Angle dependence of the Landau level spectrum in twisted bilayer graphene

Choi, Min Yeong; Hyun, Young-Hwan; Kim, Yoonbai

doi:10.1103/physrevb.84.195437

Cited by 41 publications

(44 citation statements)

References 28 publications

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“…Figure 49 shows the dependencies of the Landau levels energies on the magnetic field [panel (a)] and on the twist angle at fixed magnetic field [panel (b)] calculated in Ref. [386]. The same results are obtained also in Ref.…”

Section: Tight-binding Calculations Of the Twisted Bilayer Graphene Ssupporting

confidence: 72%

“…To avoid this difficulty, several semi-analytical theories have been developed for describing the low-energy electronic properties of tBLG [3,367,370,371,372,384,385,386,387,388,389,390]. These theories operate mainly on the electronic states near the Dirac cones, which the tBLG inherits from its two constituent layers.…”

Section: Low-energy Hamiltoniansmentioning

confidence: 99%

“…[385,386], the structure of Landau levels is studied in the framework of a simplified 2×2 effective Hamiltonian (185). In the presence of a magnetic field perpendicular to the bilayer, the Hamiltonian (185) can be rewritten asĤ…”

Section: Tight-binding Calculations Of the Twisted Bilayer Graphene Smentioning

confidence: 99%

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Electronic properties of graphene-based bilayer systems

et al. 2016

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This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental research in bilayer graphene.

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Section: Tight-binding Calculations Of the Twisted Bilayer Graphene Ssupporting

confidence: 72%

Section: Low-energy Hamiltoniansmentioning

confidence: 99%

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Electronic properties of graphene-based bilayer systems

et al. 2016

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“…For twist angles larger than a few degrees, the band structure at low energies is given by two sets of Dirac cone dispersions which are each localized on a different layer despite the small 0.34 nm interlayer spacing. The layer decoupling persists in a magnetic field, with each layer developing a Landau level spectrum similar to monolayer graphene (18)(19)(20)(21).…”

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confidence: 99%

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

et al. 2016

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†These authors contributed equally to this work. AbstractA quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Moreover, we investigate these electron-hole bilayers in the fractional quantum Hall regime, where we observe conduction through fractional and integer edge states of opposite chiralities, paving the way towards the realization of 1d helical systems with fractional quantum statistics.A helical 1d conductor is an unusual electronic system where forward and backward moving electrons have opposite spin polarizations. Theoretically, a helical state can be realized by combining two quantum Hall edge states with opposite chiralities and opposite spin polarizations (1,2). Most experimental efforts though have focused on materials with strong spin-orbit coupling(3-5), which avoids the need for magnetic fields. However, an approach based on quantum Hall edge states offers greater flexibility in system design with less dependence on material parameters. Moreover, a quantum Hall platform could harness the unique statistics of fractional quantum Hall states. Recent proposals have predicted that such a system, in the form of a fractional quantum spin Hall state(6-8), could host fractional generalizations of Majorana bound states.To simultaneously realize two quantum Hall states with opposite chiralities, it is necessary to have coexisting electron-like and hole-like bands. Such electron-hole quantum Hall states are observed in semi-metals but suffer from low hole-mobilities (9, 10). In this respect, graphene is an attractive system because it has high carrier mobilities and is electron-hole symmetric. In fact, the graphene electron and hole bands can be inverted by the Zeeman effect to realize helical states (11,12), but requires very large magnetic fields (13,14). A similar outcome could be realized more easily in a bilayer system, where an electric field can dope one layer into the electron band and the other into the hole band. In a moderate magnetic field, this electronhole bilayer will develop quantum Hall edge states with opposite chiralities in each layer. Here, we demonstrate a graphene electron-hole bilayer, which we use to realize a helical 1-dimensional conductor made from quantum Hall edge states.All studied devices consist of two monolayer graphene flakes stacked together using a dry transfer process (15,16). The stacking results in a rotational misalignment, or twist, between the layers. The domin...

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“…The in-plane magnetic field results in a relative shift of the Dirac cones of the surface states in momentum space, as discussed in related works on graphene bilayers. 22,23 However, unlike the spectrum of graphene, the spectrum of the TI thin film remains gapped until a critical value of the magnetic field is achieved. 24 Motivated by the original measurements of G versus B y for a GaAs bilayer by Eisenstein et al, 25 here we calculate the tunneling conductance for a TI film as a function of the parallel magnetic field.…”

Section: Introductionmentioning

confidence: 98%

Spin-polarized tunneling current through a thin film of a topological insulator in a parallel magnetic field

Pershoguba

Yakovenko

2012

Phys. Rev. B

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We calculate the tunneling conductance between the surface states on the opposite sides of an ultrathin film of a topological insulator in a parallel magnetic field. The parallel magnetic field produces a relative shift of the in-plane momenta of the two surfaces states. An overlap between the shifted Fermi circles and the spinor wave functions results in an unusual dependence of the tunneling conductance on the magnetic field. Because the spin orientation of the electronic surface states in topological insulators is locked to momentum, the spin polarization of the tunneling current can be controlled by the magnetic field.

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Angle dependence of the Landau level spectrum in twisted bilayer graphene

Cited by 41 publications

References 28 publications

Electronic properties of graphene-based bilayer systems

Electronic properties of graphene-based bilayer systems

Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

Spin-polarized tunneling current through a thin film of a topological insulator in a parallel magnetic field

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