Recent progress in preparing well-controlled two-dimensional van der Waals heterojunctions has opened up a new frontier in materials physics. Here we address the intriguing energy gaps that are sometimes observed when a graphene sheet is placed on a hexagonal boron nitride substrate, demonstrating that they are produced by an interesting interplay between structural and electronic properties, including electronic many-body exchange interactions. Our theory is able to explain the observed gap behaviour by accounting first for the structural relaxation of graphene’s carbon atoms when placed on a boron nitride substrate, and then for the influence of the substrate on low-energy π-electrons located at relaxed carbon atom sites. The methods we employ can be applied to many other van der Waals heterojunctions.

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...

We consider in our work single crystal thin films of Bi2Se3, grown by molecular beam epitaxy, both with and without Pb doping. Angle-resolved photoemission data demonstrate topological surface states with a Fermi level lying inside the bulk band gap in the Pb doped films. Transport data show weak localization behavior, as expected for a thin film in the two-dimensional limit (when the thickness is smaller than the inelastic mean free path), but a detailed analysis within the standard theoretical framework of diffusive transport shows that the temperature and magnetic field dependences of resistance cannot be reconciled in a theory that neglects inter-electron interactions. We demonstrate that an excellent account of quantum corrections to conductivity is achieved when both disorder and interaction are taken into account. These results clearly demonstrate that it is crucial to include electron electron interaction for a comprehensive understanding of diffusive transport in topological insulators. While both the ordinary bulk and the topological surface states presumably participate in transport, our analysis does not allow a clear separation of the two contributions.

We report the observation of the superconducting proximity effect in nanoribbons of a candidate topological insulator (Bi2Se3) which is interfaced with superconducting (tungsten) contacts. We observe a supercurrent and multiple Andreev reflections for channel lengths that are much longer than the inelastic and diffusive thermal lengths deduced from normal state transport. This suggests that the proximity effect couples preferentially to a ballistic surface transport channel, even in the presence of a coexisting diffusive bulk channel. When a magnetic field is applied perpendicular to the plane of the nanoribbon, we observe magnetoresistance oscillations that are periodic in magnetic field. Quantitative comparison with a model of vortex blockade relates the occurrence of these oscillations to the formation of Pearl vortices in the region of proximity induced superconductivity.

Twisted bilayer graphene (tBLG) forms a quasicrystal whose structural and electronic properties depend on the angle of rotation between its layers. Here we present a scanning tunneling microscopy study of gate-tunable tBLG devices supported by atomically-smooth and chemically inert hexagonal boron nitride (BN). The high quality of these tBLG devices allows identification of coexisting moiré patterns and moiré super-superlattices produced by graphene-graphene and graphene-BN interlayer interactions. Furthermore, we examine additional tBLG spectroscopic features in the local density of states beyond the first van Hove singularity. Our experimental data is explained by a theory of moiré bands that incorporates ab initio calculations and confirms the strongly non-perturbative character of tBLG interlayer coupling in the small twist-angle regime.

From a combination of careful and detailed theoretical and experimental studies, we demonstrate that the Boltzmann theory including all scattering mechanisms gives an excellent account, with no adjustable parameters, of high electric field transport in single as well as double-oxide graphene transistors. We further show unambiguously that scattering from the substrate and superstrate surface optical phonons governs the high-field transport and heat dissipation over a wide range of experimentally relevant parameters. Models that neglect surface optical phonons altogether or treat them in a simple phenomenological manner are inadequate. We outline possible strategies for achieving higher current and complete saturation in graphene devices.

Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moiré pattern pseudospin fields. Here, we present the moiré-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab-initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moiré patterns, leading to primary Dirac point gaps when the moiré strains give rise to a finite average mass, and to secondary gaps when the moiré pseudospin components are mixed appropriately. The pseudomagnetic strain fields which can reach values of up to ∼ 40 Tesla near symmetry points in the moiré cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moiré strains.

In spite of much work on topological insulators (TIs), systematic experiments for TI/TI heterostructures remain absent. We grow a high quality heterostructure containing single quintuple layer (QL) of Bi2Se3 on 19 QLs of Bi2Te3 and compare its transport properties with 20 QLs Bi2Se3 and 20 QLs Bi2Te3. All three films are grown on insulating sapphire (0001) substrates by molecular beam epitaxy (MBE). In situ angle-resolved photoemission spectroscopy (ARPES) provides direct evidence that the surface state of 1 QL Bi2Se3/19 QLs Bi2Te3 heterostructure is similar to the surface state of the 20 QLs Bi2Se3 and different with that of the 20 QLs Bi2Te3. In ex situ transport measurements, the observed linear magnetoresistance (MR) and weak antilocalization (WAL) of the hybrid heterostructure are similar to that of the pure Bi2Se3 film and not the Bi2Te3 film. This suggests that the single Bi2Se3 layer on top of 19 QLs Bi2Te3 dominates its transport properties.