## What is/are Composite Fermion?

Composite Fermion - We observe minima of the longitudinal resistance corresponding to the quantum Hall effect of composite fermions at quantum numbers $p=1$, 2, 3, 4, and 6 in an ultraclean strongly interacting bivalley SiGe/Si/SiGe two-dimensional electron system.^{[1]}Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional ’t Hooft anomaly matching equations, appear instead disfavored.

^{[2]}We present an inspection of the statistics of particles including composite fermions on a torus starting from a braid group analysis.

^{[3]}The conventional ’t Hooft anomaly matching algorithm is known to allow a confining, chirally symmetric vacuum in all these models, with a simple set of massless baryonlike composite fermions describing the infrared physics.

^{[4]}An adiabatic approach put forward by Greiter and Wilczek interpolates between the integer quantum Hall effects of electrons and composite fermions by varying the statistical flux bound to electrons continuously from zero to an even integer number of flux quanta, such that the intermediate states represent anyons in an external magnetic field with the same “effective” integer filling factor.

^{[5]}112, 016801 (2014)] in terms of the 1/3-filled second effective Landau level of the composite fermions whose correlations resemble that of electrons in the ground state of a two-body Haldane pseudo-potential of relative angular momentum 3, ${V}_{3}$.

^{[6]}We reconsider the composite fermion theory of general Jain’s sequences with filling factor ν = N/(4N ± 1).

^{[7]}Our observation explains the microscopic mechanism of vortex attachment in composite fermion theory of the fractional quantum Hall effect, allows its description in terms of self-localization of ems and represents progress towards the goal of engineering anyon properties for fault-tolerant topological quantum gates.

^{[8]}A number of detailed predictions on these experimental measurements are proposed, and we discuss their relationships to the conventional CFT arguments and the composite fermion descriptions.

^{[9]}In this article we consider a composite fermion operator, consisting of a conduction electron dressed by spin fluctuations that shares the same quantum numbers as the electron operator.

^{[10]}We also explain the composite fermion picture which describes the fractional quantum Hall effect as the integer quantum Hall effect of composite fermions.

^{[11]}In theories with a warped extra dimension, composite fermions, as e.

^{[12]}Composite fermions (CFs) are the particles underlying the novel phenomena observed in partially filled Landau levels.

^{[13]}We find that particle-hole symmetry is broken, as determined by energy gaps, between states related via particle-hole conjugation, however, we find that particle-hole symmetry is largely maintained as determined by the effective mass of composite fermions.

^{[14]}The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs.

^{[15]}The state of v = 3/2 is an example of a locally incompressible fractional state of the quantum Hall effect, which is neither a Laughlin liquid nor an integer state of composite fermions.

^{[16]}We study the integer quantum Hall plateau transition using composite fermion mean-field theory.

^{[17]}A Kohn-Sham density functional approach has recently been developed for the fractional quantum Hall effect, which maps the strongly interacting electrons into a system of weakly interacting composite fermions subject to an exchange correlation potential as well as a density dependent gauge field that mimics the “flux quanta” bound to composite fermions.

^{[18]}We also discuss the importance of incorporating nonlocal composite fermion for more accurate description.

^{[19]}In all cases, Cooper pairing of composite fermions is believed to explain the plateaus.

^{[20]}We propose a new way of breaking the Goldstone symmetry in composite Higgs models, restoring the global symmetry in the mixings between the elementary and composite fermions by completing the former to full representations of this symmetry.

^{[21]}Herein, we perform an analogous study of composite Fermi-type particles, and explore them in two major cases: (i) "boson + fermion" composite fermions (or cofermions, or CFs); (ii) "deformed boson + fermion" CFs.

^{[22]}We have studied collective spin density excitations of fractional quantum Hall effect (FQHE) in rotating Bose-Einstein condensation for the three filling fractions of first series of Jain's composite fermion sequences.

^{[23]}It is a confining phase, with a light spectrum consisting of massless composite fermions.

^{[24]}We formulate the Kohn-Sham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.

^{[25]}The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a pairing of composite fermions captured by the Moore-Read Pfaffian wave function.

^{[26]}We show that this nonlocal map provides a continuum realization of Son's composite fermions at ν=1/2.

^{[27]}We theoretically investigate the nature of the state at the 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 fractional quantum Hall state that is topologically equivalent to f-wave pairing of composite fermions.

^{[28]}In the present learning path, we stimulate a discussion about the integer and fractional quantum Hall effects, aimed at introducing a unified picture based upon composite fermions, interacting quasiparticles that may be viewed as fermions carrying attached a fictitious magnetic flux.

^{[29]}We show that, under certain conditions, an anomaly between the chiral symmetry and the BCF background rules out massless composite fermions as the sole player in the IR: either the composites do not form or additional contributions to the matching of the BCF anomaly are required.

^{[30]}We have also considered the reaches on the new physics mass scale in different new physics scenarios, including the Strongly Interacting-Light Higgs (SILH), the Strongly Coupled Multi-pole Interaction (Remedios), and the class of models with partially composite fermions.

^{[31]}In this work, two quasiparticle excitation energies per particle are calculated analytically for systems with up to $N = 7$ electrons in both Laughlin and composite fermions (CF) theories by considering the full jellium potential which consists of three parts, the electron-electron, electron-background, and background-background Coulomb interactions.

^{[32]}Specifically, electrons bind with an even number of flux quanta, and transform into composite fermions (CFs).

^{[33]}It is shown that composite fermions in the fractional quantum Hall regime form paired states in double-layer graphene.

^{[34]}Finally, we discuss spin-orbit interactions of composite fermions.

^{[35]}In the end, we have studied the composite fermions energies for the excited states for several systems at $\upsilon =1/3$ and the correspondence between the fractional quantum Hall effect (FQHE) and the IQHE.

^{[36]}In contrast to the collective localization of electrons evidenced by the reentrant integer quantum Hall effect, such reentrance to a fractional Hall resistance clearly points to the involvement of composite fermion quasiparticles.

^{[37]}We study magnetoresistance oscillations near the half-filled lowest Landau level ($\nu = 1/2$) that result from the presence of a periodic one-dimensional electrostatic potential using the Dirac composite fermion theory of Son, where the $\nu=1/2$ state is described by a $(2+1)$-dimensional theory of quantum electrodynamics.

^{[38]}The most recent theoretical proposals argue for a case that in the infrared a composite fermion composed of two quarks and an antiquark becomes massless and non-interacting as the quark mass goes to zero, while other sectors are decoupled from this low-energy fermion.

^{[39]}We study this transition using a composite fermion (CF) representation, which incorporates some of the effects of interactions.

^{[40]}According to Jain’s composite, fermion theory—a quantumentangled fractional quantum Hall state of electrons—can be viewed as an integer quantumHall effect of composite fermions without long-range entanglement.

^{[41]}However, in our structure, at ν = 1/2 it is a compressible state corresponding to gas of composite fermions which is observed.

^{[42]}Motivated by Beyond the Standard Model theories of composite fermions or top partners, we propose a holographic mechanism that generates light baryonic states in a strongly coupled gauge theory.

^{[43]}Though the tiny confinement scale for universal preons composing both quarks and leptons makes it impossible to directly confirm their composite nature, simultaneous emergence of several extra S U ( 5 ) × S U ( 3 ) F multiplets of heavy composite fermions may help with a model verification.

^{[44]}Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory.

^{[45]}Motivated by this result, we consider a clean two dimensional electron system (2DES) from the viewpoint of composite fermion mean-field theory.

^{[46]}Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory.

^{[47]}In this article, we focus on non-Abelian orders from Cooper pairing between composite fermions and the Abelian Halperin-(5,5,3) order.

^{[48]}Analysis of the spectra indicates that the majority layer screens like a dielectric medium even when its Landau filling is ~1/2, at which the layer is essentially a composite fermion (CF) metal.

^{[49]}We propose a new way of breaking the Goldstone symmetry in composite Higgs models, restoring the global symmetry in the mixings between the elementary and composite fermions by completing the former to full representations of this symmetry.

^{[50]}

## Massles Composite Fermion

Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional ’t Hooft anomaly matching equations, appear instead disfavored.^{[1]}It is a confining phase, with a light spectrum consisting of massless composite fermions.

^{[2]}We show that, under certain conditions, an anomaly between the chiral symmetry and the BCF background rules out massless composite fermions as the sole player in the IR: either the composites do not form or additional contributions to the matching of the BCF anomaly are required.

^{[3]}

## Component Composite Fermion

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 states as a function of the layer separation.^{[1]}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 interlayer vortices.

^{[2]}

## composite fermion theory

We reconsider the composite fermion theory of general Jain’s sequences with filling factor ν = N/(4N ± 1).^{[1]}Our observation explains the microscopic mechanism of vortex attachment in composite fermion theory of the fractional quantum Hall effect, allows its description in terms of self-localization of ems and represents progress towards the goal of engineering anyon properties for fault-tolerant topological quantum gates.

^{[2]}We study magnetoresistance oscillations near the half-filled lowest Landau level ($\nu = 1/2$) that result from the presence of a periodic one-dimensional electrostatic potential using the Dirac composite fermion theory of Son, where the $\nu=1/2$ state is described by a $(2+1)$-dimensional theory of quantum electrodynamics.

^{[3]}Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory.

^{[4]}Our extensive numerical calculations indicate that the undressed quasielectron excitations of the Laughlin state obtained from LECs are topologically equivalent to those obtained from the composite fermion theory.

^{[5]}Intriguingly, in the $\nu=2/5$ fractional quantum Hall effect, prominent theoretical approaches -- the composite fermion theory and conformal field theory -- have constructed two distinct states, the Jain composite fermion (CF) state and the Gaffnian state, for which many of the topological indices coincide and even the microscopic ground state wave functions have high overlap with each other in system sizes accessible to numerics.

^{[6]}

## composite fermion mean

We study the integer quantum Hall plateau transition using composite fermion mean-field theory.^{[1]}Motivated by this result, we consider a clean two dimensional electron system (2DES) from the viewpoint of composite fermion mean-field theory.

^{[2]}