ELFT HÍRADÓ

[Balazs Dora <dora AT kapica.phy.bme.hu>]

                            MEGHIVO
      a BME Fizikai Intezet, Egzotikus kvantum fazisok csoport
                         szeminariumara:


                        Dmitry Abanin
(Perimeter Institute for Theoretical Physics; Harvard University)

Fractional quantum Hall effect in graphene: phase transitions and 
non-Abelian states


Hosszu kivonat: 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 [2].

We will describe a theory of fractional quantum Hall effect in graphene 
that explains these puzzling experimental observations [3]. 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 
[5], or by screening via dielectric plate in the vicinity of the device 
[4].

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].

References:
[1] B. E. Feldman et al., arXiv:1303.0838 (2013).
[2] B. E. Feldman, B. Kraus, J. H. Smet, A. Yacoby, Science 337, 1196 
(2012).
[3] D. A. Abanin, B. E. Feldman, A. Yacoby, B. I. Halperin, 
arXiv:1303.5372 (2013).
[4] Z. Papic, D. A. Abanin, Y. Barlas, R. N. Bhatt, Phys. Rev. B 84, 
241306(R) (2012).
[5] 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.


         Minden erdeklodot szivesen latunk.


                                Dora Balazs