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.
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.)
