BME Fizikai Intezet - Fractional quantum Hall effect in graphene: phase transitions and non-Abelian states
Recent experiments [1,2] revealed a highly unusual sequence of fractional quantum Hall states in the zeroth Landau level of graphene. In particular, striking differences between filling factors in the ranges 0<|nu|<1 and 1<|nu|<2 were found, with odd-numerator fractions being absent at 1<|nu|<2, but present at 0<|nu|<1. In the filling factor interval 0<|nu|<1, multiple phase transitions between fractional states were observed .
We will describe a theory of fractional quantum Hall effect in graphene that explains these puzzling experimental observations . We argue that the differences between filling factors 0<|nu|<1 and 1<|nu|<2 can be understood as a consequence of the effects of terms in the Hamiltonian which break SU(2) valley symmetry, which we find to be important for |nu|<1 but negligible for |nu| >1. The effective absence of valley anisotropy for |nu|>1 means that states with odd numerator, e.g. |nu|=5/3 or 7/5 have to occur via spontaneous breaking of SU(2) valley symmetry. Therefore, such states can accommodate charged excitations in the form of large valley skyrmions, which have a low energy cost, and may be easily induced by coupling to impurities. The absence of observed quantum Hall states at these fractions is likely due to the effects of valley skyrmions.
For |nu|<1, the anisotropy terms favor phases in which electrons occupy states with opposite spins, similar to the antiferromagnetic state previously hypothesized to be the ground state at nu=0. The anisotropy and Zeeman energies suppress large-area skyrmions, so that quantized Hall states can be observable at a set of fractions similar to those in GaAs two-dimensional electron systems. In a perpendicular magnetic field B, the competition between the Coulomb energy, which varies as B1/2, and the Zeeman energy, which varies as B, can explain the observation of phase transitions as a function of B for fixed nu as transitions between states with different degrees of spin polarization.
Looking beyond current experiments, I will argue that, for studying fractional quantum Hall physics, an important advantage of graphene and bilaer graphene compared to GaAs is the tunability of their effective electron-electron interactions [4,5]. The tunability of interactions in these systems is achieved via external fields that change the mass gap , or by screening via dielectric plate in the vicinity of the device .
This allows one to engineer interactions favorable for various fragile fractional quantum Hall states, including non-Abelian ones. We find that non-Abelian states can be realized in bilayer graphene. Moreover, the tunability of electron interactions can be used to realize phase transitions between different compressible and incompressible fractional quantum Hall phases in a controlled manner [4,5].
 B. E. Feldman et al., arXiv:1303.0838 (2013).
 B. E. Feldman, B. Kraus, J. H. Smet, A. Yacoby, Science 337, 1196 (2012).
 D. A. Abanin, B. E. Feldman, A. Yacoby, B. I. Halperin, arXiv:1303.5372 (2013).
 Z. Papic, D. A. Abanin, Y. Barlas, R. N. Bhatt, Phys. Rev. B 84, 241306(R) (2012).
 Z. Papic, R. Thomale. D. A. Abanin, Phys. Rev. Lett. 107, 176602 (2011).
Helye: BME Fizikai Intezet, Elmeleti Fizika Tanszek: Budafoki ut 8. Szeminariumi szoba
Ideje: 2013. aprilis 15. hetfo, 14:15.
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