2,836 research outputs found
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)
Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
In this work, we explore the rich variety of topological states that arise in
two-dimensional systems, by considering the competing effects of spin-orbit
couplings and a perpendicular magnetic field on a honeycomb lattice. Unlike
earlier approaches, we investigate minimal models in order to clarify the
effects of the intrinsic and Rashba spin-orbit couplings, and also of the
Zeeman splitting, on the quantum Hall states generated by the magnetic field.
In this sense, our work provides an interesting path connecting quantum Hall
and quantum spin Hall physics. First, we consider the properties of each term
individually and we analyze their similarities and differences. Secondly, we
investigate the subtle competitions that arise when these effects are combined.
We finally explore the various possible experimental realizations of our model.Comment: 19 pages, 15 figure
Momentum Space Regularizations and the Indeterminacy in the Schwinger Model
We revisited the problem of the presence of finite indeterminacies that
appear in the calculations of a Quantum Field Theory. We investigate the
occurrence of undetermined mathematical quantities in the evaluation of the
Schwinger model in several regularization scenarios. We show that the
undetermined character of the divergent part of the vacuum polarization tensor
of the model, introduced as an {\it ansatz} in previous works, can be obtained
mathematically if one introduces a set of two parameters in the evaluation of
these quantities. The formal mathematical properties of this tensor and their
violations are discussed. The analysis is carried out in both analytical and
sharp cutoff regularization procedures. We also show how the Pauli Villars
regularization scheme eliminates the indeterminacy, giving a gauge invariant
result in the vector Schwinger model.Comment: 10 pages, no figure
Genesis of the Floquet Hofstadter butterfly
We investigate theoretically the spectrum of a graphene-like sample
(honeycomb lattice) subjected to a perpendicular magnetic field and irradiated
by circularly polarized light. This system is studied using the Floquet
formalism, and the resulting Hofstadter spectrum is analyzed for different
regimes of the driving frequency. For lower frequencies, resonances of various
copies of the spectrum lead to intricate formations of topological gaps. In the
Landau-level regime, new wing-like gaps emerge upon reducing the driving
frequency, thus revealing the possibility of dynamically tuning the formation
of the Hofstadter butterfly. In this regime, an effective model may be
analytically derived, which allows us to retrace the energy levels that exhibit
avoided crossings and ultimately lead to gap structures with a wing-like shape.
At high frequencies, we find that gaps open for various fluxes at , and
upon increasing the amplitude of the driving, gaps also close and reopen at
other energies. The topological invariants of these gaps are calculated and the
resulting spectrum is elucidated. We suggest opportunities for experimental
realization and discuss similarities with Landau-level structures in non-driven
systems.Comment: 8 pages, 4 figure
Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model
In this work, we show that, due to the alternating orientation of the spins
in the ground state of the artificial square spin ice, the influence of a set
of spins at a certain distance of a reference spin decreases faster than the
expected result for the long range dipolar interaction, justifying the use of
the nearest neighbor two dimensional square spin ice model as an effective
model. Using an extension of the model presented in ref. [Scientific Reports 5,
15875 (2015)], considering the influence of the eight nearest neighbors of each
spin on the lattice, we analyze the thermodynamics of the model and study the
monopoles and string densities dependence as a function of the temperature.Comment: 11 pages, 8 figure
Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry
We study theoretically two-dimensional single-crystalline sheets of
semiconductors that form a honeycomb lattice with a period below 10 nm. These
systems could combine the usual semiconductor properties with Dirac bands.
Using atomistic tight-binding calculations, we show that both the atomic
lattice and the overall geometry influence the band structure, revealing
materials with unusual electronic properties. In rocksalt Pb chalcogenides, the
expected Dirac-type features are clouded by a complex band structure. However,
in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb
nanogeometry leads to rich band structures, including, in the conduction band,
Dirac cones at two distinct energies and nontrivial flat bands and, in the
valence band, topological edge states. These edge states are present in several
electronic gaps opened in the valence band by the spin-orbit coupling and the
quantum confinement in the honeycomb geometry. The lowest Dirac conduction band
has S-orbital character and is equivalent to the pi-pi* band of graphene but
with renormalized couplings. The conduction bands higher in energy have no
counterpart in graphene; they combine a Dirac cone and flat bands because of
their P-orbital character. We show that the width of the Dirac bands varies
between tens and hundreds of meV. These systems emerge as remarkable platforms
for studying complex electronic phases starting from conventional
semiconductors. Recent advancements in colloidal chemistry indicate that these
materials can be synthesized from semiconductor nanocrystals.Comment: 12 pages, 12 figure
Topological states in multi-orbital HgTe honeycomb lattices
Research on graphene has revealed remarkable phenomena arising in the
honeycomb lattice. However, the quantum spin Hall effect predicted at the K
point could not be observed in graphene and other honeycomb structures of light
elements due to an insufficiently strong spin-orbit coupling. Here we show
theoretically that 2D honeycomb lattices of HgTe can combine the effects of the
honeycomb geometry and strong spin-orbit coupling. The conduction bands,
experimentally accessible via doping, can be described by a tight-binding
lattice model as in graphene, but including multi-orbital degrees of freedom
and spin-orbit coupling. This results in very large topological gaps (up to 35
meV) and a flattened band detached from the others. Owing to this flat band and
the sizable Coulomb interaction, honeycomb structures of HgTe constitute a
promising platform for the observation of a fractional Chern insulator or a
fractional quantum spin Hall phase.Comment: includes supplementary materia
Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates
We propose that the dissipative dynamics of topological defects in a spiral
state is responsible for the transport properties in the spin-glass phase of
cuprates. Using the collective-coordinate method, we show that topological
defects are coupled to a bath of magnetic excitations. By integrating out the
bath degrees of freedom, we find that the dynamical properties of the
topological defects are dissipative. The calculated damping matrix is related
to the in-plane resistivity, which exhibits an anisotropy and linear
temperature dependence in agreement with experimental data.Comment: 4 pages, as publishe
Chern-Simons theory of multi-component quantum Hall systems
The Chern-Simons approach has been widely used to explain fractional quantum
Hall states in the framework of trial wave functions. In the present paper, we
generalise the concept of Chern-Simons transformations to systems with any
number of components (spin or pseudospin degrees of freedom), extending earlier
results for systems with one or two components. We treat the density
fluctuations by adding auxiliary gauge fields and appropriate constraints. The
Hamiltonian is quadratic in these fields and hence can be treated as a harmonic
oscillator Hamiltonian, with a ground state that is connected to the Halperin
wave functions through the plasma analogy. We investigate several conditions on
the coefficients of the Chern-Simons transformation and on the filling factors
under which our model is valid. Furthermore, we discuss several singular cases,
associated with symmetric states.Comment: 11 pages, shortened version, accepted for publication in Phys. Rev.
Phase Transition in Asymmetrical Superfluids I: Equal Fermi Surfaces
In this paper, we study phase transitions in asymmetrical fermion
superfluids. In this scenario, the candidates to form pair are particles with
mismatched masses and chemical potentials. We derive an expression for the
critical temperature in terms of the gap and masses (or chemical potentials)
when the constraint of equal Fermi surfaces is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added,
accepted for publication in Phys. Rev.
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