50 research outputs found
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 and in real samples
We revisit the theory of the collective neutral excitation mode in the
fractional quantum Hall effect at Landau level filling fractions and
. 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 . 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
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 distortion are smoothly connected to a
Kekul-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
Quantum Hall fractions in ultracold fermionic vapors
We study the quantum Hall states that appear in the dilute limit of rotating
ultracold fermionic gases when a single hyperfine species is present. We show
that the p-wave scattering translates into a pure hard-core interaction in the
lowest Landau level. The Laughlin wavefunction is then the exact ground state
at filling fraction nu=1/3. We give estimates of some of the gaps of the
incompressible liquids for nu = p/(2p+-1). We estimate the mass of the
composite fermions at nu =1/2. The width of the quantum Hall plateaus is
discussed by considering the equation of state of the system.Comment: RevTex, 4 pages, 3 fig
Gaplessness of the Gaffnian
We study the Gaffnian trial wavefunction proposed to describe fractional
quantum Hall correlations at Bose filling factor and Fermi filling
. A family of Hamiltonians interpolating between a hard-core
interaction for which the physics is known and a projector whose ground state
is the Gaffnian is studied in detail. We give evidence for the absence of a gap
by using large-scale exact diagonalizations in the spherical geometry. This is
in agreement with recent arguments based on the fact that this wavefunction is
constructed from a non-unitary conformal field theory. By using the cylinder
geometry, we discuss in detail the nature of the underlying minimal model and
we show the appearance of heterotic conformal towers in the edge energy
spectrum where left and right movers are generated by distinct primary
operators.Comment: 11 pages, 5 figure
Multi-particle composites in density-imbalanced quantum fluids
We consider two-component one-dimensional quantum gases with density
imbalance. While generically such fluids are two-component Luttinger liquids,
we show that if the ratio of the densities is a rational number, p/q, and mass
asymmetry between components is sufficiently strong, one of the two eigenmodes
acquires a gap. The gapped phase corresponds to (algebraic) ordering of
(p+q)-particle composites. In particular, for attractive mixtures, this implies
that the superconducting correlations are destroyed. We illustrate our
predictions by numerical simulations of the fermionic Hubbard model with
hopping asymmetry.Comment: 4+ pages, 1 figure, published versio
Quantum Hall fractions for spinless Bosons
RevTeX 4, 11 pages, 13 figuresWe study the Quantum Hall phases that appear in the fast rotation limit for Bose-Einstein condensates of spinless bosonic atoms. We use exact diagonalization in a spherical geometry to obtain low-lying states of a small number of bosons as a function of the angular momentum. This allows to understand or guess the physics at a given filling fraction nu, ratio of the number of bosons to the number of vortices. This is also the filling factor of the lowest Landau level. In addition to the well-known Bose Laughlin stateat nu =1/2 we give evidence for the Jain principalsequence of incompressible states at nu =p/(p+- 1) for a few values of p. There is a collective mode in these states whose phenomenology is in agreement with standard arguments cominge.g. from the composite fermion picture.At filling factor one, the potential Fermi sea of composite fermions is replaced by a paired state, the Moore-Read state. This is most clearly seen from the half-flux nature of elementary excitations.We find that the hierarchy picture does not extend up to the point of transition towards a vortex lattice. While we cannot conclude, we investigate the clustered Read-Rezayi states and show evidence for incompressible states at the expected ratio of flux vs number of Bose particles
SU(3) and SU(4) singlet quantum Hall states at
We report on an exact diagonalization study of fractional quantum Hall states
at filling factor in a system with a four-fold degenerate =0
Landau level and SU(4) symmetric Coulomb interactions. Our investigation
reveals previously unidentified SU(3) and SU(4) singlet ground states which
appear at flux quantum shift 2 when a spherical geometry is employed, and lie
outside the established composite-fermion or multicomponent Halperin state
patterns. We evaluate the two-particle correlation functions of these states,
and discuss quantum phase transitions in graphene between singlet states with
different number of components as magnetic field strength is increased.Comment: 5+2 pages, 3 figure