Related papers: Introduction to Topological Phases and Electronic …
Quantum spin Hall effect is endowed with topologically protected edge modes with gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with opposite parity for winding of spin texture for…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
Time-dependent perturbations can drive a trivial two-dimensional band insulator into a quantum Hall-like phase, with protected nonequilibrium states bound to its edges. We propose an experiment to probe the existence of these topological…
We develop a Dirac fermion theory for topological phases in magnetic topological insulator films. The theory is based on exact solutions of the energies and the wave functions for an effective model of the three-dimensional topological…
The fractional quantum Hall (FQH) state is a topological state of matter resulting from the many-body effect of interacting electrons and is of vast interest in fundamental physics. The experimental observation of topological surface states…
The realization of fractional Chern insulators in moir\'e materials has sparked the search for further novel phases of matter in this platform. In particular, recent works have demonstrated the possibility of realizing quantum anomalous…
The exploration of magnetic topological insulators is instrumental in exploring axion electrodynamics and intriguing transport phenomena, such as the quantum anomalous Hall effect. Here, we report that a family of magnetic compounds…
Haldane's tight-binding model, which describes a Chern insulator in a two-dimensional hexagonal lattice, exhibits quantum Hall conductivity without an external magnetic field. Here, we explore an $\alpha -T_{3}$ lattice subjected to…
We show how the phases of interacting particles in topological flat bands, known as fractional Chern insulators, can be adiabatically connected to incompressible fractional quantum Hall liquids in the lowest Landau-level of an externally…
In 2+1-dimensions (2+1D), a gapped quantum phase with no symmetry (i.e. a topological order) can have a thermal Hall conductance $\kappa_{xy}=c \frac{\pi^2 k_B^2}{3h}T$, where the dimensionless $c$ is called chiral central charge. If there…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
Motivated by the recent experimental realization of the half-quantized Hall effect phase in a three-dimensional (3D) semi-magnetic topological insulator [M. Mogi et al., Nature Physics 18, 390 (2022)], we propose a scheme for realizing the…
We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global…
Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion…
We study a class of multi-orbital models based on those proposed by Venderbos, Hu, and Kane which exhibit an interplay of topology, interactions, and fermion incoherence. In the non-interacting limit, these models exhibit trivial and Chern…
Emergence of multiple topological phases with a series of Chern numbers, $\pm 1$, $\mp 1$, $\pm 2$, $\mp 2$, $\pm 3$ and $\mp 4$, are observed in a ferromagnetic Kitaev-Heisenberg-spin-anisotropic model on honeycomb lattice with further…
We introduce exotic gapless states---`composite Dirac liquids'---that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but…
The quantum Hall effect, fundamental in modern condensed matter physics, continuously inspires new theories and predicts emergent phases of matter. Here we experimentally demonstrate three types of Chern insulators with synthetic dimensions…
We consider a class of {\em quantum Hall topological insulators}: topologically nontrivial states with zero Chern number at finite magnetic field, in which the counter-propagating edge states are protected by a symmetry (spatial or spin)…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…