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Science 25 July 2008:
Vol. 321. no. 5888, pp. 547 - 550
DOI: 10.1126/science.1158908
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Reports

Phase Transitions of Dirac Electrons in Bismuth

Lu Li,1* J. G. Checkelsky,1 Y. S. Hor,2 C. Uher,3 A. F. Hebard,4 R. J. Cava,2 N. P. Ong1*

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.

1 Department of Physics, Princeton University, NJ 08544, USA.
2 Department of Chemistry, Princeton University, NJ 08544, USA.
3 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA.
4 Department of Physics, University of Florida, Gainesville, FL 32611, USA.

* To whom correspondence should be addressed. E-mail: luli{at}princeton.edu (L.L.); npo{at}princeton.edu (N.P.O.)

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Science. ISSN 0036-8075 (print), 1095-9203 (online)