Valley-degenerate two-dimensional electrons in the lowest Landau level

Kott, Tomasz M.; Hu, Binhui; Brown, Samuel H.; Kane, B. E.

doi:10.1103/physrevb.89.041107

Cited by 40 publications

(41 citation statements)

References 37 publications

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“…This may change the structure of domains, domain walls and their excitations, compared to the case of graphene. We also note that experiments on Si (111) 49 and Si (100) 50 have observed FQH states at various fractions, almost entirely with even numerators. However, a strong FHE state has been reported at nu = 1/3 in at least one experiment on Si (100) 51 .…”

Section: Disorder Effectsmentioning

confidence: 64%

“…It is also worth noting that suppression by disorder of quantum Hall states with a spontaneously broken symmetry has been observed in other multi-valley systems 46,47,49,50 . For example, in AlAs-2D electron system, which is characterized by a double valley degeneracy, the measured activation energy gaps of certain fractional states in valley-symmetric case can be reduced by a factor of 15 compared to the case when valley symmetry is broken by strain 47 .…”

Section: Disorder Effectsmentioning

confidence: 83%

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Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

et al. 2013

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Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0 < |ν| < 1 and 1 < |ν| < 2. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU (2) valley symmetry, which we find to be important for |ν| < 1 but negligible for |ν| > 1. The effective absence of valley anisotropy for |ν| > 1 means that states with odd numerator, such as |ν| = 5/3 or 7/5 can accommodate charged excitations in the form of large radius valley skyrmions, which should have a low energy cost, and may be easily induced by coupling to impurities. The absence of observed quantum Hall states at these fractions is likely due to the effects of valley skyrmions. For |ν| < 1, the anisotropy terms favor phases in which electrons occupy states with opposite spins, similar to the antiferromagnetic state previously hypothesized to be the ground state at ν = 0. The anisotropy and Zeeman energies suppress large-area skyrmions, so that quantized Hall states can be observable at a set of fractions similar to those in GaAs twodimensional electron systems. In a perpendicular magnetic field B, the competition between the Coulomb energy, which varies as B 1/2 , and the Zeeman energy, which varies as B, can explain the observation of apparent phase transitions as a function of B for fixed ν, as transitions between states with different degrees of spin polarization. In addition to an analysis of various fractional states from this point of view, and an examination of the effects of disorder on valley skyrmions, we present new experimental data for the energy gaps at integer fillings ν = 0 and ν = −1, as a function of magnetic field, and we examine the possibility that valley-skyrmions may account for the smaller energy gaps observed at ν = −1.

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Section: Disorder Effectsmentioning

confidence: 64%

Section: Disorder Effectsmentioning

confidence: 83%

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

et al. 2013

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“…While valley splitting due to the former mechanism is negligible compared to the cyclotron gap 27 , the latter can be more significant 28,29 . Although this problem has been largely solved by working with 2DEGs on a H-terminated Si(111) surface 10,11 , both mechanisms can still change the E-S crossover temperature T * E-S and possibly even the Class of states that are selected below T * . Third, we have ignored Landau level mixing [30][31][32] , likely to be significant in any realistic situation.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we revisit this interplay in the context of the QH states of multi-valley semiconductors, specifically those recently observed in two-dimensional electron gases (2DEGs) confined in Si(111) quantum wells [9][10][11] . We find several striking new phenomena embedded in surprisingly intricate phase diagrams -even while considering only integer quantum Hall states in the lowest Landau level (LLL).…”

Section: Introductionmentioning

confidence: 99%

Order by disorder and by doping in quantum Hall valley ferromagnets

2016

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We examine the Si(111) multi-valley quantum Hall system and show that it exhibits an exceptionally rich interplay of broken symmetries and quantum Hall ordering already near integer fillings ν in the range ν = 0−6. This six-valley system has a large [SU (2)] 3 D3 symmetry in the limit where the magnetic length is much larger than the lattice constant. We find that the discrete D3 factor breaks over a broad range of fillings at a finite temperature transition to a discrete nematic phase. As T → 0 the [SU (2)] 3 continuous symmetry also breaks: completely near ν = 3, to a residual [U (1)] 2 × SU (2) near ν = 2 and 4 and to a residual U (1) × [SU (2)] 2 near ν = 1 and 5. Interestingly, the symmetry breaking near ν = 2, 4 and ν = 3 involves a combination of selection by thermal fluctuations known as "order by disorder" and a selection by the energetics of Skyrme lattices induced by moving away from the commensurate fillings, a mechanism we term "order by doping".

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“…Electron's spin degree of freedom adds to the richness of this phenomenon, and experiments have demonstrated the existence of FQHE states with different spin polarizations as well as transitions between them as a function of the Zeeman energy [2][3][4][5][6][7][8][9][10] . Analogous transitions have been found in multi-valley systems, such as AlAs quantum wells 11,12 and 2D electron system on an H-terminated Si(111) surface 13 , where, in the SU(2) limit, the valley index formally plays the same role as spin.…”

Section: Introductionmentioning

confidence: 96%

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

et al. 2015

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Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n = 1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet et al., Nat. Commun. 6, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations in the n = 1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n = 0 Landau level. In particular, for the states at filling factors ν = s/(2s ± 1), s integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n = 1 graphene Landau level, indicating an absence of composite-fermion pairing at half filling in the n = 1 graphene Landau level.

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Valley-degenerate two-dimensional electrons in the lowest Landau level

Cited by 40 publications

References 37 publications

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

Order by disorder and by doping in quantum Hall valley ferromagnets

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

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