Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent 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 et al. [Phys. Rev. Lett. 113, 246803 (2014) 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 Hterminated 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(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 et al. [Phys. Rev. Lett. 113, 246803 (2014)

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

“…A good qualitative and semiquantitative theoretical understanding of these transitions has been obtained in terms of integer or fractional quantum Hall effect of spinful composite fermions 8,44,47,[57][58][59][60][61][62][63][64][65] , which successfully predicts the allowed spin polarizations at all of these filling factors and also provides an estimate of the the critical Zeeman energy where transitions between them occur. While these quantitative estimates are a good zeroth order approximation, their accuracy has not been carefully evaluated in the past.…”

Spontaneous polarization of composite fermions in then=1Landau level of graphene

“…The spin physics of FQHE is understood, qualitatively and semi-quantitatively, in terms of spinful composite fermions (CFs) [14][15][16][17][18][19][20] . A composite fermion [21][22][23][24][25] is the bound state of an electron and an even number (2p) of quantized vortices.…”

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

“…While the Coulomb energy scales as e 2 /ǫℓ B [K] ≈ 50 B[T], assuming free electron values for the mass and g factor in GaAs, the Zeeman splitting is only E Z [K] ≈ 0.3B [T], suggesting that in many circumstances the ground state of the system may not be fully spin-polarized. Several classes of unpolarized FQH states have been formulated, including the so-called Halperin (mmn) states [24] and spin unpolarized composite fermion states [25][26][27][28]. In materials such as AlAs or graphene, ordinary electron spin may furthermore combine with valley degrees of freedom, which can change the sequence of the observed integer and FQH states [29][30][31][32][33][34][35][36][37][38].…”