Phase Transitions of Dirac Electrons in Bismuth
Abstract
The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy.
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In stoichiometric bulk materials, the known 3D Dirac fermions in bismuth are massive because a band gap exists in the bulk Dirac spectrum.
“In stoichiometric bulk materials, the known 3D Dirac fermions in bismuth are in fact of massive variety as there clearly exists a band gap in the bulk Dirac spectrum10.”
From Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 (2014) · cites this paper as [10]
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- Authors
- Li, L., Checkelsky, J. G., Hor, Y. S., Uher, C., Hebard, A. F., Cava, R. J., & Ong, N. P.
- Affiliations
- Department of Physics, Princeton University, NJ 08544, USA.
- Princeton University (US)
- Corresponding author
- Ong, N. P.
- Venue
- Science
- Published
- 2008-07-25
- Volume
- 321
- Issue
- 5888
- Pages
- 547-550
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W1910452405
- Cited by
- 166
- References
- 19
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 7 · 2023: 5 · 2022: 3 · 2021: 11 · 2020: 7 · 2019: 11 · 2018: 12 · 2017: 10 · 2016: 17 · 2015: 16 · 2014: 16 · 2013: 4 · 2012: 7
- FWCI
- 6.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- Bulletin of the American Physical Society
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- Dirac fermions, bismuth, Dirac Hamiltonian, lowest Landau level, valley degeneracy, magnetic anisotropy, field-induced phase transition, torque magnetometry, magnetization, relativistic fermions
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