Spontaneous Symmetry Breaking in Graphene Quantum Hall States

Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-like low-energy excitations. Graphene displays an unconventional quantization of the Hall conductivity when subjected to a magnetic field. The Hall conductivity is measured to be a half-integer in units of 4 times the conductance quantum. In the presence of a strong magnetic field, graphene's 4 fold degeneracy is lifted by the exchange Coulomb interaction. Recent experiments indicate that high quality graphene samples exhibit a very unusual high-resistance metallic state and a transition to a complete insulating phase at the charge neutral point. We propose that the current carriers in this state are charged vortices of the XY valley-pseudospin order parameter, a situation which is dual to a conventional thin superconducting film. We study energetic and the stability of this phase in the presence of disorder. A phase diagram as a function of magnetic fields and the sample mobility is determined.

References

Quantum Hall Ferromagnetism in Graphene
Kentaro Nomura and A.H. MacDonald
Phys. Rev. Lett. 96, 256602 (2006). pdf

Field-induced Kosterlita-Thouless transition in the N=0 Landau level of graphene
Kentaro Nomura, Shinsei Ryu and Dung-Hai Lee
Phys. Rev. Lett. 103, 216801 (2009). pdf

Coupled charge and valley excitations in graphene quantum Hall ferromegnets
Naokazu Shibata, and Kentaro Nomura
Phys. Rev. B 77, 235426 (2008) pdf

Fractional quantum Hall effect in double-layer system

Fractional quantum Hall states in bilayer system at total filling fraction $\nu=1/2$ are examined numerically under some ranges of the layer separation and interlayer tunneling. It is shown that the ground state changes continuously from two-component state to one-component state as the interlayer tunneling rate is increased, while the lowest excited state changes discontinuously. This fact explains observed unusual behavior of the activation energy which reveals upward cusp as a function of interlayer tunneling. Some trial wave functions for the ground state and quasihole states are inspected.

Figures

ground state evolves continuously

quasihole states reveal level crossing

References

Kentaro Nomura and Daijiro Yoshioka
Gap evolution in nu=1/2 bilayer quantum Hall systems
J. Phys. Soc. Jpn. 73 2612 (2004). pdf