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Starting with a description of the motivation underlying the analysis presented in this paper and a brief survey of the chiral anomaly, I proceed to review some basic elements of the theory of the quantum Hall effect in 2D incompressible…
The prediction of non-trivial topological phases in Bloch insulators in three dimensions has recently been experimentally verified. Here, I provide a picture for obtaining the $Z_{2}$ invariants for a three dimensional topological insulator…
Chern insulator ferromagnets are characterized by a quantized anomalous Hall effect, and have so far been identified experimentally in magnetically-doped topological insulator (MTI) thin films and in bilayer graphene moir{\'e}…
The long-sought Chern insulators that manifest quantum anomalous Hall effect are typically considered to occur solely in ferromagnets. Here, we theoretically predict the realizability of Chern insulators in antiferromagnets, of which the…
The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field.…
We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on $\emph{p}_{x}$ and \emph{p}_{y} orbitals exhibit very interesting doubly…
We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined three-fold or four-fold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves…
Under suitable conditions, some twisted graphene multilayers and transition-metal dichalcogenides become Chern insulators, exhibiting the anomalous quantum Hall effect and orbital magnetization due to spontaneous valley polarization. We…
The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In…
A Chern insulator (quantum anomalous Hall insulator) phase is demonstrated to exist in a typical semi-Dirac system, the TiO2/VO2 heterostructure. By combining first-principles calculations with Wannier-based tight-binding model, we…
Starting from a minimal model for a 2D nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase winding number of the mass gap terms on the loop. We…
In this paper, we formulate the real-space Chern number in a supercell framework. In this framework, the overlap matrix between two corners of the Brillouin zone (BZ) is derived from diagonalizing the real-space Hamiltonian with periodic…
The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrisically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems, or…
Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…
The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based…
The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as…
We study the behaviour of electrons interacting with a classical magnetic background via a strong Hund coupling. The magnetic background results from a Hamiltonian which favours at low temperature the emergence of a phase with non-zero…
Two-dimensional Euler insulators are novel kind of systems that host multi-gap topological phases, quantified by a quantised first Euler number in their bulk. Recently, these phases have been experimentally realised in suitable…
This work explores the topological properties of altermagnets, a novel class of collinear magnetic materials. We employ equivariant K-theory of magnetic groups and Hamiltonian models to formulate a robust $C^z_4 \mathbb{T}$ topological…