Ground state and excitations in single and double fractional quantum hall systems

Ahmed Jellal

Naokazu Shibata, Kentaro Nomura

Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with the valley degrees of freedom (so called valley skyrmions). The excitation gaps are calculated and extrapolated to the thermodynamic limit. The largest excitation gap at effective filling 1/3 is obtained in bilayer graphene, which is a good candidate for experimental observation of fractional quantum Hall effect.

N. F. Johnson, Simon C. Benjamin

An analytically solvable few-electron model of a double-layer electron system is presented which includes mixing with all Landau levels. Inter-layer correlations are found to give rise to novel ground states which differ fundamentally from previously suggested Jastrow-like wavefunctions for double layer N-electron systems. Comparison with experimental data suggests that these states may represent small-N precursors of recently observed fractional quantum Hall states in double-layer (large-N) systems.

Ying-Hai Wu

Takashi Nakajima, Hideo Aoki

Min Lu, Na Jiang, Xin Wan

Fractional quantum Hall systems are often described by model wave functions, which are the ground states of pure systems with short-range interaction. A primary example is the Laughlin wave function, which supports Abelian quasiparticles with fractionalized charge. In the presence of disorder, the wave function of the ground state is expected to deviate from the Laughlin form. We study the disorder-driven collapse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state. In particular, we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.