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Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged…

In the framework of a recently developed model of interacting composite fermions restricted to a single level, we calculate the activation gaps of a second generation of spin-polarized composite fermions. These composite particles consist…

A recently developed model of interacting composite fermions, is used to investigate different composite-fermion phases. Their interaction potential allows for the formation of both solid and new quantum-liquid phases, which are interpreted…

Almost all quantum Hall effect to date can be understood as {\em integral} quantum Hall effect of appropriate particles, namely electrons or composite fermions. This paper investigates theoretically the feasibility of nested states of…

Pairing interaction between fermionic particles leads to composite Bosons that condense at low temperature. Such condensate gives rise to long range order and phase coherence in superconductivity, superfluidity, and other exotic states of…

Theory predicts that double layer systems realize "two-component composite fermions," which are formed when electrons capture both intra- and inter-layer vortices, to produce a wide variety of new strongly correlated liquid and crystal…

A rich pattern of fractional quantum Hall states in graphene double layers can be naturally explained in terms of two-component composite fermions carrying both intra- and inter-layer vortices.

We consider a collection of fermions in a strong magnetic field coupled by a purely three body repulsive interaction, and predict the formation of composite fermions, leading to a remarkably rich phase diagram containing a host of…

Cyclotron braid subgroups are defined in order to identify the topological origin of Laughlin correlations in 2D Hall systems. Flux-tubes and vortices for composite fermion constructions are explained in terms of unavoidably multilooped…

Even though composite fermions in the fractional quantum Hall liquid are well established, it is not yet known up to what energies they remain intact. We probe the high-energy spectrum of the 1/3 liquid directly by resonant inelastic light…

The Hall-resistance curve of a two-dimensional electron system in the presence of a strong perpendicular magnetic field is an example of self-similarity. It reveals plateaus at low temperatures and has a fractal structure. We show that this…

We propose a two-fluid description of fractional quantum Hall systems, in which one component is a condensate of composite bosons and the other a Fermi liquid formed by composite fermions (or simply electrons). We employ the theory to model…

We study fractional quantum Hall states in double layer systems that can be interpreted as exciton condensates of composite fermions. An electron in one layer is dressed by two fluxes from the same layer and two fluxes from the other layer…

The even denominator fractional quantum Hall effect has been experimentally observed in graphene in the fourth Landau level ($n = 3$). This paper is motivated by recent studies regarding the possibility of pairing and the nature of the…

Quasiperiodically driven fermionic systems can support topological phases not realized in equilibrium. The fermions are localized in the bulk, but support quantized energy currents at the edge. These phases were discovered through an…

We study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component…

In contemporary physics, especially in condensed matter physics, fermionic topological order and its protected edge modes are one of the most important objects. In this work, we propose a systematic construction of the cylinder partition…

Recent quantum Hall experiments have observed `daughter states' next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wavefunctions for the Moore-Read state by Levin…

Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for…

The occurrence of incompressible quantum fluid states of a two dimensional system is a result of electron--electron interactions in a highly degenerate fractionally filled Landau level. Novel quasiparticles (QP's) called composite Fermions…