Related papers: Comments on the Chern Number Argument of the Integ…
Two microscopic theories have been proposed for the explanation of the fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory and the composite fermion theory. Contradictory statements have been made regarding the…
A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $\nu=1/3$ and…
We propose to realize the quantum anomalous Hall effect (QAHE) in two-dimensional compensated antiferromagnets without net spin magnetization.} We consider antiferromagnetic MnBi$_2$Te$_4$ as a concrete example. \textcolor{blue}{By breaking…
We study the electromagnetic response of a chiral ${\rm d_{xy}+id_{x^2-y^2}}$ charge density wave state. Due to parity (${\cal P}$) and time reversal (${\cal T}$) violation, Chern-Simons terms emerge in the effective action of the U(1)…
We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…
When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are…
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory.…
We report a spectral asymmetry effect in the quantum harmonic oscillator, where its partition function is identified as the Chern character. This establishes a direct link between statistical mechanics, and topological invariants…
We present recent experimental results confirming previously predicted strong asymmetries of the current distribution in narrow Hall bars under the conditions of the integer quantum Hall effect (IQHE). Using a previously developed…
We show in this article that if a holomorphic vector bundle has a nonnegative Hermitian metric in the sense of Bott and Chern, which always exists on globally generated holomorphic vector bundles, then some special linear combinations of…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
It has been claimed recently that the black hole information-loss paradox has been resolved: the evolution of quantum states in the presence of a black hole is unitary and information preserving. We point out that, contrary to some claims…
The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface…
The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In…
Electrons of $d$-symmetry interacting with a localized non-collinear antiferromagnetic spin order on a kagome lattice are considered. Even in the absence of an external magnetic field, spin-orbit coupling or relativistic effects, the spin…
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically…
The fractional quantum Hall effect at $\nu=2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class…
The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…
Inferring causal relations from experimental observations is of primal importance in science. Instrumental tests provide an essential tool for that aim, as they allow one to estimate causal dependencies even in the presence of unobserved…