Phase Transitions of Dirac Electrons in Bismuth

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 elec...

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Published inScience (American Association for the Advancement of Science) Vol. 321; no. 5888; pp. 547 - 550
Main Authors Li, Lu, Checkelsky, J.G, Hor, Y.S, Uher, C, Hebard, A.F, Cava, R.J, Ong, N.P
Format Journal Article
LanguageEnglish
Published Washington, DC American Association for the Advancement of Science 25.07.2008
The American Association for the Advancement of Science
Subjects
Bismuth
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Domain effects, magnetization curves, and hysteresis
Electrons
Ellipsoids
Exact sciences and technology
Flavors
Graphene
Landau levels
Magnetic fields
Magnetic properties and materials
Magnetization
Magnetization curves, magnetization reversal, hysteresis, barkhausen and related effects
Phase transitions
Physics
Quantum theory
Symmetry
Torque
Phase diagrams
Magnetization
Phase transformations
Magnetic anisotropy
Hamiltonians
Bismuth
Landau levels
Dirac approximation
Quantum oscillation
Coulomb interaction
Symmetry breaking
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Summary: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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ISSN:0036-8075
1095-9203
DOI:10.1126/science.1158908