Related papers: From The Quantum Hall Effect To Topological Insula…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
Modern material science has been revolutionized by the discovery of novel topological states of quantum matter, which sheds new lights on solving long-standing scientific challenges. However, the exotic quantum phenomena are typically…
The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…
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…
Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…
The quantum Hall effect is widely used for the investigation of fundamental phenomena, ranging from topological phases to composite fermions. In particular, the discovery of a room temperature resistance quantum in graphene is significant…
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…
In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating 2D bulk, without requiring an external…
Topological insulating states in two-dimensional (2D) materials are ideal systems to study different types of quantized response signals due to their in gap metallic states. Very recently, the quantum spin Hall (QSH) effect was discovered…
As a new quantum state, topological insulators have become the focus of condensed matter and material science. The open system research of topological insulators has aroused the interest of many researchers. Recently, many aspects,…
The quantum Hall effects, discovered about thirty years ago have remained one of the most spectacular discoveries in condensed matter physics in the past century. Those discoveries triggered huge expansion in the field of low-dimensional…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the…
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and…
The quantum anomalous Hall effect (QAHE) in magnetic topological insulators offers great potential to revolutionize quantum electrical metrology by establishing primary resistance standards operating at zero external magnetic field and…
We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…
Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee…
Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system…
The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a new type of fractional quantum Hall system, which has the special property that it lives in…