Related papers: Four-Dimensional Quantum Hall Effect in a Two-Dime…
A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded…
Scaling properties of the quantum Hall metal-insulator transition are severely affected by finite size effects in small systems. Surprisingly, despite the narrow spatial range where probability structure functions exhibit multifractal…
The integer quantum anomalous Hall (QAH) effect is a lattice analog of the quantum Hall effect at zero magnetic field. This striking transport phenomenon occurs in electronic systems with topologically nontrivial bands and spontaneous…
The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the…
A new picture of both integer and fractional incompressible quantum Hall fluids as fluids carrying a electric quadrupole is introduced. This clarifies their geometric properties, provides a generic expression for Hall viscosity, and allows…
We consider the quantum Hall effect induced by magnetic field and rotation, which can drive the Hall samples into the quantum Hall regime and induce fractional excitations. Both the mass and the charge of the Laughlin quasiparticles are…
Most of our current knowledge on condensed matters contains a default assumption: the matters are neutral charged. On the other hand, the two-dimension(2D) vortex-Coulomb gas charge analogy is a very successful theoretical tool in…
We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=\theta/2\pi$, with $\theta$ being…
Quasicrystals, a fascinating class of materials with long-range but nonperiodic order, have revolutionized our understanding of solid-state physics due to their unique properties at the crossroads of long-range-ordered and disordered…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…
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…
A long skinny gate across a fractional quantum Hall fluid at filling $\nu=1/m$ with odd integer $m$, creates a novel one-dimensional (1d) system which is isomorphic to a disordered 1d electron gas with {\it attractive} interactions. By…
We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust…
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…
Quantum spin Hall (QSH) effect, where electrons with opposite spin channels are deflected to opposite sides of a two-dimensional system with a quantized conductance, was believed to be characterized by a nontrivial topological index…
The fractional quantum Hall effect (FQHE), observed in two-dimensional (2D) charged particles at high magnetic fields, is one of the most fascinating, macroscopic manifestations of a many-body state stabilized by the strong Coulomb…
The non-Hermitian extension of quasicrystals (QC) are highly tunable system for exploring novel material phases. While extended-localized phase transitions have been observed in one dimension, quantum phase transition in higher dimensions…
In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions…
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size…
The two-dimensional surface of a coupled multilayer integer quantum Hall system consists of an anisotropic chiral metal. This unusual metal is characterized by ballistic motion transverse and diffusive motion parallel (\hat{z}) to the…