Magnetoconductance Oscillations and Evidence for Fractional Quantum Hall States in Suspended Bilayer and Trilayer Graphene

Bao, Wenzhong; Zhao, Zhenyu; Zhang, Hang; Liu, Gang; Kratz, Philip; Jing, Lei; Velasco, Jairo; Smirnov, Dmitry; Lau, Chun Ning

doi:10.1103/physrevlett.105.246601

Cited by 79 publications

(92 citation statements)

References 34 publications

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“…Depending on sample quality, electron-electron interactions also contribute to symmetry breaking and Landau level splitting, [67][68][69][70][71][72][73][74][75][76][77][78][79] as does interlayer asymmetry due to the presence of an external gate or doping. 28,31,42,45,[80][81][82] Nevertheless, an experimental observation of features related to next-nearest layer couplings should be possible in high-mobility samples including suspended graphene 69,[83][84][85][86] or graphene on a boron nitride substrate. 66,72,73,87 In fact, Landau level crossings in trilayer graphene were recently observed, 66 and they allowed the determination of Slonczewski-Weiss-McClure parameter values in remarkably close agreement with those of bulk graphite.…”

Section: Discussionmentioning

confidence: 99%

Landau level spectra and the quantum Hall effect of multilayer graphene

2011

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The Landau level spectra and the quantum Hall effect of ABA-stacked multilayer graphenes are studied in the effective-mass approximation. The low-energy effective-mass Hamiltonian may be partially diagonalized into an approximate block-diagonal form, with each diagonal block contributing parabolic bands except for an additional block describing Dirac-like bands with a linear dispersion in a multilayer with an odd number of layers. We fully include the band parameters and, taking into account the symmetry of the lattice, we analyze their effect on the block-diagonal Hamiltonian. Next-nearest-layer couplings are shown to be particularly important in determining the low-energy spectrum and the phase diagram of the quantum Hall conductivity by causing energy shifts, level anticrossings, and valley splitting of the low-lying Landau levels.

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Section: Discussionmentioning

confidence: 99%

Landau level spectra and the quantum Hall effect of multilayer graphene

2011

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“…The order at which the degeneracy is broken reflects the underlying competing symmetries. Prior works have reported resolution of several symmetry-broken QH states [38][39][40] , albeit only in single-gated samples where the interlayer potential U⊥ and charge density n are not independently controlled. In this Letter, by using transport measurements on high mobility dual-gated r-TLG devices, we explore symmetry-broken LLs via careful control of U⊥, B and n. All integer plateaus of the zeroth LL in the hole-doped regime are resolved in high B.…”

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confidence: 99%

Multicomponent Quantum Hall Ferromagnetism and Landau Level Crossing in Rhombohedral Trilayer Graphene

et al. 2015

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Using transport measurements, we investigate multicomponent quantum Hall (QH) ferromagnetism in dual-gated rhombohedral trilayer graphene (r-TLG), in which the real spin, orbital pseudospin and layer pseudospins of the lowest Landau level form spontaneous ordering. We observe intermediate quantum Hall plateaus, indicating a complete lifting of the degeneracy of the zeroth Landau level (LL) in the hole-doped regime. In charge neutral r-TLG, the orbital degeneracy is broken first, and the layer degeneracy is broken last and only the in presence of an interlayer potential U⊥. In the phase space of U⊥ and filling factor ν, we observe an intriguing "hexagon" pattern, which is accounted for by a model based on crossings between symmetry-broken LLs.Keywords: quantum Hall ferromagnetism, graphene, trilayer, rhombohedral stacking, Landau level crossing * Emails: kenosis101@gmail.com, yafisb@gmail.com; lau@physics.ucr.edu In the quantum Hall (QH) regime, when the energies of two or more Landau levels (LLs) are brought to alignment, the spinor language is often used to describe the different degrees of freedom, such as layer and orbital pseudospins, due to their close analogy to the spins in a twodimensional ferromagnet. When these LLs are less than completely full, competition between these degrees of freedom leads to formation of electronic states with spontaneous ordering of pseudospins, much like the spontaneous real spin alignment in a ferromagnet. For this reason, these symmetry-broken QH states are called QH ferromagnets, with real or pseudo-spin orderings that maybe easy-plane, i.e. akin to a XY Heisenberg magnet, or easy-axis, i.e. akin to an Ising ferromagnet. These QH ferromagnetic states provide a rich platform for investigation of the competition among different symmetries, as well as providing insight into the itinerant magnetism in standard magnets.The recent emergence of two-dimensional (2D) graphene provides new playground for multicomponent QH ferromagnetic states and the associated phase transitions 1-6 7-19 20-28 . With the advent of high mobility samples that may be either suspended 29,30 or supported on BN substrates 31,32 , and advanced device geometry such as dual-gates or split top gates [33][34][35] , few-layer graphene provides QH systems with unusual symmetries and unprecedented tunability.In particular, rhombohedral trilayer graphene is such a QH system with very flat bands near the charge neutrality point. Its LL energies are given bywhere N is an integer denoting the LL index, e the electron charge, v F~1 0 6 m/s the Fermi velocity of single layer graphene, γ 1~0 .3 eV the interlayer hopping energy, and h Planck's constant. The degeneracy between the N=0, 1 and 2 LLs, together with the spin and valley degrees of freedom, yield the 12-fold degeneracy of the lowest LL, and give rise to plateaus at filling factors ν=±6, ±10, ±14… Interactions and/or single particle effects lift this 12-fold degeneracy, leading to incompressible QH ferromagnetic states at intermediate fillings 36,37 , with ex...

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“…11 Further broken symmetry states have been observed [12][13][14][15][16] in the central Landau band at ν = 0, ±1, ±2 and ±3, and by careful tilted-field measurements it has been shown that they arise predominantly from many-body effects, i.e., from quantum Hall ferromagnetism (QHF). 17 Quantum Hall states with broken symmetry have also been found in the n = −2 Landau level 18 , and there is also some evidence for a fractional quantum Hall plateau.…”

Section: Introductionmentioning

confidence: 98%

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

Sári

Tőke

2013

Phys. Rev. B

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If bilayer graphene is placed in a strong perpendicular magnetic field, several quantum Hall plateaus are observed at low enough temperatures. Of these, the σxy = 4ne 2 /h sequence (n = 0) is explained by standard Landau quantization, while the other integer plateaus arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single-and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, but essentially changes their spectra and orbital character at finite wave length. These predictions can be probed in inelastic light scattering experiments.

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Magnetoconductance Oscillations and Evidence for Fractional Quantum Hall States in Suspended Bilayer and Trilayer Graphene

Cited by 79 publications

References 34 publications

Landau level spectra and the quantum Hall effect of multilayer graphene

Landau level spectra and the quantum Hall effect of multilayer graphene

Multicomponent Quantum Hall Ferromagnetism and Landau Level Crossing in Rhombohedral Trilayer Graphene

Theory of inter-Landau-level magnetoexcitons in bilayer graphene

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