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

• Published in: Physical review. B, Condensed matter and materials physics Vol. 91; no. 4
• Main Authors: Balram, Ajit C., Tőke, Csaba, Wójs, A., Jain, J. K.
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 09-01-2015
• Subjects: Approximation; Condensed matter; Feasibility; Fermions; Mathematical analysis; Phase diagrams; Quantum Hall effect; Quantum wells; Wave functions
• ISSN: 1098-0121; 1550-235X
• DOI: 10.1103/PhysRevB.91.045109

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 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. 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.