Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems

Abstract

While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual interaction between composite fermions. We study the spin phase diagram of these states, motivated by the recent experimental observation by Liu {\em et al.} \cite{Liu14a,Liu14b} of several spin-polarization transitions at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the FQHE of composite fermions is much more prevalent in multicomponent systems, and consider the feasibility of such states for systems with $\mathcal{N}$ components for an SU($\mathcal{N}$) symmetric interaction. Our results apply to GaAs quantum wells, wherein electrons have two components, to AlAs quantum wells and graphene, wherein electrons have four components (two spins and two valleys), and to an H-terminated Si(111) surface, which can have six components. The aim of this article is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU($\mathcal{N}$) spin content, their energies, and their phase diagram as a function of the generalized "Zeeman" energy. We obtain results at three levels of approximation: from ground state wave functions of the composite fermion theory, from composite fermion diagonalization, and, whenever possible, from exact diagonalization. Effects of finite quantum well thickness and Landau level mixing are neglected in this study. We compare our theoretical results with the experiments of Liu {\em et al.} \cite{Liu14a,Liu14b} as well as of Yeh {\em et al.} \cite{Yeh99} for a two component system.

29 pages, 6 figures

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Cited by in corpus (10)

• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Fractional Quantum Hall Effect at Landau Level Filling nu=4/11
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• SU(N) fractional quantum Hall effects in topological flat bands
• Theoretical phase diagram of two-component composite fermions in double layer graphene
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions