Theory of unconventional quantum Hall effect in strained graphene

We show through both theoretical arguments and numerical calculations that graphene discerns an unconventional sequence of quantized Hall conductivity, when subject to both magnetic fields (B) and strain. The latter produces time-reversal symmetric pseudo/axial magnetic fields (b). The single-electron spectrum is composed of two interpenetrating sets of Landau levels (LLs), located at $\pm \sqrt{2 n |b \pm B|}$, $n=0, 1, 2, \cdots$. For $b>B$, these two sets of LLs have opposite \emph{chiralities}, resulting in {\em oscillating} Hall conductivity between 0 and $\mp 2 e^2/h$ in electron and hole doped system, respectively, as the chemical potential is tuned in the vicinity of the neutrality point. The electron-electron interactions stabilize various correlated ground states, e.g., spin-polarized, quantum spin-Hall insulators at and near the neutrality point, and possibly the anomalous Hall insulating phase at incommensurate filling $\sim B$. Such broken-symmetry ground states have similarities as well as significant differences from their counterparts in the absence of strain. For realistic strength of magnetic fields and interactions, we present scaling of the interaction-induced gap for various Hall states within the zeroth Landau level.Comment: 5 pages and 2 figures + supplementary (3.5 pages and 5 figures); Published version, cosmetic changes and updated reference

The Monte Carlo simulation of the topological quantities in FQH systems

Generally speaking, for a fractional quantum Hall (FQH) state, the electronic occupation number for each Landau orbit could be obtained from numerical methods such as exact diagonalization, density matrix renormalization group or algebraic recursive schemes (Jack polynomial). In this work, we apply a Metroplis Monte Carlo method to calculate the occupation numbers of several FQH states in cylinder geometry. The convergent occupation numbers for more than 40 particles are used to verify the chiral bosonic edge theory and determine the topological quantities via momentum polarization or dipole moment. The guiding center spin, central charge and topological spin of different topological sectors are consistent with theoretical values and other numerical studies. Especially, we obtain the topological spin of $e/4$ quasihole in Moore-Read and 331 states. At last, we calculate the electron edge Green's functions and analysis position dependence of the non-Fermi liquid behavior.Comment: 12 pages, 11 figure

Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect

We construct model wavefunctions for the collective modes of fractional quantum Hall systems. The wavefunctions are expressed in terms of symmetric polynomials characterized by a root partition and a "squeezed" basis, and show excellent agreement with exact diagonalization results for finite systems. In the long wavelength limit, the model wavefunctions reduce to those predicted by the single-mode approximation, and remain accurate at energies above the continuum of roton pairs.Comment: 4 pages, 3 figures, minor changes for the final prl versio