SU(3) and SU(4) Singlet Quantum Hall States atν=2/3

Abstract

We report on an exact diagonalization study of fractional quantum Hall states at a filling factor of ν ¼ 2=3 in a system with a fourfold degenerate n ¼ 0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at a flux quantum shift 2 when a spherical geometry is employed and lie outside the established composite-fermion or multicomponent Halperin state patterns. We evaluate the two-particle correlation functions of these states and discuss quantum phase transitions in graphene between singlet states with a different number of components as the magnetic field strength is increased. [7,8] in GaAs quantum wells; spins and/or valleys in graphene [9]; anomalous additional orbital indices in the N ¼ 0 Landau levels of few-layer graphene [10][11][12]; valleys in AlAs [13]; and cyclotron and Zeeman splittings that have been tuned to equality in ZnO [14,15]. In monolayer and bilayer graphene, in particular, the nearly fourfold and eightfold degenerate N ¼ 0 Landau levels have recently been shown to give rise to interesting examples of ground states with competing orders [16][17][18][19][20][21][22][23][24][25][26].A diverse toolkit of theoretical approaches that can be successfully applied to understand fractional quantum Hall states has accumulated over the nearly three decades of research. One of the most widely employed frameworks is that of composite fermions [27,28]. The success of the composite fermion picture stems in part from its simplicity, since it allows fractional quantum Hall states of electrons to be viewed as integer quantum Hall states of composite fermions. An important success of the composite fermion approach is that it provides explicit trial wave functions that accurately approximate the ground states computed using exact diagonalization for the Jain sequence of filling fractions ν ¼ n=ð2n AE 1Þ [27,28]. The composite fermion picture can be generalized to account for a multicomponent

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

“…Recently states involving the full SU(3) or SU(4) symmetry in graphene in the n = 0 GLL have been discussed in Ref. 51.…”

Spin and valley ordering of fractional quantum Hall states in monolayer graphene

“…Of course there are also multicomponent states that cannot be generated from the 2-component case. Some of them have been found at filling factor ν = 2/3 in a previous study 44 . It is possible also to use these mappings to construct trial wavefunctions once we have a one or two-component state as obtained for example by the composite fermion construction 47,48 .…”

“…Beyond these obvious symmetries, we note that for u ⊥ = 0 (θ = π/2, 3π/2) one can make spin rotations independently in each valley so there is a symmetry SU (2) K × SU (2) K . There is also an additional SO(5) symmetry when u z + u ⊥ = 0 (θ = 3π/4, 7π/4) which is not obvious in the present formulation 44 .…”

“…All these pure Coulomb eigenstates can be embedded in the four-component case giving rise to degenerate SU (4) multiplets. Of course the SU (4) singlet 44 observed for N e = 8 is unaffected by anisotropies apart from a change in energy. The polarized 2/3 state does not feel the delta function interactions of Eq.…”

Moiré assisted fractional quantum Hall state spectroscopy

“…The FQH effect in graphene is enriched by spin and valley degrees of freedom 24,25 . For N = 0 LLs, electron states in opposite valleys are localized on opposite sublattices.…”