Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

/pdf/orbital-magnetization-in-periodic-insulators-4qut1yv0zj.pdf

Orbital Magnetization in Periodic Insulators

Many Body Problem

Photoemission established tantalum phosphide as a Weyl semimetal, which hosts exotic Weyl fermion quasiparticles and Fermi arcs. Weyl semimetals are expected to open up new horizons in physics and materials science because they provide the first realization of Weyl fermions and exhibit protected Fermi arc surface states. However, they had been found to be extremely rare in nature. Recently, a family of compounds, consisting of tantalum arsenide, tantalum phosphide (TaP), niobium arsenide, and niobium phosphide, was predicted as a Weyl semimetal candidates. We experimentally realize a Weyl semimetal state in TaP. Using photoemission spectroscopy, we directly observe the Weyl fermion cones and nodes in the bulk, and the Fermi arcs on the surface. Moreover, we find that the surface states show an unexpectedly rich structure, including both topological Fermi arcs and several topologically trivial closed contours in the vicinity of the Weyl points, which provides a promising platform to study the interplay between topological and trivial surface states on a Weyl semimetal’s surface. We directly demonstrate the bulk-boundary correspondence and establish the topologically nontrivial nature of the Weyl semimetal state in TaP, by resolving the net number of chiral edge modes on a closed path that encloses the Weyl node. This also provides, for the first time, an experimentally practical approach to demonstrating a bulk Weyl fermion from a surface state dispersion measured in photoemission.

Experimental discovery of a topological Weyl semimetal state in TaP

Moir\'e superlattices formed in two-dimensional semiconductor heterobilayers provide a new realization of Hubbard model physics in which the number of electrons per effective atom can be tuned at will. We report on an exact diagonalization study of the electronic properties of half-filled narrow moir\'e bands in which correlation strengths are varied by changing twist angles or interaction strengths. We construct a phase diagram for the bilayer, identifying where the metal-insulator phase transition occurs, estimating the sizes of the charge gaps in the insulating phase, and commenting on the nature of the transition and the importance of subdominant interaction parameters.

Metal-insulator transition in transition metal dichalcogenide heterobilayer moiré superlattices

Author(s): Szasz, Aaron; Motruk, Johannes | Abstract: In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. When one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice N #x27;{e}el order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

/pdf/phase-diagram-of-the-anisotropic-triangular-lattice-hubbard-rgaf933zvi.pdf

Phase diagram of the anisotropic triangular lattice Hubbard model

Effets des corrélations électroniques et du champ magnétique dans les semi-métaux de Weyl

The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.

Orbital effect of the magnetic field in dynamical mean-field theory

Negative magnetoresistance is one of the manifestations of the chiral anomaly in Weyl semimetals. The magneto-optical conductivity also shows transitions between Landau levels that are not spaced as in an ordinary electron gas. How are such topological properties modified by interactions and temperature? We answer this question by studying a lattice model of Weyl semimetals with an onsite Hubbard interaction. Such an interacting Weyl semimetal, dubbed as Weyl liquid, may be realized in ${\mathrm{Mn}}_{3}\mathrm{Sn}$. We solve that model with single-site dynamical mean-field theory. We find that in a Weyl liquid, quasiparticles can be characterized by a quasiparticle spectral weight $Z$, although their lifetime increases much more rapidly as frequency approaches zero than in an ordinary Fermi liquid. The negative magnetoresistance still exists, even though the slope of the linear dependence of the dc conductivity with respect to the magnetic field is decreased by the interaction. At elevated temperatures, a Weyl liquid crosses over to bad-metallic behavior where the Drude peak becomes flat and featureless. We comment on the effect of a Zeeman term.

Interaction and temperature effects on the magneto-optical conductivity of Weyl liquids

Ferromagnetic Weyl semimetals exhibit an anomalous Hall effect, a consequence of their topological properties. In the noninteracting case, the derivative of the orbital magnetization with respect to chemical potential is proportional to this anomalous Hall effect, the St\ifmmode \check{r}\else \v{r}\fi{}eda formula. Motivated by compounds such as ${\text{Mn}}_{3}\text{Sn}$, here we investigate how interactions modeled by a Hubbard $U$ impact on both quantities when the Fermi energy is either aligned with the Weyl nodes or away from them. Using dynamical mean-field theory, we first find interaction-induced Mott- and band-insulating transitions. In the Weyl semimetal regime, away from insulators, interactions lead to an increase in the imbalance between the densities of spin species induced by a Zeeman term $h$. This increased imbalance leads to an increase of the anomalous Hall effect that can also be understood from the displacement of the Weyl nodes and topological arguments. This interaction-induced spin imbalance also compensates the reduction in orbital magnetization of each spin species that comes from smaller quasiparticle weight. In the small interaction regime, the combined effects lead to an orbital magnetization that depends weakly on interaction and still changes linearly with chemical potential at small doping. In the intermediate and strong correlation regimes, the localization due to interaction affects strongly the orbital magnetization, which becomes small. A quasiparticle picture explains the anomalous Hall effect but does not suffice for the orbital magnetization. We propose a modified St\ifmmode \check{r}\else \v{r}\fi{}eda formula to relate anomalous Hall effect and orbital magnetization in the weak correlation limit. We also identify mirror and particle-hole symmetries of the lattice model that explain, respectively, the vanishing of the anomalous Hall effect at $h=0$ for all $U$ and $\ensuremath{\mu}$ of the orbital magnetization at half-filling $\ensuremath{\mu}=0$ for all $U$ and $h$.

Orbital magnetization and anomalous Hall effect in interacting Weyl semimetals

Spin-liquid behavior was recently suggested experimentally in the moderately one-dimensional organic compound $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{H}}_{3}{(\text{Cat-EDT-TTF})}_{2}$. This compound can be modeled by the one-band Hubbard model on the anisotropic triangular lattice with ${t}^{\ensuremath{'}}/t\ensuremath{\simeq}1.5$, where ${t}^{\ensuremath{'}}$ is the minority hopping. It thus becomes important to extend previous studies, that were performed in the range $0\ensuremath{\le}{t}^{\ensuremath{'}}/t\ensuremath{\le}1.2$, to find out whether there is a regime where Mott insulating behavior can be found without long-range magnetic order. To this end, we study the above model in the range $1.2\ensuremath{\le}{t}^{\ensuremath{'}}/t\ensuremath{\le}2$ using cluster dynamical mean-field theory (CDMFT). We argue that it is important to choose a symmetry-preserving cluster rather than a quasi-one-dimensional cluster. We find that, upon increasing ${t}^{\ensuremath{'}}/t$ beyond ${t}^{\ensuremath{'}}/t\ensuremath{\approx}1.3$, the Mott transition at zero temperature is replaced by a first-order transition separating a metallic state from a collinear magnetic insulating state excluding the possibility to find a quantum spin liquid for the physically relevant value ${t}^{\ensuremath{'}}/t\ensuremath{\simeq}1.5$. The phase diagram obtained in this study can provide a working basis for moderately one-dimensional compounds on the anisotropic triangular lattice.

Mott transition and magnetism on the anisotropic triangular lattice

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