Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems

Ajit C. Balram, Csaba Toke, A. Wójs, Jainendra K. Jain

Research output: Contribution to journalArticle

19 Citations (Scopus)

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 and co-workers [Phys. Rev. Lett. 113, 246803 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.246803 and private communication] 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 N components for an SU(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 paper is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU(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 and co-workers [Phys. Rev. Lett. 113, 246803 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.246803 and private communication] as well as of Yeh et al., [Phys. Rev. Lett. 82, 592 (1999)PRLTAO0031-900710.1103/PhysRevLett.82.592] for a two-component system.

Original languageEnglish (US)
Article number045109
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number4
DOIs
StatePublished - Jan 9 2015

Fingerprint

Quantum Hall effect
Fermions
quantum Hall effect
Phase diagrams
fermions
phase diagrams
composite materials
Composite materials
Semiconductor quantum wells
quantum wells
Electrons
communication
Spin polarization
electrons
Graphite
Communication
Wave functions
lists
Graphene
Ground state

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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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 and co-workers [Phys. Rev. Lett. 113, 246803 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.246803 and private communication] 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 N components for an SU(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 paper is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU(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 and co-workers [Phys. Rev. Lett. 113, 246803 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.246803 and private communication] as well as of Yeh et al., [Phys. Rev. Lett. 82, 592 (1999)PRLTAO0031-900710.1103/PhysRevLett.82.592] for a two-component system.",
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Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems. / Balram, Ajit C.; Toke, Csaba; Wójs, A.; Jain, Jainendra K.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 91, No. 4, 045109, 09.01.2015.

Research output: Contribution to journalArticle

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