Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene

Cao, Yuan; Luo, Jason; Fatemi, Valla; Fang, Shiang; Sanchez-Yamagishi, Javier; Watanabe, Kenji; Taniguchi, Takashi; Kaxiras, Efthimios; Jarillo‐Herrero, Pablo

doi:10.1103/physrevlett.117.116804

Cited by 366 publications

(376 citation statements)

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“…Away from the flat band, the situation in the two cases is quite different. Mini-gaps around the flat bands start appearing only after relaxing the sample [74,75], and agree with recent experiments [76,77]. The P -complexity factor for this calculation (Eq.…”

Section: (A) Complex Structures: Low-angle Twisted Bilayer Graphenesupporting

confidence: 90%

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

Anđelković

Covaci

et al. 2020

R. Soc. open sci.

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We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals (N ∼ 10 10 ). KITE's core is written in C++, with a versatile Python-based interface, and is fully optimised for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green's functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution. Several functionalities are demonstrated, ranging from simulations of local density of states and photo-emission spectroscopy of disordered materials to large-scale computations of optical conductivity tensors and real-space wave-packet propagation in the presence of magneto-static fields and spin-orbit coupling. On-the-fly calculations of real-space Green's functions are carried out with an efficient domain decomposition technique, allowing KITE to achieve nearly ideal linear scaling in its multi-threading performance. Crystalline defects and disorder, including vacancies, adsorbates and charged impurity centers, can be easily set up with KITE's intuitive interface, paving the way to user-friendly large-scale quantum simulations of equilibrium and nonequilibrium properties of molecules, disordered crystals and heterostructures subject to a variety of perturbations and external conditions. arXiv:1910.05194v1 [cond-mat.mes-hall] 11 Oct 2019 2 IntroductionComputational modelling has become an essential tool in both fundamental and applied research that has propelled the discovery of new materials and their translation into practical applications [1]. The study of condensed phases of matter has benefited from significant advances in electronic structure theory and simulation methodologies. Among these advances are: explicitly correlated wave-function-based techniques achieving sub-chemical accuracy [2], first-principles methods to tackling electronic excitations [3], charge-self-consistent atomistic models for accurate electronic structure calculations [4], and the use of machine learning as means to finding density functionals without solving the Khon-Sham equations [5,6].Semi-empirical atomistic methods are amongst the most simple and effective methods to calculate ground-and excited-state properties of materials [7][8][9][10]. The increasingly popular tight-binding approach [11] has been employed for accurate and fast calculations of total energies and electronic structure in complex materials, including semiconductors [12,13], quantum dots [14] and super-lattices [15,16], and is particularly well-suited for implementation of O(N ) (linear scaling) algorithms for efficient calculations of total energies and forces [17].Accurate tight-binding models have been devised for a plethora of model systems, ranging from metals to ionic materials [18], and shown to correctly p...

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Section: (A) Complex Structures: Low-angle Twisted Bilayer Graphenesupporting

confidence: 90%

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

Anđelković

Covaci

et al. 2020

R. Soc. open sci.

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“…The counterpart for electron doping (n > 0) exhibits a lower T c as has also been measured [11]. Near half-filling (n (0) ) where insulating states are observed [9,11,35,36], we find T c = 0. This is not surprising since particle-hole pairing is not included in our model.…”

supporting

confidence: 79%

Prominent Cooper pairing away from the Fermi level and its spectroscopic signature in twisted bilayer graphene

Schrodi

Aperis

Oppeneer

2020

Phys. Rev. Research

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We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in the superconducting state. We predict several such features in tunneling and angle resolved photoemission spectra for future experiments.

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“…We associate the appearance of satellite resistance peaks at ±8 electrons per moiré period for twist angles below the first magic angle, instead of at the ±4 electron density expected in the perturbative regime (28,29), with the second flat band present near the Dirac point. The appearance of an electron-electron interaction-induced pseudogap at neutrality can be understood in terms of the expected instability of linear band crossings (Dirac bands) in two dimensions at small Fermi velocities, and its insensitivity to a displacement field between the layers can be understood in terms of the strong hybridization between layers in low-energy bands at STA (15,30).…”

Section: Resultsmentioning

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.

514

404

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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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Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene

Cited by 366 publications

References 44 publications

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

KITE: high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

Prominent Cooper pairing away from the Fermi level and its spectroscopic signature in twisted bilayer graphene

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

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