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 $E=0$, 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 $m_a\mu_a = m_b\mu_b$ is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added, accepted for publication in Phys. Rev.