Journal
PHYSICAL REVIEW B
Volume 79, Issue 24, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.79.241101
Keywords
bismuth; charge density waves; Landau levels; magnetic hysteresis; solid-state phase transformations; spin-orbit interactions; Wigner crystal; Zeeman effect
Funding
- Lee A. DuBridge Foundation
- Packard Foundation and National Science Foundation [DMR-0804564, PHY05-51164]
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While the behavior of strongly interacting two-dimensional electrons in high magnetic fields is by now well understood, our understanding of the three-dimensional (3D) case is comparatively rudimentary. Illuminating this disparity are recent experiments on 3D bismuth, where unanticipated transport and magnetization structure-including hysteresis-persist even when all carriers are expected to reside in the lowest Landau level. Motivated by these findings, we derive a low-energy Hamiltonian for the hole and three Dirac electron pockets in bismuth which, crucially, encodes an unconventional Zeeman effect generated by spin-orbit coupling. We show that (1) this Zeeman coupling strongly suppresses the quantum limit for the Dirac electrons, giving rise to the observed magnetization structure, and (2) the hysteresis coincides with one of the pockets emptying its second Landau level, which is where Coulomb effects are most pronounced. Incorporating interactions, we find instabilities toward charge-density-wave and Wigner crystal phases and propose that hysteresis arises from a first-order transition out of the latter.
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