Evidence for Interlayer Coupling and Moiré Periodic Potentials in Twisted Bilayer Graphene

Ohta, Taisuke; Robinson, Jeremy T.; Feibelman, Peter J.; Bostwick, Aaron; Rotenberg, Eli; Beechem, Thomas E.

doi:10.1103/physrevlett.109.186807

Cited by 207 publications

(223 citation statements)

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“…The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5)(6)(7)(8)(9)(10)(11)(12). In bilayer graphene, this ratio is small when twist angles exceed about 2° (10,13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5).…”

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confidence: 99%

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Kim

DaSilva

Huang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

541

408

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According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1°and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1°, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with fourfold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors ±1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.moiré crystal | graphene | twisted bilayer | moiré band | Hofstadter butterfly M oiré patterns form when nearly identical two-dimensional (2D) crystals are overlaid with a small relative twist angle (1-4). The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5-12). In bilayer graphene, this ratio is small when twist angles exceed about 2°(10, 13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5). At smaller twist angles, electronic properties become increasingly complex. Theory (14, 15) has predicted that extremely flat bands appear at a series of magic angles, the largest of which is close to 1°. Flat bands in 2D electron systems, for example the Landau level bands that appear in the presence of external magnetic fields, allow for physical properties that are dominated by electron-electron interactions, and have been friendly territory for the discovery of fundamentally new states of matter. Here we report transport and scanning probe microscopy (SPM) studies of bilayer graphene moiré crystals with carefully controlled small-twist angles (STA), below 1°. We find that conductivity minima emerge in transport at neutrality, and at anomalous satellite densities that correspond to ±8 additional electrons in the moiré crystal unit cell, and that the conductivity minimum at neutrality is not weakened by a transverse electric field applied between the layers. Our observations can be explained only by strong electronic correlations. MethodsOur STA bilayer graphene samples are fabricated by sequential graphene and hexagonal boron-nitride (hBN) flake pick-up steps using a hemispherical handle substrate (16) that allows an individual flake to be detached from a substrate while leaving flakes in its immediate proximity intact. To...

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confidence: 99%

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Kim

DaSilva

Huang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

541

408

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“…The cross-plane thermovoltage which is nonmonotonic in both temperature and density, is generated through scattering of electrons by the out-of-plane layer breathing (ZO /ZA2) phonon modes and differs dramatically from the expected LandauerButtiker formalism in conventional tunnel junctions. The Tunability of cross-plane seebeck effect in van der Waals junctions may be valuable in creating a new genre of versatile thermoelectric systems with layered solidsIn spite of subnanometer separation of the van der Waals gap (∼ 0.5 nm), the coupling of the two graphene layers in twisted bilayer graphene (tBLG) varies strongly with temperature (T ), and the twist or misorientation angle θ between the hexagonal lattices of participating graphene layers [1][2][3][4][5][6][7][8][9]. At T Θ BG , where Θ BG is the Bloch-Grüneisen temperature, the layers are coherently coupled either for θ 10…”

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confidence: 99%

Seebeck Coefficient of a Single van der Waals Junction in Twisted Bilayer Graphene

et al. 2017

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When two planar atomic membranes are placed within the van der Waals distance, the charge and heat transport across the interface are coupled by the rules of momentum conservation and structural commensurability, lead to outstanding thermoelectric properties. Here we show that an effective 'inter-layer phonon drag' determines the Seebeck coefficient (S) across the van der Waals gap formed in twisted bilayer graphene (tBLG). The cross-plane thermovoltage which is nonmonotonic in both temperature and density, is generated through scattering of electrons by the out-of-plane layer breathing (ZO /ZA2) phonon modes and differs dramatically from the expected LandauerButtiker formalism in conventional tunnel junctions. The Tunability of cross-plane seebeck effect in van der Waals junctions may be valuable in creating a new genre of versatile thermoelectric systems with layered solidsIn spite of subnanometer separation of the van der Waals gap (∼ 0.5 nm), the coupling of the two graphene layers in twisted bilayer graphene (tBLG) varies strongly with temperature (T ), and the twist or misorientation angle θ between the hexagonal lattices of participating graphene layers [1][2][3][4][5][6][7][8][9]. At T Θ BG , where Θ BG is the Bloch-Grüneisen temperature, the layers are coherently coupled either for θ 10• with a renormalized Fermi velocity [4,8], or at specific values of θ, such as θ = 30• ± 8.21• , when the hexagonal crystal structures become commensurate [1]. For θ > 10• (and away from the 'magic' angles), the layers are essentially decoupled at low T , but get effectively re-coupled at higher T (> Θ BG ), when the interlayer phonons drive cross-plane electrical transport through strong electron-phonon scattering [2,3]. These phonons are also expected to determine thermal and thermoelectric transport across the interface [10][11][12][13][14][15]. In fact, since the in-plane transverse and longitudinal phonons are effectively filtered out from contributing to cross-plane transport because they do not substantially alter the tunneling matrix elements, theoretical calculations predict enhanced cross-plane thermoelectric properties in van der Waals heterojunctions, including high ZT factors at room temperature [12]. However, although the impact of interlayer coherence and electron-phonon interaction on electrical conductance has been studied in detail [1,3], their relevance to the thermal and thermoelectric properties of tBLG remains unexplored.We assembled the tBLG devices with layer-by-layer mechanical transfer method, which is common in van der Waals epitaxy [16][17][18]. Three devices were constructed which show very similar behavior, and we present the results from one of the devices here. The device consists of two graphene layers oriented in a "cross" configuration (inset of Fig. 1a and an optical micrograph in Fig. 1b), and entirely encapsulated within two layers of hexagonal boron nitride (hBN). The carrier mobilities in the upper and lower layers are ≈ 25000 cm 2 V −1 s −1 and ≈ 60000 cm 2 V −1 s −1 , at room tem...

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“…Twisted bilayer graphene (tBLG), a prototypical bilayer system, has been the subject of many recent theoretical and experimental studies [1][2][3][4][5][6] . In tBLG, the interlayer interactions perturb the band structure of each graphene layer to create new, θ-dependent van Hove singularities (vHSs), which have been observed by scanning tunneling spectroscopy 5,7,8 and optical spectroscopy [9][10][11][12][13][14] .…”

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confidence: 99%

Van Hove Singularities and Excitonic Effects in the Optical Conductivity of Twisted Bilayer Graphene

Havener

Liang

Brown³

et al. 2014

Nano Lett.

145

163

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Abstract:We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2 eV to 5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands, as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations is essential to reproduce the shape of the conductivity spectra, and we find evidence of coherent interactions between the states associated with the multiple vHSs in tBLG.Keywords: graphene, twisted bilayer graphene, optical spectroscopy, GW-BSE In two-dimensional materials with van der Waals interlayer coupling, the rotation angle (θ) between layers has emerged as an important degree of freedom with significant effects on these materials' electronic and optical properties. Twisted bilayer graphene (tBLG), a prototypical bilayer system, has been the subject of many recent theoretical and experimental studies [1][2][3][4][5][6] . In tBLG, the interlayer interactions perturb the band structure of each graphene layer to create new, θ-dependent van Hove singularities (vHSs), which have been observed by scanning tunneling spectroscopy 5,7,8 and optical spectroscopy [9][10][11][12][13][14] . However, these previous studies focused on relatively low energies where single layer graphene (SLG) has a unique linear band structure. On the contrary, the band structure of SLG becomes more complex at higher energies: the bands lose their linearity, electrons and holes are no longer symmetric, and a saddle point vHS occurs at the M point in the SLG Brillouin zone 15,16 . To date, little is known about how this asymmetry and nonlinearity affects the θ-dependent vHSs and associated optical properties in tBLG.In addition, while it is known that there are resonant excitons associated with the M point vHS in SLG [17][18][19] , the excitonic effects associated with the interlayer vHSs in tBLG are poorly understood. Furthermore, new excitonic states could form as coherent combinations of the multiple intralayer and interlayer vHSs in tBLG, particularly those closest in energy. Understanding these effects in tBLG would also aid our understanding of other stacked and twisted two-dimensional materials, such as hexagonal boron nitride and transition metal dichalcogenides, whose single layers have intrinsic band gaps and other higher energy vHSs.In this work, we perform optical absorption spectroscopy of tBLG with known θ to explore the tBLG band structure and many-body states. For the first time, we present the full optical absorption spectra of tBLG with various θ over a large energy range (1.2 -5.6 eV), which encompasses multiple θ-dependent vHSs in tBLG as well as the absorption peak associated with the M point vHS in SLG. We find that the

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Evidence for Interlayer Coupling and Moiré Periodic Potentials in Twisted Bilayer Graphene

Cited by 207 publications

References 56 publications

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Seebeck Coefficient of a Single van der Waals Junction in Twisted Bilayer Graphene

Van Hove Singularities and Excitonic Effects in the Optical Conductivity of Twisted Bilayer Graphene

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