Related papers: Split-Quaternionic Hopf Map, Quantum Hall Effect, …
We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness…
In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected inter-electron interaction. Haldane's pseudopotential formalism has been an extremely…
Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive…
Scattering immune propagation of light in topological photonic systems may revolutionarize the design of integrated photonic circuits for information processing and communications. In optics, various photonic topological circuits have been…
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel…
We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau level mixing by electron-electron interactions. To second order in the ratio of electron-electron…
It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian…
We study theoretically the parallel quantum wires of the experiment by Auslaender et al. [Science 308, 88 (2005)] at low electron density. It is shown that a Hall effect as observed in two- or three-dimensional electron systems develops as…
The quantum valley Hall effect (QVHE) has been observed in a variety of experimental setups, both quantum and classical. While extremely promising for applications, one should be reminded that QVHE is not an exact topological phenomenon and…
We propose a geometric description of all gapped excitations in fractional quantum Hall phases that reveals several fundamental understandings with experimental consequences. These include a duality between the Hilbert space of multiple…
The quantum deformation of the Hopf algebra describes the skeleton of quantum field theory, namely its characterizing feature consisting in the existence of infinitely many unitarily inequivalent representations of the canonical commutation…
In the fractional quantum Hall effect regime we measure diagonal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions,…
We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on supermanifolds. On each of…
This is a theoretical review of the quantum Hall effect observed in quasi-one-dimensional organic conductors such as (TMTSF)2X. It is written for a book "Physics of Organic Superconductors and Conductors" to be published by Springer and…
These pedagogical lecture notes present a general introduction to most aspects of the integer and fractional quantum Hall effects. This is followed by an extensive discussion of quantum Hall ferromagnetism, both for spins in single-layer…
In certain backgrounds string theory exhibits quantum Hall-like behavior. These backgrounds provide an explicit realization of the effective non-commutative gauge theory description of the fractional quantum Hall effect (FQHE), and of the…
We study a pairing mechanism for the quantum Hall system using a mean field theory with a basis on the von Neumann lattice, on which the magnetic translations commute. In the Hartree-Fock-Bogoliubov approximation, we solve the gap equation…
We present a microscopic theory to give a physical picture of the formation of quantum anomalous Hall (QAH) effect in graphene due to a joint effect of Rashba spin-orbit coupling $\lambda_R$ and exchange field $M$. Based on a continuum…
In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres $\mathbb{S}^n$. First, we propose a new approach to isoperimetric inequalities based on energy index.…
The topological $p$-wave pairing of composite fermions, believed to be responsible for the 5/2 fractional quantum Hall effect (FQHE), has generated much exciting physics. Motivated by the parton theory of the FQHE, we consider the…