Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Tőke, Csaba; Jain, J. K.

doi:10.1088/0953-8984/24/23/235601

Cited by 21 publications

(24 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Supporting Information). Observing ν = 4/3 in our experiments is consistent with theoretical predictions of the FQHE states ν = 4/3, 2/3 and 1/3 being the most robust ones in the i = 0 and 1 LL in, both, SU(4) and SU(2) symmetry considerations 33, 34. Within SU(4) the spin‐valley symmetry needs to be broken 33 by extrinsic influences to stabilise these FQHE states.…”

supporting

confidence: 90%

“…Within SU(4) the spin‐valley symmetry needs to be broken 33 by extrinsic influences to stabilise these FQHE states. On the other hand, SU(2) composite fermion theory was noted to be able to reproduce many FQHE features in graphene at high magnetic fields, too 34. We note that the magnetic field strengths available in our study were insufficient to reach ν = 2/3 or 1/3 at the n investigated (large $\ell/d$ requirement); also neither 2/3 or 1/3 were observed at lower n .…”

contrasting

confidence: 65%

See 1 more Smart Citation

Suppression of short‐range scattering via hydrophobic substrates and the fractional quantum Hall effect in graphene

Hansel

Lafkioti

Krstić

2012

Physica Rapid Research Ltrs

View full text Add to dashboard Cite

The great diversity of electronic properties of graphene [1,2] can be addressed and fine-tuned by direct chemical manipulation [3]. In particular, charged impurities that contribute to surface doping and limit mobility by Coulomb interaction [4,5] can be removed [6,7]. Here we investigate the electronic properties of graphene on hydrophobic substrates, specifically the reduction of short-rangescattering and its association with the many-body electronelectron interaction (EEI) based FQHE [8][9][10][11][12].Graphene was deposited via mechanical cleavage [13] onto a thermally grown SiO 2 surface functionalized with noctadecyltrichlorosilan (OTS) [14,15] or hexamethyldisilizane (HMDS) [6] on a degeneratively doped Si substrate that serves as back gate (cf. Supporting Information, online at: www.pss-rapid.com, for electrical contacting). Raman microscopy [16,17] indicated that the hydrophobic layers considerably reduce the substrate doping (cf. Supporting Information). We demonstrate that a hydrophobic layer between substrate and graphene largely eliminates Coulomb interaction between the graphene monolayer and charged impurities on the substrate, significantly reducing short-range scattering. At high carrier concentrations the mobilities thus obtained, deliver a ratio of Coulomb scattering mean free path to average charge carrier separation comparable to that of the highest mobility samples that exhibit the fractional quantum Hall effect (FQHE). We observe the FQHE in the lowest mobility samples reported up to now and conclude that increasing the ratio of Coulomb scattering mean free path to charge carrier separation overcomes the limitations for the observation of the FQHE imposed by overall mobility.

show abstract

supporting

confidence: 90%

contrasting

confidence: 65%

Suppression of short‐range scattering via hydrophobic substrates and the fractional quantum Hall effect in graphene

Hansel

Lafkioti

Krstić

2012

Physica Rapid Research Ltrs

View full text Add to dashboard Cite

show abstract

“…Surprisingly, we find ∆ 5/3 to be the most robust at 10.4 ± 1.4 K, followed by ∆ 4/38 .9 ± 0.6 K, ∆ 2/34 .6 ± .3 K and ∆ 1/33 .5 ± .2 K. Theoretical estimates of these gaps are one order of magnitude larger. ∆ 4/3 and ∆ 2/3 were predicted to be the largest gaps, ranging from 0.08 [20,23] . Theoretical estimates for ∆ 1/3 and ∆ 5/3 are slightly smaller: 0.03 to 0.1 e 2 / l B (or 8-26 K× B[T ] ) [23,46] .…”

Section: Fractional Quantum Hall Effect In the Zeroth Landau Levelmentioning

confidence: 99%

“…These grant Landau levels an approximate SU(4) symmetry [1][2][3][4] , broken at high magnetic fields [11] by Zeeman splitting E Z = gµ B B and valley symmetry breaking on order (a/l B )E c ∼ ae 2 / l 2 B [12][13][14] , where a is the graphene lattice constant, l B the mag-netic length, E c the typical energy of Coulomb interactions at a length scale l B , and the dielectric constant. While the nature of the broken-symmetry phases at integer filling factors has been under intense scrutiny [11][12][13][14][15][16] , little is known about the impact of symmetry-breaking interactions on FQH states [17][18][19][20][21][22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

Composite fermions and broken symmetries in graphene

et al. 2015

View full text Add to dashboard Cite

The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.

show abstract

“…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 Hilbert space, and it has been argued that it correctly captures the incompressible ground states of fourcomponent systems with SU(4) invariant Coulomb interactions [29][30][31]. However, a detailed test of the composite fermion theory in the SU(3) and SU(4) cases has been absent.…”

mentioning

confidence: 99%

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

Sodemann

MacDonald

et al. 2015

Phys. Rev. Lett.

View full text Add to dashboard Cite

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

show abstract

Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Cited by 21 publications

References 48 publications

Suppression of short‐range scattering via hydrophobic substrates and the fractional quantum Hall effect in graphene

Suppression of short‐range scattering via hydrophobic substrates and the fractional quantum Hall effect in graphene

Composite fermions and broken symmetries in graphene

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

Contact Info

Product

Resources

About