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

Abstract

We propose a fully quantum approach to nonperturbatively 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. We show an application of this method to PbTe, a typical Dirac electron system. Contrary to popular belief, we show 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 also show 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.