Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level

Abstract

It has long been puzzling that fractional quantum Hall states in the first excited Landau level (1LL) often differ significantly from their counterparts in the lowest Landau level. We show that the dispersion of composite fermions (CFs) is a deterministic factor driving the distinction. We find that CFs with two quantized vortices in the 1LL have a non-quasiconvex dispersion. Consequently, in the filling fraction $7/3$, CFs occupy the second $\Lambda$-level instead of the first. The corresponding ground state wave function, based on the CF wave function ansatz, is identified to be the fermionic Haffnian wave function rather than the Laughlin wave function. The conclusion is supported by numerical evidence from exact diagonalizations in both disk and spherical geometries. Furthermore, we show that the dispersion becomes quasiconvex in wide quantum wells or for CFs with four quantized vortices in the filling fraction $11/5$, coinciding with observations that the distinction between the Landau levels disappears under these circumstances.

arXiv comment5 pages, 4 figures

References in corpus (29)

• Non-Abelian Anyons and Topological Quantum Computation
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• Observation of Fractionally Quantized Anomalous Hall Effect
• Integer and fractional Chern insulators in twisted bilayer MoTe2
• Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Theory of the half-filled Landau level
• Fractional (Chern and topological) insulators
• Experimental probe of topological orders and edge excitations in the second Landau level
• Is the charge determined via shot noise measurements unique?
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Chiral Operator Product Algebra Hidden in Certain Fractional Quantum Hall Wave Functions
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Excitation Spectrum and Collective Modes of Composite Fermions
• Electron Correlations in Partially Filled Lowest and Excited Landau Levels
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• ${\mathbb{Z}}_n$ superconductivity of composite bosons and the $7/3$ fractional quantum Hall effect
• Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction
• From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions
• Analytic Coulomb matrix elements in the lowest Landau level in disk geometry
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Electron correlations in a partially filled first excited Landau level
• Quantum mechanics of composite fermions

Cited by in corpus (1)

• Generalizing the composite fermion theory for fractional Chern insulators