Optical properties of the Hofstadter butterfly in the moiré superlattice

Moon, Pilkyung; Koshino, Mikito

doi:10.1103/physrevb.88.241412

Cited by 36 publications

(39 citation statements)

References 50 publications

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“…When the primitive lattice vectors of layer 1 and those of layer 2 are slightly different, the interference of two lattice structures gives rise to a long-period moiré pattern, and then we can use the long-range effective theory to describe the interlayer interaction [2][3][4][5][6][7][8][9][10][11][12][13][14]. Here we show that the long-range effective theory can be naturally derived from the present general formulation, just by assuming that the two lattice structures are close to each other.…”

Section: Long-period Moiré Superlatticementioning

confidence: 71%

“…A well-known example of irregularly stacked multilayer system is the twisted bilayer graphene, in which two graphene layers are rotationally stacked at an arbitrary angle [1]. When the rotation angle is small, in particular, the system exhibits a moiré interference pattern of which period can be much greater than the atomic scale, and such a longperiod modulation is known to strongly influence the low-energy electronic motion [2][3][4][5][6][7][8][9][10][11][12][13][14]. Graphene-hBN composite system has also been intensively studied as another example of incommensurate multilayer system, where the two layers share the same hexagonal lattice structure but with slightly-different lattice constants, leading to the long-period modulation even at zero rotation angle [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Interlayer interaction in general incommensurate atomic layers

2015

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We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By using the generic tight-binding description, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattice structures and relative orientations. We apply the method to the incommensurate bilayer graphene with a large rotation angle, which cannot be treated as a long-range moiré superlattice, and obtain the quasi band structure and density of states within the first-order approximation.

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Section: Long-period Moiré Superlatticementioning

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Interlayer interaction in general incommensurate atomic layers

2015

Self Cite

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“…Such a potential is formed, for instance, by a grid of electron-beam deposited adatoms on graphene [12,15], by the misalignment of graphene layers in twisted bilayer graphene [16,17], or by a small lattice mismatch between graphene and a hexagonal substrate (BN or Ir), resulting in a so-called moiré pattern [9,10,18]. For hexagonal boron nitride, the layer-substrate interaction is of van der Waals type.…”

Section: Introductionmentioning

confidence: 99%

Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

2014

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Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replicas of the original Dirac cone and Hofstadter butterflies. Our large-scale tight-binding simulation reveals an unexpected coexistence of a relativistic and nonrelativistic Landau level structure. The presence of the zeroth Landau level and its associated butterfly is shown to be the unambiguous signature for the occurrence of the Dirac cone replica.

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“…α(ω) is essentially the real part of the dynamic conductivity [40,41], and our matrix diagonalization gives us access to both the wave functions and energies so we may compute it directly. The results with chemical potential μ = 0 are illustrated in Fig.…”

Section: A In-plane Electric Fieldmentioning

confidence: 99%

Probing layer localization in twisted graphene bilayers via cyclotron resonance

Fertig

2014

Phys. Rev. B

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Electron wave functions in twisted bilayer graphene may have a strong single-layer character or be intrinsically delocalized between layers, with their nature often determined by how energetically close they are to the Dirac point. In this paper, we demonstrate that in magnetic fields, optical absorption (cyclotron resonance) spectra contain signatures that may be used to distinguish the nature of these wave functions at low energies, as well as to locate low-energy critical points in the zero-field energy spectrum. Optical absorption for two different configurations-electric field parallel and perpendicular to the bilayer-is calculated, and the configurations are shown to have different selection rules with respect to which states are connected by the perturbation. Interlayer bias further distinguishes transitions involving states of a single-layer nature from those with support in both layers. For doped systems, a sharp increase in intra-Landau-level absorption occurs with increasing field as the level passes through the zero-field saddle-point energy, where the states change character from single layer to bilayer.

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Optical properties of the Hofstadter butterfly in the moiré superlattice

Cited by 36 publications

References 50 publications

Interlayer interaction in general incommensurate atomic layers

Interlayer interaction in general incommensurate atomic layers

Graphene quantum dot on boron nitride: Dirac cone replica and Hofstadter butterfly

Probing layer localization in twisted graphene bilayers via cyclotron resonance

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