Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Effective masses of composite fermions

No author provided

Published Sep 10, 2026• 0 citations
Publisher

Abstract

The close correspondence we find between the ground-state energy and that for the free fermions as a function of system size in small systems allows us to make theoretical estimates of the CF effective mass m*, not based on the scaling of gap energies away from half-filling. The quasi-particle-quasi-hole excitations for systems with filled shells also yield an estimate of the effective mass of CFs. Both these estimates agree.

DOI
10.82444/warw.33541564

Related papers

Stability and Effective Masses of Composite Fermions in the First and Second Landau Level

R. Morf, N. d’Ambrumenil

We report finite-size studies of composite fermions (CF's) at even-denominator filling fractions. These show that, in the absence of strong Landau level (LL) mixing effects, the CF liquid cannot form for a half-filled second LL. We relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3<\ensuremath{\nu}<2+2/3$. We find that a polarized CF liquid should exist for a quarter-filled second LL. We also show that, for CF states, the variation with system size of the ground state energy of interacting electrons follows that for noninteracting particles in zero magnetic field. We use this to estimate the CF effective masses. We suggest an explanation of these results based on the Rezayi-Read trial wave function and present estimates for the flux-binding energy.

arXiv:cond-mat/9409008•Physical Review Letters•Jun 19, 1995•69 citations

Excitation Spectrum and Effective Mass of the Even-Fraction Quantum Hall Liquid

Masaru Onoda, T. Mizusaki, Takaharu Otsuka +1 more

To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell structure) between the spectrum and those for free (composite) fermions, (ii) a surprisingly straight scaling plot for the excitation energy that gives a zero gap (metal) in the thermodynamic limit, (iii) the effective mass evaluated from the scaling becoming heavier for nu = 1/2,1/4,1/6, but (iv) some deviations from the single-mode or the Hartree-Fock composite fermion approximation.

arXiv:cond-mat/9912129•Physical Review Letters•Apr 24, 2000•11 citations

Ground-state energy and quasiparticle gaps in ν=N/(2N±1) fractional-quantum-Hall-effect states

Dmitri V. Khveshchenko

Applying the transformation of fermion operators to the fermion quasiparticles introduced by Halperin, Lee, and Read, we estimate the scaling behavior of the ground-state energy and quasiparticle gaps as a function of filling fraction for a ``principal sequence'' of fractional-quantum-Hall-effect \ensuremath{\nu}=N/(2N\ifmmode\pm\else\textpm\fi{}1) states converging towards the gapless state at half filling. The exponent describing the shape of the cusp \ensuremath{\delta}E(\ensuremath{\nu})\ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\delta}\ensuremath{\nu}${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\eta}}}$ is found to be greater than 1 and to depend nontrivially on the interaction potential. The dependence of quasiparticle gaps agrees with the results of recent measurements by R. R. Du et al.

arXiv:cond-mat/9401066•Physical review. B, Condensed matter•Apr 15, 1994•2 citations

CONCERNING A MODEL FOR A NON-IDEAL FERMI GAS

A. A. Abrikosov, Isaak M. Khalatnikov

>The energy of the ground state and the effective mass of the excitations are found for a non-ideal Fermi gas with short-range forces. the radii of action of which are small in comparison with the average wavelength. (auth)

Journal of Experimental and Theoretical Physics•May 1, 1958•11 citations

POSSIBLE NEW PHASES OF COMPOSITE FERMIONS

V. W. Scarola, Seong-Young Lee, Jainendra K. Jain

When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].

International Journal of Modern Physics B•Aug 30, 2002•0 citations

Pairing instabilities of Dirac composite fermions

Milica V. Milovanović, Marija Dimitrijević Ćirić, Vladimir Juričić

Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of $p$-wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.

arXiv:1606.03919•Physical review. B./Physical review. B•Sep 8, 2016•6 citations
The close correspondence we find between the ground-state energy and that for the free fermions as a function of system size in small systems allows us to make theoretical estimates of the CF effective mass m*, not based on the scaling of gap energies away from half-filling. The quasi-particle-quasi-hole excitations for systems with filled shells also yield an estimate of the effective mass of CFs. Both these estimates agree.
We report finite-size studies of composite fermions (CF's) at even-denominator filling fractions. These show that, in the absence of strong Landau level (LL) mixing effects, the CF liquid cannot form for a half-filled second LL. We relate this to the absence of a hierarchy of incompressible states for filling fractions $2+1/3<\ensuremath{\nu}<2+2/3$. We find that a polarized CF liquid should exist for a quarter-filled second LL. We also show that, for CF states, the variation with system size of the ground state energy of interacting electrons follows that for noninteracting particles in zero magnetic field. We use this to estimate the CF effective masses. We suggest an explanation of these results based on the Rezayi-Read trial wave function and present estimates for the flux-binding energy.
To probe the nature of the even-fraction quantum Hall system, we have investigated the low-lying excitation spectrum by exact diagonalization for finite systems. We have found (i) a striking one-to-one correspondence (i.e., a shell structure) between the spectrum and those for free (composite) fermions, (ii) a surprisingly straight scaling plot for the excitation energy that gives a zero gap (metal) in the thermodynamic limit, (iii) the effective mass evaluated from the scaling becoming heavier for nu = 1/2,1/4,1/6, but (iv) some deviations from the single-mode or the Hartree-Fock composite fermion approximation.
Applying the transformation of fermion operators to the fermion quasiparticles introduced by Halperin, Lee, and Read, we estimate the scaling behavior of the ground-state energy and quasiparticle gaps as a function of filling fraction for a ``principal sequence'' of fractional-quantum-Hall-effect \ensuremath{\nu}=N/(2N\ifmmode\pm\else\textpm\fi{}1) states converging towards the gapless state at half filling. The exponent describing the shape of the cusp \ensuremath{\delta}E(\ensuremath{\nu})\ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\delta}\ensuremath{\nu}${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\eta}}}$ is found to be greater than 1 and to depend nontrivially on the interaction potential. The dependence of quasiparticle gaps agrees with the results of recent measurements by R. R. Du et al.
When the effective filling factor of composite fermions is an integer, the residual interaction between them can often be neglected because the ground state of the non-interacting model is unique and incompressible. However, at non-integer composite fermion (CF) filling factors the ground state of composite fermions is enormously degenerate if the interaction between them is neglected, and consideration of the inter composite fermion interaction is necessary for determining the true ground state. In this article, we summarize certain results regarding what new states the inter composite fermion interaction can possibly produce. More details can be found in Refs. [11] and [12].
Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of ppp-wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.