151 research outputs found

### Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets

Inspired by the four-fold spin-valley symmetry of relativistic electrons in
graphene, we investigate a possible SU(4) fractional quantum Hall effect, which
may also arise in bilayer semiconductor quantum Hall systems with small Zeeman
gap. SU(4) generalizations of Halperin's wave functions [Helv. Phys. Acta 56,
75 (1983)], which may break differently the original SU(4) symmetry, are
studied analytically and compared, at nu=2/3, to exact-diagonalization studies.Comment: 4+epsilon pages, 4 figures; published version with minor correction

### Flat-band ferromagnetism in a topological Hubbard model

We study the flat-band ferromagnetic phase of a topological Hubbard model
within a bosonization formalism and, in particular, determine the spin-wave
excitation spectrum. We consider a square lattice Hubbard model at 1/4-filling
whose free-electron term is the \pi-flux model with topologically nontrivial
and nearly flat energy bands. The electron spin is introduced such that the
model either explicitly breaks time-reversal symmetry (correlated flat-band
Chern insulator) or is invariant under time-reversal symmetry (correlated
flat-band $Z_2$ topological insulator). We generalize for flat-band Chern and
topological insulators the bosonization formalism [Phys. Rev. B 71, 045339
(2005)] previously developed for the two-dimensional electron gas in a uniform
and perpendicular magnetic field at filling factor \nu=1. We show that, within
the bosonization scheme, the topological Hubbard model is mapped into an
effective interacting boson model. We consider the boson model at the harmonic
approximation and show that, for the correlated Chern insulator, the spin-wave
excitation spectrum is gapless while, for the correlated topological insulator,
gapped. We briefly comment on the possible effects of the boson-boson
(spin-wave--spin-wave) coupling.Comment: 16 pages, 5 figure

### On the self-similarity in quantum Hall systems

The Hall-resistance curve of a two-dimensional electron system in the
presence of a strong perpendicular magnetic field is an example of
self-similarity. It reveals plateaus at low temperatures and has a fractal
structure. We show that this fractal structure emerges naturally in the
Hamiltonian formulation of composite fermions. After a set of transformations
on the electronic model, we show that the model, which describes interacting
composite fermions in a partially filled energy level, is self-similar. This
mathematical property allows for the construction of a basis of higher
generations of composite fermions. The collective-excitation dispersion of the
recently observed 4/11 fractional-quantum-Hall state is discussed within the
present formalism.Comment: 7 pages, 4 figures; version accepted for publication in Europhys.
Lett., new version contains energy calculations for collective excitations of
the 4/11 stat

### Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multi-component structure due
to the electronic spin and chirality degrees of freedom. While the applied
field breaks the spin symmetry explicitly, we show that the fate of the
chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms
differ in origin when the Hamiltonian is projected onto the central (n=0)
rather than any of the other Landau levels. Our description at the lattice
level leads to a Harper equation; in its continuum limit, the ratio of lattice
constant a and magnetic length l_B assumes the role of a small control
parameter in different guises. The leading symmetry-breaking terms are direct
(n=0) and exchange (n different from 0) terms, which are algebraically small in
a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate
the easy-plane anisotropy of the graphene ferromagnet.Comment: 4 pages, 1 figure; revised version contains a more detailed
comparison with experimental results; accepted for publication in PR

### Measure of Diracness in two-dimensional semiconductors

We analyze the low-energy properties of two-dimensional direct-gap
semiconductors, such as for example the transition-metal dichalcogenides
MoS$_2$, WS$_2$, and their diselenide analogues MoSe$_2$, WSe$_2$, etc., which
are currently intensively investigated. In general, their electrons have a
mixed character -- they can be massive Dirac fermions as well as simple
Schr\"odinger particles. We propose a measure (Diracness) for the degree of
mixing between the two characters and discuss how this quantity can in
principle be extracted experimentally, within magneto-transport measurements,
and numerically via ab initio calculations.Comment: 6 pages, 2 figures ; new version (with minor modifications) accepted
for publication in EP

### Charged exctions in two-dimensional transition-metal dichalcogenides - semiclassical calculation of Berry-curvature effects

We theoretically study the role of the Berry curvature on neutral and charged
excitons in two-dimensional transition-metal dichalcogenides. The Berry
curvature arises due to a strong coupling between the conduction and valence
bands in these materials that can to great extent be described within the model
of massive Dirac fermions. The Berry curvature lifts the degeneracy of exciton
states with opposite angular momentum. Using an electronic interaction that
accounts for non-local screening effects, we find a Berry-curvature induced
splitting of $\sim 17$ meV between the 2$p_{-}$ and 2$p_{+}$ exciton states in
WS$_2$, consistent with experimental findings. Furthermore, we calculate the
trion binding energies in WS$_2$ and WSe$_2$ for a large variety of screening
lenghts and different dielectric constants for the environment. Our approach
indicates the prominent role played by the Berry curvature along with non-local
electronic interactions in the understanding of the energy spectra of neutral
and charged excitons in transition-metal dichalcogenides and in the the
interpretation of their optical properties.Comment: 11 pages, 3 figure

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