Related papers: Comments on the Chern Number Argument of the Integ…
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We…
The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators - topologically non-trivial states of two-dimensional matter with broken…
We study the behavior of two-dimensional electron gas in the fractional quantum Hall regime in the presence of finite layer thickness and correlated disordered potential. Generalizing the Chern number calculation to many-body systems, we…
We study the practicability of achieving quantum anomalous Hall (QAH) effect with field-tunable Chern number in a magnetically doped, topologically trivial insulating thin film. Specifically in a candidate material,…
We study the nu=1/3 quantum Hall state in presence of the random disorder. We calculate the topologically invariant Chern number, which is the only quantity known at present to unambiguously distinguish between insulating and current…
A square lattice model which exhibits a nonzero quantized Hall conductance in a zero net magnetic field at certain values of the parameters is presented. The quantization is due to the existence of a topological winding number that…
We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a ${\cal W}_{1+\infty}$ for the fractional quantum Hall effect such that the negative modes annihilate the…
A quantum anomalous Hall state with high Chern number has so far been realized in multiplayer structures consisting of alternating magnetic and undoped topological insulator layers. However, in previous proposals, the Chern number can be…
We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk…
We show analytically and numerically that omission of quantum interference from the Chalker-Coddington model of the integer quantum Hall effect gives a localization length exponent nu=4/3 as in ordinary two-dimensional percolation. Thus,…
We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For…
In this paper we make attempt to obtain a description of the Quantum Hall Effect (both integer and fractional) by means of electron's Green functions of three-dimensional (planar) electrodynamics. We show that expression for the free…
We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
The integer quantum Hall effect is analysed using a transport mechanism with a semi-classic wave packages of electrons in this paper. A strong magnetic field perpendicular to a slab separates the electron current into two branches with…
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…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…