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Motivated by the observation of even denominator fractional quantum Hall effect in the $n=3$ Landau level of monolayer graphene [Y. Kim $\textit{et al.}$, Nature Physics $\textbf{15}$, 154 (2019)], we consider a Bardeen-Cooper-Schrieffer…
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the…
In the extreme quantum limit, when the Landau level filling factor $\nu<1$, the dominant electron-electron interaction in low-disorder two-dimensional electron systems leads to exotic many-body phases. The ground states at even-denominator…
The flux quanta attachment to the electrons creates composite fermions (CFs). The mass, the size and the density of the CF are inconsistent with real material. The sequence of fractional charges which suggest formation of CF agrees with the…
We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that…
Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtube-quark system the topology of a baryon consisting three heavy flavor quarks resembles that of the fractional quantum Hall effect (FQHE) in condensed…
Fractional quantum Hall states (FQHS) with the filling factor nu = p/q of q < 21 are examined and their energies are calculated. The classical Coulomb energy is evaluated among many electrons; that energy is linearly dependent on 1/nu. The…
The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the…
The fractional quantum Hall (FQH) effect is a macroscopic manifestation of strong electron-electron interactions. Even denominator FQH states (FQHSs) at half-filling are particularly interesting as they are predicted to host non-Abelian…
One of the most intriguing phenomena in nature is the fractional quantum Hall effect (FQHE) observed in the half-filled second Landau level which, arising in even-denominator filling factors, $\nu=5/2$ and $7/2$, is completely different…
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged…
The realization of the quantum spin Hall effect in HgTe quantum wells has led to the development of topological materials which, in combination with magnetism and superconductivity, are predicted to host chiral Majorana fermions. However,…
We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi…
Charged excitons of composite fermions (CFs) are considered in the fractional quantum Hall effect. Energies of the charged CF excitons are computed at $\nu=1/3$ as a function of the size of exciton. We show that the charged CF exciton with…
We construct an effective Hamiltonian for electrons in the fractional quantum Hall regime for GaAs and graphene that takes into account Landau level mixing (for both GaAs and graphene) and subband mixing (for GaAs, due to the nonzero width…
Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0<|\nu|<1 and 1<|\nu|<2. We argue that these differences can be largely…
We discuss the properties of Skyrmions in the Fractional Quantum Hall effect (FQHE). We begin with a brief description of the Chern-Simons-Landau-Ginzburg description of the FQHE, which provides the framework in which to understand a new…
We have investigated the effect of unidirectional periodic potential modulation on the fractional quantum Hall (FQH) states located within the filling factor range $1<\nu<2$. We find that odd-numerator FQH states are strongly suppressed,…
We study fermions and hardcore bosons with long range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors \cite{Neupert2011}. We consider the case…
The fractional quantum Hall effect (FQHE) in the second orbital Landau level at filling factor 5/2 remains enigmatic and motivates our work. We consider the effect of the quasi-2D nature of the experimental FQH system on a number of FQH…