band structure and the multiband effect of spin-orbit coupling irrespective of the magnetic field strength. An application of this method to PbTe, a typical Dirac electron system, is shown. Contrary to popular belief, it is shown that the spin-splitting parameter M, which is the ratio of the Zeeman to cyclotron energy, exhibits a remarkable magnetic-field-dependence. This field-dependence can rectify the existing discrepancy between experimental and theoretical results. We have also shown that M evaluated from the fan diagram plot is different from that determined as the ratio of the Zeeman to cyclotron energy, which also overturns common belief.