Two-band Lattice Model Research Articles

Chiral magnetic effect in lattice models of tilted multi-Weyl semimetals

We study the chiral magnetic effect (CME) in tilted multi-Weyl semimetals (mWSMs) employing a two-band lattice model. We focus on the type-II phase of mWSMs, introduced by incorporating a Lorentz symmetry violating tilt term. Our work adds to the current understanding of the CME (and also the anomalous Hall effect) in the type-II phase of mWSMs and near the Lifshitz transition by varying tilt. Like the elementary Weyl semimetal case, our results also indicate that the Berry curvature drives the CME for higher monopole charges. We find a peak in the CME at the transition point and discuss its significance using the density of states. Along the way we also examine both observables as a function of the energy separation of the Weyl points.

Winding Vector: How to Annihilate Two Dirac Points with the Same Charge.

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite (+- scenario) or identical (++ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the same winding number emerge under appropriate distortion (interaction, etc.), following the ++ scenario. Under further distortion, these Dirac points merge following the +- scenario, that is corresponding to opposite winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.

Formula omitted]- and [formula omitted]-wave superconductivity in a two-band model

Superconductivity in strongly correlated systems is a remarkable phenomenon that attracts a huge interest. The study of this problem is relevant for materials such as the high Tc oxides, pnictides and heavy fermions. In this work we study a realistic model that includes the relevant physics of superconductivity in the presence of strong Coulomb correlations. We consider a two-band model, since most of these correlated systems have electrons from at least two different atomic orbitals coexisting at their Fermi surface. The Coulomb repulsion is taken into account through a local repulsive interaction. Pairing is considered among quasi-particles in neighboring sites and we allow for different symmetries of the order parameter. In order to deal with the strong local correlations, we use the well known slave boson approach that has proved very successful for this problem. Here we are interested in obtaining the zero temperature properties of the model, specifically its phase diagram and the existence and nature of superconducting quantum critical points. We show that these can arise by increasing the mixing between the two bands. Since this can be controlled by external pressure or doping, our results have a direct relation with experiments. We show that the superconductor-to-normal transition can be either to a metal, a correlated metal or to an insulator. Also we compare the relative stability of s and d-wave paired states for different regions of parameter space and investigate the BCS–BEC crossover in the two-band lattice model as function of the strength of the pairing interaction.

Chiral magnetic effect in the absence of Weyl node

The nodal points in a Weyl semimetal are generally considered as the causes of the chiral anomaly and the chiral magnetic effect (CME). Employing a linear-response analysis of a two-band lattice model, we show that the Weyl nodes and thus the chirality are not required for the CME, while they remain crucial for the chiral anomaly. Similar to the anomalous Hall effect, the CME results directly from the Berry curvature of energy bands, even when there is no monopole source from the Weyl nodes. Therefore, the phenomenon of the CME could be observed in a wider class of materials. Motivated by this result, we suggest that the nodeless CME may appear in three-dimensional quantum anomalous Hall insulators, but after they become metallic due to the band deformation caused by inversion symmetry breaking.

Chiral magnetic effect in a two-band lattice model of Weyl semimetal

Employing a two-band model of Weyl semimetal, the existence of the chiral magnetic effect (CME) is established within the linear-response theory. The crucial role played by the limiting procedure in deriving correct transport properties is clarified. Besides, in contrast to the prediction based on linearized effective models, the value of the CME coefficient in the uniform limit shows a nontrivial dependence on various model parameters. Even when these parameters are away from the region of the linearized models, such that the concept of chirality may not be appropriate, this effect still exists. This implies that the Berry curvature, rather than the chiral anomaly, provides a better understanding of this effect.

Geometric tensor and the topological characterization of the Bloch band in a two-band lattice model

We investigate the quantum Riemannian metric and the Euler characteristic number of the Bloch states manifold in a two-band lattice model, where a topological phase transition from the normal to the Chern insulator occurs. We derive the topological Euler number of the band from the Gauss–Bonnet theorem on the closed Bloch states manifold in the first Brillouin zone, where the Riemannian metric of the states manifold is established by the real part of the quantum geometric tensor in the 2D quasi-momentum space. Meanwhile, we show that the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization of the band insulator. We discuss the topological numbers induced by the geometric tensor analytically in the case of two-band Hamiltonian and characteristic the zero-temperature phase diagram by the Euler number and first Chern number, respectively.

Enhancing the stability of a fractional Chern insulator against competing phases

We construct a two-band lattice model whose bands can carry the Chern numbers $C=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2$. By means of numerical exact diagonalization, we show that the most favorable situation that selects fractional Chern insulators (FCIs) is not necessarily the one that mimics Landau levels, namely a flat band with Chern number 1. First, we find that the gap, measured in units of the on-site electron-electron repulsion, can increase by almost two orders of magnitude when the bands are flat and carry a Chern number $C=2$ instead of $C=1$. Second, we show that giving a width to the bands can help to stabilize a FCI. Finally, we put forward a tool to characterize the real-space density profile of the ground state that is useful to distinguish FCI from other competing phases of matter supporting charge density waves or phase separation.

Properties of a Unique Type of Critical State in the Two-Dimensional Two-Band Anderson Lattice Model in the Presence of Site-Selective Disorder

The two-band Anderson lattice model is a minimum model for compounds where the bands near the Fermi energy arise from the hybridization among different atoms. In the presence of site-selective disorder via atomic doping, we show by using the standard transfer matrix method that a unique type of critical state appears at the edge of a less disorder-affected band but with strong van Hove singularity, the asymptotic localization length λ M neither depends on the lateral size M nor the disorder strength W . λ M is five orders of magnitude larger than the lateral size and increases linearly with sample size up to the largest layer number L =10 9 the machine can handle. λ M / L approaches a constant signifying the existence of a critical state at this particular energy. Except for the localization length for this energy, the reduced localization lengths for all other energies in both bands satisfy the single-parameter scaling law and the scaling parameter ξ is obtained and compared. The two-band lattice model with site-selective disorder has the advantage of simulating both diagonal and off-diagonal disorders over the one-band model, and the disparity between electron- and hole-doped bands can be attributed to such nonuniform disorder.

Persistent current in a mesoscopic semiconductor ring with electron-phonon interaction in the two-band model

We have studied, in the framework of the two-band lattice model, the persistent current in a one-dimensional mesoscopic semiconductor ring threaded by a flux , taking into consideration the electron-phonon interaction at absolute zero temperature. The current is a continuous function and periodic in , with a flux quantum , without jumps occurring when each period is over. The interband coupling enhances the current while the electron-phonon interaction suppresses it.