Dirac Valleys in Bismuth
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" Bulk bismuth is a compensated semi-metal with an extremely low concentration of electron-like and hole-like carriers. The electrons are described by the Dirac Hamiltonian and their band mass becomes a thousandth of the bare electron mass along one crystalline axis. These Dirac electrons present a huge mass anisotropy and can occupy each of the three rotationally equivalent elongated ellipsoids of the Fermi surface. The strong anisotropy, inverted for holes and electrons, combined with a strong spin-orbit coupling and unusually anisotropic Zeeman coupling generates a Landau spectrum of impressive complexity [1].�
The valley degeneracy offers electrons an additional degree of freedom, a subject of recent research in a variety of systems [2]. According to theory [3], at least in two dimensions, the mass anisotropy should favor a valley-nematic ground state. Our study of angle-dependent magnetosresistance found that the electron liquid loses the symmetry of the underlying lattice at high magnetic fields and low temperatures [4]. Recent thermodynamic measurements confirm the loss of symmetry and document a valley-dependent density of states in presence of quantizing magnetic field [5]. Our latest extensive study og magnetoconductivity uncovers a phase transition induced by magnetic field to a ground state with spontaneous valley polarization.
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[1] Z. Zhu et al., PNAS 109, 14813 (2012)
[2] K. Behnia, Nature Nanotechnology 7, 488 (2012)
[3] D. Abanin et al., Phys. Rev. B 82, 035428 (2010)
[4] Z. Zhu et al., Nature Physics 8, 89 (2012)
[5] R. Keuchler et al., Nature Materials 13, 461 (2014)"
The valley degeneracy offers electrons an additional degree of freedom, a subject of recent research in a variety of systems [2]. According to theory [3], at least in two dimensions, the mass anisotropy should favor a valley-nematic ground state. Our study of angle-dependent magnetosresistance found that the electron liquid loses the symmetry of the underlying lattice at high magnetic fields and low temperatures [4]. Recent thermodynamic measurements confirm the loss of symmetry and document a valley-dependent density of states in presence of quantizing magnetic field [5]. Our latest extensive study og magnetoconductivity uncovers a phase transition induced by magnetic field to a ground state with spontaneous valley polarization.
�
[1] Z. Zhu et al., PNAS 109, 14813 (2012)
[2] K. Behnia, Nature Nanotechnology 7, 488 (2012)
[3] D. Abanin et al., Phys. Rev. B 82, 035428 (2010)
[4] Z. Zhu et al., Nature Physics 8, 89 (2012)
[5] R. Keuchler et al., Nature Materials 13, 461 (2014)"
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