Related papers: Fractional Quantum Hall Physics in Topological Fla…
Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…
We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local…
We provide a characterization of tunneling between coupled topological insulators in 2D and 3D under the influence of a ferromagnetic layer. We explore conditions for such systems to exhibit integer quantum Hall physics and localized…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Recent experiments on bilayer graphene twisted near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride (hBN) substrate. These states arise from valley ferromagnetism,…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
We derive the macroscopic charge and current densities of a Chern insulator initially occupying its electronic ground state as it responds to a finite-frequency electric field; we use a previously developed formalism based on microscopic…
Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous…
We explain the appearance of magic angles and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic…
Even if a noninteracting system has zero Berry curvature everywhere in the Brillouin zone, it is possible to introduce interactions that stabilise a fractional Chern insulator. These interactions necessarily break time-reversal symmetry…
We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from…
A large number of recent works point to the emergence of intriguing analogs of fractional quantum Hall states in lattice models due to effective interactions in nearly flat bands with Chern number C=1. Here, we provide an intuitive and…
Among the extensive studies of fractional quantum anomalous Hall (FQAH) states, there recently appears a growing interest in the topological states with coexisting charge density wave (CDW) orders. Such states are referred to as Hall…
We study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component…
A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional…
We provide a parton construction of wavefunctions and effective field theories for fractional Chern insulators. We also analyze a strong coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto…
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here we demonstrate through numerical calculations on model wave…
We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern…
The study of topological property of band insulators is an interesting branch of condensed matter physics. Two types of topologically nontrivial insulators have been extensively studied. The first type is characterized by a nonzero TKNN…
The fractional quantum Hall (FQH) effect refers to the strongly-correlated phenomena and the associated quantum phases of matter realized in a two-dimensional gas of electrons placed in a large perpendicular magnetic field. In such systems,…