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

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.

arXiv comment5 pages, 4 figures

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Cited by in corpus (6)

• Landau level spectroscopy of Bi${}_2$Te${}_3$
• Angular dependence of magnetoresistance and planar Hall effect in semimetals in strong magnetic fields
• A field-induced reentrant insulator state of a gap-closed topological insulator (Bi_{1-x}Sb_x) in quantum-limit states
• Weak anti-localization in spin-orbit coupled lattice systems
• Quantum--classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena
• Impact of spin--orbit coupling on orbital diamagnetism in a narrow-gap semiconductor ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$