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We study the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states can be viewed as symmetric combinations of a spin-up and spin-down half-integer fractional quantum Hall state (FQH)…
The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of {\em charged} winding number in the super-plane, we represent the braid group generators as homotopically constrained…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to…
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…
Among the extensive studies of fractional quantum anomalous Hall (FQAH) states, there recently appears a growing interest in the topological states with coexisting charge density wave (CDW) orders. Such states are referred to as Hall…
The recent discovery of fractional quantum anomalous Hall (FQAH) states - fractional quantum Hall (FQH) states realized without an external magnetic field - in twisted transition-metal dichalcogenide (TMD) bilayers represents a significant…
There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two- component FQH systems at total filling fraction $\nu = n+ 2/3$, for integer $n$. Some of…
Rotationally invariant fractional quantum Hall (FQH) states have long been understood in terms of composite bosons or composite fermions. Recent investigations of both incompressible and compressible states in highly tilted fields, which…
We theoretically investigate the nature of the state at quarter filled lowest Landau level and predict that, as the quantum well width is increased, a transition occurs from the composite fermion Fermi sea into a novel non-Abelian…
We consider the fractional quantum Hall effect at the filling factor $\nu=4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the "$4\bar{2}1^{3}$"…
The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The…
We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes.…
In this paper we study the conditions under which an N-electron wave function for a fractional quantum Hall (FQH) state can be viewed as N-point correlation function in a conformal field theory (CFT). Several concrete examples are presented…
The observed fractional quantum Hall (FQH) plateaus follow a recurring hierarchical structure that allows an understanding of complex states based on simpler ones. Condensing the elementary quasiparticles of an Abelian FQH state results in…
It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring…
We compute the electron diffusion thermopower at compressible Quantum Hall states corresponding to even denominator fractions in the framework of the composite fermion approach. It is shown that the deviation from the linear low temperature…
We report observation of the fractional quantum Hall effect (FQHE) in high mobility multi-terminal graphene devices, fabricated on a single crystal boron nitride substrate. We observe an unexpected hierarchy in the emergent FQHE states that…
It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) \cite{Tsui1982} will emerge when electrons move in Landau levels. In this letter, we report the discovery of the…
Fractional Quantum Hall effect (FQHE) is a unique many-body phenomenon, which was discovered in a two-dimensional electron system placed in a strong perpendicular magnetic field. It is entirely due to the electron-electron interactions…