Nonperturbative Matrix Mechanics Approach to Spin-Split Landau Levels and the 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.

Landau level spectroscopy of Bi2Te3

“…The validity of the proposed model also implies that the Zeeman splitting in Bi 2 Te 3 should be equal to cyclotron energy E Z = E C that is typical of massive Dirac electrons [54,55] and the g factors of electrons and holes should reach g e = g h = 2m 0 /m D ≈ 30. In fact, large values of g factors are expected in systems composed of heavy elements with strong spin-orbit coupling [56,57].…”

Weak anti-localization in spin–orbit coupled lattice systems

“…Studying the effect of pressure may be more suitable to see the WAL-WL crossover because this allows the localization effect by excluding the alloying. A good candidate for this would be PbTe, another typical Dirac electron system [23][24][25][26]. The band gap of PbTe can be reduced by applying pressure [27].…”

Quantum–classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

“…The oscillation is primarily caused by σ yy because the oscillation in Hall conductivity is suppressed owing to the cancellation of the dissipative transport. Furthermore, determining the crosspoints of Landau levels and chemical potential is a critical problem in experiments with semimetals, considering the Berry curvature or the effective g-factor in metals and semimetals [33][34][35]. The nonnegligible Hall conductivity shifts the position of peaks in ρ xx and may cause misinterpretation of the phase information in the oscillation.…”