Non-Abelian states with negative flux: a new series of quantum Hall states

By applying the idea of parafermionic clustering to composite bosons with positive as well as negative flux, a new series of trial wavefunctions to describe fractional quantum Hall states is proposed. These non-Abelian states compete at filling factors k/(3k +/- 2) with other ground states like stripes or composite fermion states. These two series contain all the states recently discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] including the even denominator cases. Exact diagonalization studies on the sphere and torus point to their possible relevance for filling factors 3/7, 3/11, and 3/8.Comment: 4 pages, 5 figure

Shape of the magnetoroton at ν=1/3\nu=1/3 and ν=7/3\nu=7/3 in real samples

We revisit the theory of the collective neutral excitation mode in the fractional quantum Hall effect at Landau level filling fractions $\nu=1/3$ and $\nu=7/3$. We include the effect of finite thickness of the two-dimensional electron gas and use extensive exact diagonalizations in the torus geometry. In the lowest Landau level the collective gapped mode i.e. the magnetoroton always merges in the continuum in the long-wavelength limit. In the second Landau level the mode is well-defined only for wavevectors smaller than a critical value and disappears in the continuum beyond this point. Its curvature near zero momentum is opposite to that of the LLL. It is well separated from the continuum even at zero momentum and the gap of the continuum of higher-lying states is twice the collective mode gap at $k=0$. The shape of the dispersion relation survives a perturbative treatment of Landau level mixing.Comment: 10 pages, 11 figures, published versio

Phase diagram of a graphene bilayer in the zero-energy Landau level

Bilayer graphene under a magnetic field has an octet of quasidegenerate levels due to spin, valley, and orbital degeneracies. This zero-energy Landau level is resolved into several incompressible states whose nature is still elusive. We use a Hartree-Fock treatment of a realistic tight-binding four-band model to understand the quantum ferromagnetism phenomena expected for integer fillings of the octet levels. We include the exchange interaction with filled Landau levels below the octet states. This Lamb-shift-like effect contributes to the orbital splitting of the octet. We give phase diagrams as a function of applied bias and magnetic field. Some of our findings are in agreement with experiments. We discuss the possible appearance of phases with orbital coherence

Quantum Hall fractions in ultracold atomic vapors

Atomic vapors can be prepared and manipulated at very low densities and temperatures. When they are rotating, they can reach a quantum Hall regime in which there should be manifestations of the fractional quantum Hall effect. We discuss the appearance of the principal sequence of fractions nu =p/(p+- 1) for bosonic atoms. The termination point of this series is the paired Moore-Read Pfaffian state. Exotic states fill the gap between the paired state and the vortex lattice expected at high filling of the lowest Landau level. In fermionic vapors, the p-wave scattering typical of ultralow energy collisions leads to the hard-core model when restricted to the lowest Landau level.Comment: 7 pages, 2 figs, brief review submitted to Modern Physics Letters

Generalized nonlinear sigma model approach to alternating spin chains and ladders

We generalize the nonlinear sigma model treatment of quantum spin chains to cases including ferromagnetic bonds. When these bonds are strong enough, the classical ground state is no longer the standard Neel order and we present an extension of the known formalism to deal with this situation. We study the alternating ferromagnetic-antiferromagnetic spin chain introduced by Hida. The smooth crossover between decoupled dimers and the Haldane phase is semi-quantitatively reproduced. We study also a spin ladder with diagonal exchange couplings that interpolates between the gapped phase of the two-leg spin ladder and the Haldane phase. Here again we show that there is good agreement between DMRG data and our analytical results.Comment: 10 pages, 5 encapsulated figures, REVTeX 3.

Edge structure of graphene monolayers in the {\nu} = 0 quantum Hall state

Monolayer graphene at neutrality in the quantum Hall regime has many competing ground states with various types of ordering. The outcome of this competition is modified by the presence of the sample boundaries. In this paper we use a Hartree-Fock treatment of the electronic correlations allowing for space-dependent ordering. The edge influence is modeled by a simple perturbative effective magnetic field in valley space. We find that all phases found in the bulk of the sample, ferromagnetic, canted antiferromagnetic, charge-density wave and Kekul$\'e$ distortion are smoothly connected to a Kekul$\'e$-distorted edge. The single-particle excitations are computed taking into account the spatial variation of the order parameters. An eventual metal-insulator transition as a function of the Zeeman energy is not simply related to the type of bulk order.Comment: 18 pages, 11 figures, corresponds to published versio