Fractional Quantum Hall Phase Transitions and Four-Flux States in Graphene

Abstract

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.

SO(5) symmetry in the quantum Hall effect in graphene

“…When lattice corrections to the continuum Dirac model's Coulomb interactions are ignored the ground state at neutrality (ν = 0) is a Slater determinant 7 with all the N = 0 single-particle states of two arbitrarily chosen flavors occupied and, because the Hamiltonian is SU(4) invariant, has four independent degenerate Goldstone modes. The rich flavor physics of graphene in the quantum Hall regime has already been established by experiments which demonstrate that phase transitions between distinct many-electron states with the same filling factor ν can be driven by tuning magnetic field strength or tilt-angle [8][9][10][11][12] .…”

Broken SU(4) Symmetry and the Fractional Quantum Hall Effect in Graphene

“…However, because graphene sheets on substrates generally have stronger disorder than modulation-doped GaAs/AlGaAs 2DESs, it has until recently not been possible to observe their fractional quantum Hall effects. Recent studies of highquality graphene samples have started to clear the fog [6][7][8][9][10][11] however, and the view that has emerged is surprising. Experiments indicate that the graphene FQHE is stronger for 0 < |ν| < 1 than for 1 < |ν| < 2, and that phase transitions between distinct states at the same ν occur as a function of magnetic field strength [10,11].…”

“…Recent studies of highquality graphene samples have started to clear the fog [6][7][8][9][10][11] however, and the view that has emerged is surprising. Experiments indicate that the graphene FQHE is stronger for 0 < |ν| < 1 than for 1 < |ν| < 2, and that phase transitions between distinct states at the same ν occur as a function of magnetic field strength [10,11]. In this Letter we shed light [12] on these trends by using a variational approach to account for weak SU(4) symmetry breaking, and by constructing rules that allow SU(4) FQHE states in the range 0 < |ν| < 1 to be generated starting from well known seed states in the range 1 < |ν| < 2.…”

“…Ground states and gaps atν = p/3-The hard-core seed states atν = 1/3 andν = 2/3 do not experience the short range valley-dependent interactions [11,12]. Atν = 1/3 we therefore expect a fully spin polarized Laughlin state, with a remnant valley SU(2) symmetry.…”

SU(N) fractional quantum Hall effect in topological flat bands

“…Here we refer the different components of the system as the (pseudo) spin degrees of freedom. Experimentally, the zeroth Landau level of monolayer graphene which hosts an approximate SU(4) pseudospin symmetry in the presence of spin and valley degrees of freedom, provides a door to exploring the SU(4) symmetric FQH states or other competing broken symmetry states at partial filling under the interplay between electronic correlations and the inherent symmetries of graphene [30][31][32][33][34][35] . The SU(4) generalizations of Halperin's wavefunctions characterized by the integer valued symmetric K matrix, to these SU(4) FQH states in graphene sheets, are proposed in Refs.…”