8,862 research outputs found
Rashba and intrinsic spin-orbit interactions in biased bilayer graphene
We investigate the effect that the intrinsic spin-orbit and the inter- and
intra-layer Rashba interactions have on the energy spectrum of either an
unbiased or a biased graphene bilayer. We find that under certain conditions, a
Dirac cone is formed out of a parabolic band and that it is possible to create
a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in
the presence of only an intralayer Rashba interaction, the K (K') point splits
into four distinct ones, contrarily to the case in single-layer graphene, where
the splitting also takes place, but the low-energy dispersion at these points
remains identical.Comment: 10 pages, 10 figure
Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach
We study the quantum Hall effect in graphene at filling factors \nu = 0 and
\nu = \pm, concentrating on the quantum Hall ferromagnetic regime, within a
non-perturbative bosonization formalism. We start by developing a bosonization
scheme for electrons with two discrete degrees of freedom (spin-1/2 and
pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases
are considered, namely the so-called spin-pseudospin, spin, and pseudospin
phases. The first corresponds to a quarter-filled (\nu =-1) while the others to
a half-filled (\nu = 0) lowest Landau level. In each case, we show that the
elementary neutral excitations can be treated approximately as a set of
n-independent kinds of boson excitations. The boson representation of the
projected electron density, the spin, pseudospin, and mixed spin-pseudospin
density operators are derived. We then apply the developed formalism to the
effective continuous model, which includes SU(4) symmetry breaking terms,
recently proposed by Alicea and Fisher. For each quantum Hall state, an
effective interacting boson model is derived and the dispersion relations of
the elementary excitations are analytically calculated. We propose that the
charged excitations (quantum Hall skyrmions) can be described as a coherent
state of bosons. We calculate the semiclassical limit of the boson model
derived from the SU(4) invariant part of the original fermionic Hamiltonian and
show that it agrees with the results of Arovas and co-workers for SU(N) quantum
Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking
terms in the skyrmion energy.Comment: 16 pages, 4 figures, final version, extended discussion about the
boson-boson interaction and its relation with quantum Hall skyrmion
Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
For two-dimensional lattices in a tight-binding description, the intrinsic
spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens
gaps that exhibit the quantum spin Hall effect. In this paper, we study the
effect of a real next-nearest-neighbor hopping term on the band structure of
several Dirac systems. In our model, the spin is conserved, which allows us to
analyze the spin Chern numbers. We show that in the Lieb, kagome, and T_3
lattices, variation of the amplitude of the real next-nearest-neighbor hopping
term drives interesting topological phase transitions. These transitions may be
experimentally realized in optical lattices under shaking, when the ratio
between the nearest- and next-nearest-neighbor hopping parameters can be tuned
to any possible value. Finally, we show that in the honeycomb lattice,
next-nearest-neighbor hopping only drives topological phase transitions in the
presence of a magnetic field, leading to the conjecture that these transitions
can only occur in multigap systems.Comment: 10 pages, 9 figures [erratum: corrected colors in Fig. 7(a)
Supersolid phases of dipolar bosons in optical lattices with a staggered flux
We present the theoretical mean-field zero-temperature phase diagram of a
Bose-Einstein condensate (BEC) with dipolar interactions loaded into an optical
lattice with a staggered flux. Apart from uniform superfluid, checkerboard
supersolid and striped supersolid phases, we identify several supersolid phases
with staggered vortices, which can be seen as combinations of supersolid phases
found in earlier work on dipolar BECs and a staggered-vortex phase found for
bosons in optical lattices with staggered flux. By allowing for different
phases and densities on each of the four sites of the elementary plaquette,
more complex phase patterns are found.Comment: 11 pages; added references, minor changes in tex
Conformal QED in two-dimensional topological insulators
It has been shown recently that local four-fermion interactions on the edges
of two-dimensional time-reversal-invariant topological insulators give rise to
a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). In this
work, we provide a first-principle derivation of this non-Fermi-liquid phase
based on the gauge-theory approach. Firstly, we derive a gauge theory for the
edge states by simply assuming that the interactions between the Dirac fermions
at the edge are mediated by a quantum dynamical electromagnetic field. Here,
the massless Dirac fermions are confined to live on the one-dimensional
boundary, while the (virtual) photons of the U(1) gauge field are free to
propagate in all the three spatial dimensions that represent the physical space
where the topological insulator is embedded. We then determine the effective
1+1-dimensional conformal field theory (CFT) given by the conformal quantum
electrodynamics (CQED). By integrating out the gauge field in the corresponding
partition function, we show that the CQED gives rise to a 1+1-dimensional
Thirring model. The bosonized Thirring Hamiltonian describes exactly a HLL with
a parameter K and a renormalized Fermi velocity that depend on the value of the
fine-structure constant .Comment: (5+4) pages, 2 figure
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