TY - JOUR
T1 - Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems
AU - Balram, Ajit C.
AU - Toke, Csaba
AU - Wójs, A.
AU - Jain, J. K.
N1 - Publisher Copyright:
© 2015 American Physical Society.
PY - 2015/1/9
Y1 - 2015/1/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84921044701&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84921044701&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.91.045109
DO - 10.1103/PhysRevB.91.045109
M3 - Article
AN - SCOPUS:84921044701
SN - 1098-0121
VL - 91
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 4
M1 - 045109
ER -