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

arXiv:cond-mat/0604533 · Physical Review B

Second generation of Moore-Read quasiholes in a composite-fermion liquid

Arkadiusz Wójs, D. Wodziński, John J. Quinn

Published Jul 13, 2006• 18 citations
arXivHTMLPDF

Abstract

Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at ${\ensuremath{\nu}}_{e}=4∕11$. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at ${\ensuremath{\nu}}_{e}=4∕11$. Electron pairing occurs at ${\ensuremath{\nu}}_{e}=7∕3$ and $13∕3$, but with different pair-pair correlations. Signatures of triplets are found at higher fillings.

DOI
10.1103/physrevb.74.035315

Related papers

Condensation of Nonabelian Moore-Read Quasiholes in Correlated Composite Fermion Liquids

D. Wodziński, Arkadiusz Wójs, J. J. Quinn

Two-and three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids.It is shown directly that the νe = 4/11 liquid (corresponding to a ν = 1/3 filling of composite fermions in their first excited Landau level) is a paired state of quasielectrons, hence interpreted as a condensate of "second-generation" quasiholes of Moore-Read ν = 1/2 state of composite fermions.

Acta Physica Polonica A•Sep 1, 2006•0 citations

Second generation of incompressible quantum liquids in the fractional quantum Hall effect

Arkadiusz Wójs

We study 'second generation' of fractional quantum Hall states which contain a partially filled composite fermion (CF) Landau level (LL). We explain the role of CF-CF interaction in the incompressibility of the underlying quantum electron liquid. In particular, using exact diagonalization on a Haldane sphere, we determine two- and three-body CF correlation functions for these liquids and show that the CFs form a paired state (instead of a Laughlin liquid) when filling v = 1/3 of their second LL. At v = 1/2 we show that the CFs group into even larger clusters rather than form a Moore—Read paired state. We also address the problem of spin polarization of interacting CFs and predict transition to the partially unpolarized ground state in sufficiently narrow quantum wells and/or weak magnetic fields.

Journal of Physics Conference Series•Mar 1, 2008•0 citations

Numerical evidence for non-Abelian quantum liquids in the lowest Landau level

Arkadiusz Wójs

Signatures of non-Abelian statistics are sought in correlated liquids of composite fermions (CFs) responsible for a ``second generation'' of fractional quantum Hall effect. The hierarchy stems from the zero-energy state of a model CF interaction by means of a flux attachment procedure converting this uniquely correlated state of ``first-generation'' CFs to a filled shell of second-generation ${\text{CF}}^{\ensuremath{\ast}}$'s. Quasiholes of this state do not obey Abelian statistics. The hierarchy is confirmed numerically, including known states at filling factors ${\ensuremath{\nu}}_{e}=4/11$ and 3/8 and a hypothetical state at ${\ensuremath{\nu}}_{e}=9/25$.

Physical Review B•Jan 27, 2009•5 citations

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

Topological pairing of composite fermions via criticality

N. Nešković, Ivana Vasić, Milica V. Milovanović

The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator $\frac{5}{2}$ occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper pairing of underlying quasiparticles, composite fermions (CFs), leads to the explanation of this effect. Such a state should have a Pfaffian form of the BCS wave function (due to the fully polarized spin) and non-Abelian statistics of possible vortexlike excitations (due to the $p$-wave nature of the pairing). Here we expose the origin of pairing by using the effective dipole representation of the problem and show that pairing is encoded in a Hamiltonian that describes the interaction of the charge density with dipoles, i.e., the current of CFs. The necessary condition for the paired state to exist is the effective dipole physics at the Fermi level as a consequence of the nontrivial topology of the ideal band in which electrons live, a Landau level (LL); the paired state is a resolution of the unstable, critical behavior characterized by the distancing of correlation hole with respect to electron (and thus dipole) at the Fermi level due to the topology. We describe analytically this deconfined critical point, at which deconfinement of Majorana neutral fermions takes place. In the presence of large, short-range repulsive interaction inside a LL, the critical behavior may be stabilized into a regularized Fermi-liquid-like state, like the one that characterizes the physics in the lowest LL, but in general, for an interaction with slowly decaying pseudopotentials, the system is prone to pairing.

arXiv:2406.09050•Physical review. B./Physical review. B•Sep 3, 2024•2 citations

Moore-Read states on a sphere: Three-body correlations and finite-size effects

Arkadiusz Wójs

Energy spectra of a model short‐range three‐body repulsion are calculated for a half‐filled Landau level. The Moore‐Read ground state and its quasielectron (QE), quasihole (QH), magnetoroton (QE+QH), and pair‐breaking excitations are all identified. Two‐ and three‐body correlations of these states are analyzed. The QE/QH excitations are described by a composite fermion model for Laughlin‐correlated electron pairs. Comparison with the results obtained for the Coulomb interaction suggests that finite‐size effects are important in numerical diagonalization for the v = 5/2 quantum Hall state.

AIP conference proceedings•Jan 1, 2005•0 citations
Two- and three-body correlations of incompressible quantum liquids are studied numerically. Pairing of composite fermions (CFs) in the 1/3-filled second CF Landau level is found at \ensuremathνe=4∕11{\ensuremath{\nu}}_{e}=4∕11\ensuremathνe​=4∕11. It is explained by reduced short-range repulsion due to ring-like single-particle charge distribution. Although Moore-Read state of CFs is unstable in the 1/2-filled second CF level, condensation of its quasiholes is a possible origin of incompressibility at \ensuremathνe=4∕11{\ensuremath{\nu}}_{e}=4∕11\ensuremathνe​=4∕11. Electron pairing occurs at \ensuremathνe=7∕3{\ensuremath{\nu}}_{e}=7∕3\ensuremathνe​=7∕3 and 13∕313∕313∕3, but with different pair-pair correlations. Signatures of triplets are found at higher fillings.
Two-and three-body correlation functions (number of pairs or triplets vs. relative angular momentum) of electrons or Laughlin quasielectrons (i.e., composite fermions in their first excited Landau level) are studied numerically in several fractional quantum Hall liquids.It is shown directly that the νe = 4/11 liquid (corresponding to a ν = 1/3 filling of composite fermions in their first excited Landau level) is a paired state of quasielectrons, hence interpreted as a condensate of "second-generation" quasiholes of Moore-Read ν = 1/2 state of composite fermions.
We study 'second generation' of fractional quantum Hall states which contain a partially filled composite fermion (CF) Landau level (LL). We explain the role of CF-CF interaction in the incompressibility of the underlying quantum electron liquid. In particular, using exact diagonalization on a Haldane sphere, we determine two- and three-body CF correlation functions for these liquids and show that the CFs form a paired state (instead of a Laughlin liquid) when filling v = 1/3 of their second LL. At v = 1/2 we show that the CFs group into even larger clusters rather than form a Moore—Read paired state. We also address the problem of spin polarization of interacting CFs and predict transition to the partially unpolarized ground state in sufficiently narrow quantum wells and/or weak magnetic fields.
Signatures of non-Abelian statistics are sought in correlated liquids of composite fermions (CFs) responsible for a ``second generation'' of fractional quantum Hall effect. The hierarchy stems from the zero-energy state of a model CF interaction by means of a flux attachment procedure converting this uniquely correlated state of ``first-generation'' CFs to a filled shell of second-generation ${\text{CF}}^{\ensuremath{\ast}}$'s. Quasiholes of this state do not obey Abelian statistics. The hierarchy is confirmed numerically, including known states at filling factors ${\ensuremath{\nu}}_{e}=4/11$ and 3/8 and a hypothetical state at ${\ensuremath{\nu}}_{e}=9/25$.
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.
The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator 52\frac{5}{2}25​ occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper pairing of underlying quasiparticles, composite fermions (CFs), leads to the explanation of this effect. Such a state should have a Pfaffian form of the BCS wave function (due to the fully polarized spin) and non-Abelian statistics of possible vortexlike excitations (due to the ppp-wave nature of the pairing). Here we expose the origin of pairing by using the effective dipole representation of the problem and show that pairing is encoded in a Hamiltonian that describes the interaction of the charge density with dipoles, i.e., the current of CFs. The necessary condition for the paired state to exist is the effective dipole physics at the Fermi level as a consequence of the nontrivial topology of the ideal band in which electrons live, a Landau level (LL); the paired state is a resolution of the unstable, critical behavior characterized by the distancing of correlation hole with respect to electron (and thus dipole) at the Fermi level due to the topology. We describe analytically this deconfined critical point, at which deconfinement of Majorana neutral fermions takes place. In the presence of large, short-range repulsive interaction inside a LL, the critical behavior may be stabilized into a regularized Fermi-liquid-like state, like the one that characterizes the physics in the lowest LL, but in general, for an interaction with slowly decaying pseudopotentials, the system is prone to pairing.
Energy spectra of a model short‐range three‐body repulsion are calculated for a half‐filled Landau level. The Moore‐Read ground state and its quasielectron (QE), quasihole (QH), magnetoroton (QE+QH), and pair‐breaking excitations are all identified. Two‐ and three‐body correlations of these states are analyzed. The QE/QH excitations are described by a composite fermion model for Laughlin‐correlated electron pairs. Comparison with the results obtained for the Coulomb interaction suggests that finite‐size effects are important in numerical diagonalization for the v = 5/2 quantum Hall state.