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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. Graphene doesn’t usually have a bandgap but one can appear when the two-dimensional material is placed on a hexagonal boron nitride substrate. Jung et al . now develop a theory that indicates that this occurs because the graphene’s carbon atoms structurally relax when placed on boron nitride.

Understanding and tuning correlated states is of great interest and importance to modern condensed-matter physics. The recent discovery of unconventional superconductivity and Mott-like insulating states in magic-angle twisted bilayer graphene presents a unique platform to study correlation phenomena, in which the Coulomb energy dominates over the quenched kinetic energy as a result of hybridized flat bands. Extending this approach to the case of twisted multilayer graphene would allow even higher control over the band structure because of the reduced symmetry of the system. Here we study electronic transport properties of twisted monolayer–bilayer graphene (a bilayer on top of monolayer graphene heterostructure). We observe the formation of van Hove singularities that are highly tunable by changing either the twist angle or external electric field and can cause strong correlation effects under optimum conditions. We provide basic theoretical interpretations of the observed electronic structure.A structure of monolayer and bilayer graphene with a small twist between them shows correlated insulating states that can be tuned by changing the twist angle or applying an electric field.

The electric-field-induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor 1 – 4 . In this scheme, ‘on’ is the ballistic flow of charge and spin along dissipationless edges of a two-dimensional quantum spin Hall insulator 5 – 9 , and ‘off’ is produced by applying an electric field that converts the exotic insulator to a conventional insulator with no conductive channels. Such a topological transistor is promising for low-energy logic circuits 4 , which would necessitate electric-field-switched materials with conventional and topological bandgaps much greater than the thermal energy at room temperature, substantially greater than proposed so far 6 – 8 . Topological Dirac semimetals are promising systems in which to look for topological field-effect switching, as they lie at the boundary between conventional and topological phases 3 , 10 – 16 . Here we use scanning tunnelling microscopy and spectroscopy and angle-resolved photoelectron spectroscopy to show that mono- and bilayer films of the topological Dirac semimetal 3 , 17 Na 3 Bi are two-dimensional topological insulators with bulk bandgaps greater than 300 millielectronvolts owing to quantum confinement in the absence of electric field. On application of electric field by doping with potassium or by close approach of the scanning tunnelling microscope tip, the Stark effect completely closes the bandgap and re-opens it as a conventional gap of 90 millielectronvolts. The large bandgaps in both the conventional and quantum spin Hall phases, much greater than the thermal energy at room temperature (25 millielectronvolts), suggest that ultrathin Na 3 Bi is suitable for room-temperature topological transistor operation. An electrically controlled phase transition from topological insulator to conventional insulator in ultrathin films of the topological Dirac semimetal, Na 3 Bi.

We demonstrate theoretically that most of the observed transport properties of graphene sheets at zero magnetic field can be explained by scattering from charged impurities. We find that, contrary to common perception, these properties are not universal but depend on the concentration of charged impurities nimp. For dirty samples (250 x 10¹⁰ cm⁻² < nimp < 400 x 10¹⁰ cm⁻²), the value of the minimum conductivity at low carrier density is indeed 4e²/h in agreement with early experiments, with weak dependence on impurity concentration. For cleaner samples, we predict that the minimum conductivity depends strongly on nimp, increasing to 8e²/h for nimp [almost equal to] 20 x 10¹⁰ cm⁻². A clear strategy to improve graphene mobility is to eliminate charged impurities or use a substrate with a larger dielectric constant.

Despite their name, the bulk electrical conductivity of most topological insulators is relatively high, masking many of the important characteristics of its protected, surface conducting states. Counter-doping reduces the bulk conductivity of Bi 2 Se 3 significantly, allowing these surface states and their properties to be clearly identified. The newly discovered three-dimensional strong topological insulators (STIs) exhibit topologically protected Dirac surface states 1 , 2 . Although the STI surface state has been studied spectroscopically, for example, by photoemission 3 , 4 , 5 and scanned probes 6 , 7 , 8 , 9 , 10 , transport experiments 11 , 12 , 13 , 14 , 15 , 16 , 17 have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (∼ 10 nm), low-doped Bi 2 Se 3 (≈10 17  cm −3 ) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk charge carriers and bring both surfaces through the Dirac point simultaneously. We observe clear surface band conduction with a linear Hall resistivity and a well-defined ambipolar field effect, as well as a charge-inhomogeneous minimum conductivity region 18 , 19 , 20 . A theory of charge disorder in a Dirac band 19 , 20 , 21 explains well both the magnitude and the variation with disorder strength of the minimum conductivity (2 to 5 e 2 / h per surface) and the residual (puddle) carrier density (0.4×10 12 to 4×10 12  cm −2 ). From the measured carrier mobilities 320–1,500 cm 2  V −1  s −1 , the charged impurity densities 0.5×10 13 to 2.3×10 13  cm −2 are inferred. They are of a similar magnitude to the measured doping levels at zero gate voltage (1×10 13 to 3×10 13  cm −2 ), identifying dopants as the charged impurities.

Spatially tailored pseudo-magnetic fields (PMFs) can give rise to pseudo-Landau levels and the valley Hall effect in graphene. At an experimental level, it is highly challenging to create the specific strain texture that can generate PMFs over large areas. Here, we report that superposing graphene on multilayer black phosphorus creates shear-strained superlattices that generate a PMF over an entire graphene–black phosphorus heterostructure with edge size of tens of micrometres. The PMF is intertwined with the spatial period of the moiré pattern, and its spatial distribution and intensity can be modified by changing the relative orientation of the two materials. We show that the emerging pseudo-Landau levels influence the transport properties of graphene–black phosphorus field-effect transistor devices with Hall bar geometry. The application of an external magnetic field allows us to enhance or reduce the effective field depending on the valley polarization with the prospect of developing a valley filter.

Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids, electron transport is dominated by extrinsic factors, such as sample geometry and scattering from impurities. However, in the hydrodynamic regime, Coulomb interactions transform the electron motion from independent particles to the collective motion of a viscous “electron fluid.” The fluid viscosity is an intrinsic property of the electron system, determined solely by the electron-electron interactions. Resolving the universal intrinsic viscosity is challenging, as it affects the resistance only through interactions with the sample boundaries, whose roughness not only is unknown but also varies from device to device. Here, we eliminate all unknown parameters by fabricating samples with smooth sidewalls to achieve the perfect slip boundary condition, which has been elusive in both molecular fluids and electronic systems. We engineer the device geometry to create viscous dissipation and reveal the true intrinsic hydrodynamic properties of a 2D system. We observe a clear transition from ballistic to hydrodynamic electron motion, driven by both temperature and magnetic field. We directly measure the viscosity and electron-electron scattering lifetime (the Fermi quasiparticle lifetime) over a wide temperature range without fitting parameters and show they have a strong dependence on electron density that cannot be explained by conventional theories based on the random phase approximation.

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry. Employing the so-called “golden rule of three”, here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where the twist angles between graphene and top/bottom hBN are both close to zero. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than ~ 0.2°. Finally, we extend our technique to low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials. The reliable fabrication of 2D heterostructures with controllable moiré patterns is important for the investigation of their emergent physical properties. Here, the authors report an alignment technique enabling the fabrication of double-aligned hBN/graphene/hBN supermoiré lattice structures with a yield close to 100%.

Understanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments. The mechanisms responsible for the strongly correlated insulating and superconducting phases in twisted bilayer graphene are still debated. The authors provide a theory for phonon-dominated transport that explains several experimental observations, and contrast it with the Planckian dissipation mechanism.

Graphene's quantum quartet The unique electronic structure of graphene, a material made of carbon sheets just one atom thick, makes it of interest both to materials scientists looking for possible technological applications and to the study of fundamental aspects of physics. Young Jae Song et al . have studied one aspect of graphene's uniqueness — the fourfold energy degeneracy that means that a single Landau level (a peak in the density of states produced by a magnetic field) consists of four separate quantum states. Using a high-resolution scanning tunnelling microscope that operates at a record low temperature of down to 10 millikelvin, they perform tunnelling spectroscopy measurements on epitaxial graphene. They obtain spectral fingerprints of the Landau levels, showing in fine detail how they evolve with magnetic fields and how they split (at high fields) into the four separate quantum states. The authors observe states with fractional Landau level filling factors of 7/2, 9/2 and 11/2, which are suggestive of new many-body states in graphene. In graphene, two particular sets of electrons exist that have a fourfold energy degeneracy. To study the corresponding four quantum states comprising a Landau level, these authors perform measurements on epitaxial graphene at 10 millikelvin. They take spectral 'fingerprints' of the Landau levels, showing in detail how they evolve with magnetic field and how they split into the four separate quantum states. They also observe states with Landau level filling factors of 7/2, 9/2 and 11/2. Electrons in a single sheet of graphene behave quite differently from those in traditional two-dimensional electron systems. Like massless relativistic particles, they have linear dispersion and chiral eigenstates. Furthermore, two sets of electrons centred at different points in reciprocal space (‘valleys’) have this dispersion, giving rise to valley degeneracy. The symmetry between valleys, together with spin symmetry, leads to a fourfold quartet degeneracy of the Landau levels, observed as peaks in the density of states produced by an applied magnetic field. Recent electron transport measurements have observed the lifting of the fourfold degeneracy in very large applied magnetic fields, separating the quartet into integer 1 , 2 , 3 , 4 and, more recently, fractional 5 , 6 levels. The exact nature of the broken-symmetry states that form within the Landau levels and lift these degeneracies is unclear at present and is a topic of intense theoretical debate 7 , 8 , 9 , 10 , 11 . Here we study the detailed features of the four quantum states that make up a degenerate graphene Landau level. We use high-resolution scanning tunnelling spectroscopy at temperatures as low as 10 mK in an applied magnetic field to study the top layer of multilayer epitaxial graphene. When the Fermi level lies inside the fourfold Landau manifold, significant electron correlation effects result in an enhanced valley splitting for even filling factors, and an enhanced electron spin splitting for odd filling factors. Most unexpectedly, we observe states with Landau level filling factors of 7/2, 9/2 and 11/2, suggestive of new many-body states in graphene.