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. When Zeeman and spin-orbit interactions are neglected its Landau levels are four-fold degenerate, explaining the $4 e^2/h$ separation between quantized Hall conductivity values seen in recent experiments. In this paper we derive a criterion for the occurrence of interaction-driven quantum Hall effects near intermediate integer values of $e^2/h$ due to charge gaps in broken symmetry states.

References

Quantum Hall Ferromagnetism in Graphene

Kentaro Nomura and A.H. MacDonald

Phys. Rev. Lett. 96, 256602 (2006). 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