Composite Fermion Excitations Research Articles

Positions of the magnetoroton minima in the fractional quantum Hall effect

The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like $\Lambda$ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called "magnetoroton" minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B {\bf 48}, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar \emph{et al.} [Phys. Rev. Lett. {\bf 117}, 216403 (2016)] have modeled the neutral excitations as deformations of the composite fermion Fermi sea, which results in a prediction for the positions of the magnetoroton minima. Using methods of the microscopic composite fermion theory we calculate the positions of the roton minima for filling factors up to 5/11 along the sequence $s/(2s+1)$ and find them to be in reasonably good agreement with both the Chern-Simons field theory of composite fermions and Golkar \emph{et al.}'s theory. We also find that the positions of the roton minima are insensitive to the microscopic interaction in agreement with Golkar \emph{et al.}'s theory. As a byproduct of our calculations, we obtain the charge and neutral gaps for the fully spin polarized states along the sequence $s/(2s\pm 1)$ in the lowest Landau level and the $n=1$ Landau level of graphene.

Singularity in self-energy and composite fermion excitations of interacting electrons

We propose that a composite fermion operator $f_{i\sigma}(2n_{i{\bar \sigma}}-1)$ could have coherent excitations, where $f_{i\sigma}$ is the fermion operator for interacting electrons and $n_{i{\bar \sigma}}$ is the number operator of the opposite spin. In the two-impurity Anderson model, it is found that the excitation of this composite fermion has a pseudogap in the Kondo regime, and has a finite spectral weight in the regime where the excitation of the regular fermion $f_{i\sigma}$ has a pseudogap. In the latter regime, the self-energy of $f_{i\sigma}$ is found to be singular near Fermi energy. We argue that this composite fermion could develop a Fermi surface with Fermi liquid behaviors but "hidden" from charge excitations in lattice generalizations. We further illustrate that this type of excitations is essential in addressing the pseudogap state and unconventional superconductivity.

Collective excitations of composite fermions across multiple Λ levels

A recent experimental study of the fractional quantum Hall state—a prototypical system exhibiting strong collective quantum behaviour—provided evidence for the existence of unexpected collective modes at a filling factor of 1/3. Fully microscopic calculations now explain these modes as arising from collective excitations within the composite fermion theory.

Spin excitations in the fractional quantum Hall regime at [formula omitted

We report inelastic light scattering experiments in the fractional quantum Hall regime at filling factors ν ≲ 1 3 . A spin mode is observed below the Zeeman energy. The filling factor dependence of the mode energy is consistent with its assignment to spin flip excitations of composite fermions (CF) with four attached flux quanta ( φ = 4 ) . Our findings reveal a CF Landau level structure in the φ = 4 sequence.

Charge and statistics of quasiholes in Pfaffian states of composite fermion excitations

The charge of quasiparticles in Pfaffian states of composite fermion excitations (the presence of which is indicated by recent experiments) is found. At the filling fraction of the Pfaffian state ν= p/ q (of the lowest Landau level) the charge is ± e/(2 q). As in the case of the Pfaffian state of electrons the statistics of N qh quasiholes in the Pfaffian state corresponds to the spinor representation of U(1)× SO(2 N qh) (the continuous extension of the braid group). Here U(1) is given by the phase factor e i(1/8+1/(4 m)) π with m=1+ α, α is the exclusion statistics parameter of Jain quasiparticles. The possibility of Read–Rezayi states of Jain quasiparticles is also discussed.

Exclusion statistics of quasiparticles in condensed states of composite fermion excitations

The exclusion statistics of quasiparticles is found at any level of the hierarchy of condensed states of composite fermion excitations (for which experimental indications have recently been found). The hierarchy of condensed states of excitations in boson Jain states is introduced and the statistics of quasiparticles is found. The quantum Hall states of charged $\alpha$-anyons ($\alpha$ -- the exclusion statistics parameter) can be described as incompressible states of $(\alpha+2p)$-anyons ($2p$ -- an even number).

Evidence of Landau levels and interactions in low-lying excitations of composite fermions at 1/3

Excitation modes in the range 2/5>or=nu>or=1/3 of the fractional quantum Hall regime are observed by resonant inelastic light scattering. Spectra of spin-reversed excitations suggest a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Spin-flip energies determined from spectra reveal significant composite fermion interactions. The filling factor dependence of mode energies displays an abrupt change in the middle of the range when there is partial population of a composite fermion level.

Exclusion statistics of composite fermions

The exclusion statistics parameter of composite fermions is determined as an odd number ( α=3, 5, ...). The statistics of composite fermion excitations at ν= n/(2 pn+1) is rederived as α qe CF=1+2 p/(2 pn+1), α qh CF=1−2 p/(2 pn+1). The duality 1/( α qe( n,2 p))= α qh( n+1,2 p) is found. The distribution function for α=3 is obtained.

Edge State: A Toy Model Study from Composite Fermion Point of View**The project supported in part by National Natural Science Foundation of China

By using a toy model of the composite fermion excitations at edge states, we study the structure of the edge state in fractional quantum Hall liquid. The electron density distribution is given by the numerical diagonalization method with the existence of an edge potential, either smooth or sharp one.

Ground-state wave functions of general filling factors in the lowest Landau level

We present a set of explicit trial wavefunctions for the filling factors \nu=n/(2n\pm 1) and \nu=1/2 in the symmetric gauge. We show that the zeroes of the wavefunction, except those dictated by the Fermi statistics, are detached from the particles. The evolution of zeroes as the filling factor is varied is examined. We show that the wavefunction at half-filling exhibits a 2k_F-like oscillation in its occupation number profile. The center-of-mass motion of the ground state droplet is described in terms of the intra-Landau- level excitations of composite fermions.

Fermi-liquid shell model for N electrons on a spherical surface: A test of the composite fermion hierarchy picture

The extension of the Jain theory of fractional quantum Hall states to all odd denominator filling states is proposed in analogy to the Haldane hierarchy. The composite fermion hierarchy is a natural consequence of the Fermi-liquid quasiparticle picture when applied to composite fermion excitations on the sphere. It is shown that the “finite size corrections” defined as 1/ ν−2 S/( N−1), where ν is the filling factor, 2 S the magnetic monopole strength in flux quanta, and N the number of electrons, exhibit periodicity as a function of 2 S with period 2( N−1). The results of numerical diagonalization for ν= 4 11 and ν= 4 13 ( N=8) show no indication of a condensed state. It is also the case for the system of 4QE of the 2 3 Jain state ( N=12) seen as the “half-filled state” of quasielectrons.

Composite-fermion excitations and the electronic spectra of fractional quantum Hall systems.

In the composite-fermion (CF) mean-field theory of a two-dimensional electron system, an electron Landau level whose filling factor is an odd denominator fraction can be transformed into an integral number of filled CF Landau levels. This CF state corresponds to the ground state of a Laughlin incompressible liquid, with an energy gap equal to the ``effective'' CF cyclotron energy. Excited states are described by ${\mathit{n}}_{\mathrm{QE}}$ and ${\mathit{n}}_{\mathrm{QH}}$, the number of quasielectron and quasihole CF excitations. The energies of individual quasielectrons or quasiholes and their ``Fermi liquid'' interactions can be investigated by comparing the CF picture with exact numerical results for a small number of electrons on a spherical surface. \textcopyright{} 1996 The American Physical Society.

Angular momenta of composite Fermion excitations and the band structure of fractional quantum Hall systems

The transformation from electrons to composite Fermions turns a fractionally filled electron Landau level into an integrally filled composite Fermion (CF) Landau level. The eigenstates can be described in terms of n QE and n QE , the numbers of quasi-electron and quasihole CF excitations. In the absence of interactions between CF excitations, the energy is the sum of the energies of the individual excitations. For the CF filling ν ∗ = 1 of a system of N e electrons, the angular momentum of a quasi-electron excitation is given by l QE = N e 2 +(n QH-n QE+1)/2 , and l QH = l QE -1. The allowed values of the total angular momentum L can be obtained by the addition of the angular momenta of the quasielectrons and quasiholes treated as distinguishable sets of Fermions.