Evidence for electron-hole crystals in a Mott insulator.

The coexistence of correlated electron and hole crystals enables the realization of quantum excitonic states, capable of hosting counterflow superfluidity and topological orders with long-range quantum entanglement. Here we report evidence for imbalanced electron-hole crystals in a doped Mott insulator, namely, α-RuCl3, through gate-tunable non-invasive van der Waals doping from graphene. Real-space imaging via scanning tunnelling microscopy reveals two distinct charge orderings at the lower and upper Hubbard band energies, whose origin is attributed to the correlation-driven honeycomb hole crystal composed of hole-rich Ru sites and rotational-symmetry-breaking paired electron crystal composed of electron-rich Ru-Ru bonds, respectively. Moreover, a gate-induced transition of electron-hole crystals is directly visualized, further corroborating their nature as correlation-driven charge crystals. The realization and atom-resolved visualization of imbalanced electron-hole crystals in a doped Mott insulator opens new doors in the search for correlated bosonic states within strongly correlated materials.

Topological Flat Bands in Graphene Super-Moiré Lattices.

Moiré-pattern-based potential engineering has become an important way to explore exotic physics in a variety of two-dimensional condensed matter systems. While these potentials have induced correlated phenomena in almost all commonly studied 2D materials, monolayer graphene has remained an exception. We demonstrate theoretically that a single layer of graphene, when placed between two bulk boron nitride crystal substrates with the appropriate twist angles, can support a robust topological ultraflat band emerging as the second hole band. This is one of the simplest platforms to design and exploit topological flat bands.

Dynamic band-structure tuning of graphene moiré superlattices with pressure.

Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics 1 . In many cases, beyond simply realizing new material combinations, interlayer interactions lead to emergent electronic properties that are fundamentally distinct from those of the constituent layers 2 . A critical parameter in these structures is the interlayer coupling strength, but this is often not easy to determine and is typically considered to be a fixed property of the system. Here we demonstrate that we can controllably tune the interlayer separation in van der Waals heterostructures using hydrostatic pressure, providing a dynamic way to modify their electronic properties. In devices in which graphene is encapsulated in boron nitride and aligned with one of the encapsulating layers, we observe that increasing pressure produces a superlinear increase in the moiré-superlattice-induced bandgap-nearly doubling within the studied range-together with an increase in the capacitive gate coupling to the active channel by as much as 25 per cent. Comparison to theoretical modelling highlights the role of atomic-scale structural deformations and how this can be altered with pressure. Our results demonstrate that combining hydrostatic pressure with controlled rotational order provides opportunities for dynamic band-structure engineering in van der Waals heterostructures.

Electric-field-tuned topological phase transition in ultrathin Na3Bi.

The electric-field-induced quantum phase transition from topological to conventional insulator has been proposed as the basis of a topological field effect transistor1-4. In this scheme, 'on' is the ballistic flow of charge and spin along dissipationless edges of a two-dimensional quantum spin Hall insulator5-9, 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 circuits4, 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 far6-8. 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 phases3,10-16. Here we use scanning tunnelling microscopy and spectroscopy and angle-resolved photoelectron spectroscopy to show that mono- and bilayer films of the topological Dirac semimetal3,17 Na3Bi 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 Na3Bi is suitable for room-temperature topological transistor operation.

Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions.

Recent experimental [I. Jo et al., Phys. Rev. Lett. 119, 016402 (2017)] and numerical [M. Ippoliti, S. D. Geraedts, R. N. Bhatt, Phys. Rev. B 95, 201104 (2017)] evidence suggests an intriguing universal relationship between the Fermi surface anisotropy of the noninteracting parent 2-dimensional (2D) electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filling. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed [H. -K. Tang et al., Science 361, 570 (2018)] nonperturbative and numerically exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac fermions with long-range Coulomb interactions do we find a universal square-root decrease of the Fermi-surface anisotropy. For the [Formula: see text] composite Fermi liquid, this result is surprising since a Dirac fermion ground state was only recently proposed as an alternative to the usual Halperin-Lee-Read state. Our proposed universality can be tested in several anisotropic Dirac materials including graphene, topological insulators, organic conductors, and magic-angle twisted bilayer graphene.

Tunable Optical Properties of Thin Films Controlled by the Interface Twist Angle.

Control of materials properties has been the driving force of modern technologies. So far, materials properties have been modulated by their composition, structure, and size. Here, by using cathodoluminescence in a scanning transmission electron microscope, we show that the optical properties of stacked, >100 nm thick hexagonal boron nitride (hBN) films can be continuously tuned by their relative twist angles. Due to the formation of a moiré superlattice between the two interface layers of the twisted films, a new moiré sub-band gap is formed with continuously decreasing magnitude as a function of the twist angle, resulting in tunable luminescence wavelength and intensity increase of >40×. Our results demonstrate that moiré phenomena extend beyond monolayer-based systems and can be preserved in a technologically relevant, bulklike material at room temperature, dominating optical properties of hBN films for applications in medicine, environmental, or information technologies.

Evidence of Rotational Fröhlich Coupling in Polaronic Trions.

Electrons commonly couple through Fröhlich interactions with longitudinal optical phonons to form polarons. However, trions possess a finite angular momentum and should therefore couple instead to rotational optical phonons. This creates a polaronic trion whose binding energy is determined by the crystallographic orientation of the lattice. Here, we demonstrate theoretically within the Fröhlich approach and experimentally by photoluminescence emission that the bare trion binding energy (20 meV) is significantly enhanced by the phonons at the interface between the two-dimensional semiconductor MoS_{2} and the bulk transition metal oxide SrTiO_{3}. The low-temperature binding energy changes from 60 meV in [001]-oriented substrates to 90 meV for [111] orientation, as a result of the counterintuitive interplay between the rotational axis of the MoS_{2} trion and that of the SrTiO_{3} phonon mode.

Phonon-Mediated Colossal Magnetoresistance in Graphene/Black Phosphorus Heterostructures.

There is a huge demand for magnetoresistance (MR) sensors with high sensitivity, low energy consumption, and room temperature operation. It is well-known that spatial charge inhomogeneity due to impurities or defects introduces mobility fluctuations in monolayer graphene and gives rise to MR in the presence of an externally applied magnetic field. However, to realize a MR sensor based on this effect is hampered by the difficulty in controlling the spatial distribution of impurities and the weak magnetoresistance effect at the monolayer regime. Here, we fabricate a highly stable monolayer graphene-on-black phosphorus (G/BP) heterostructure device that exhibits a giant MR of 775% at 9 T magnetic field and 300 K, exceeding by far the MR effects from devices made from either monolayer graphene or few-layer BP alone. The positive MR of the G/BP device decreases when the temperature is lowered, indicating a phonon-mediated process in addition to scattering by charge impurities. Moreover, a nonlocal MR of >10 000% is achieved for the G/BP device at room temperature due to an enhanced flavor Hall effect induced by the BP channel. Our results show that electron-phonon coupling between 2D material and a suitable substrate can be exploited to create giant MR effects in Dirac semimetals.

Emergence of Tertiary Dirac Points in Graphene Moiré Superlattices.

The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces a moiré superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moiré superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekulé superstructure on top of the moiré superlattice under appropriate carrier doping and magnetic fields.

Electronic Properties of High-Quality Epitaxial Topological Dirac Semimetal Thin Films.

Topological Dirac semimetals (TDS) are three-dimensional analogues of graphene, with linear electronic dispersions in three dimensions. Nanoscale confinement of TDSs in thin films is a necessary step toward observing the conventional-to-topological quantum phase transition (QPT) with increasing film thickness, gated devices for electric-field control of topological states, and devices with surface-state-dominated transport phenomena. Thin films can also be interfaced with superconductors (realizing a host for Majorana Fermions) or ferromagnets (realizing Weyl Fermions or T-broken topological states). Here we report structural and electrical characterization of large-area epitaxial thin films of TDS Na3Bi on single crystal Al2O3[0001] substrates. Charge carrier mobilities exceeding 6,000 cm(2)/(V s) and carrier densities below 1 × 10(18) cm(-3) are comparable to the best single crystal values. Perpendicular magnetoresistance at low field shows the perfect weak antilocalization behavior expected for Dirac Fermions in the absence of intervalley scattering. At higher fields up to 0.5 T anomalously large quadratic magnetoresistance is observed, indicating that some aspects of the low field magnetotransport (µB < 1) in this TDS are yet to be explained.

High-resolution tunnelling spectroscopy of a graphene quartet.

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 and, more recently, fractional 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. 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.

Van der Waals force: a dominant factor for reactivity of graphene.

Reactivity control of graphene is an important issue because chemical functionalization can modulate graphene's unique mechanical, optical, and electronic properties. Using systematic optical studies, we demonstrate that van der Waals interaction is the dominant factor for the chemical reactivity of graphene on two-dimensional (2D) heterostructures. A significant enhancement in the chemical stability of graphene is achieved by replacing the common SiO2 substrate with 2D crystals such as an additional graphene layer, WS2, MoS2, or h-BN. Our theoretical and experimental results show that its origin is a strong van der Waals interaction between the graphene layer and the 2D substrate. This results in a high resistive force on graphene toward geometric lattice deformation. We also demonstrate that the chemical reactivity of graphene can be controlled by the relative lattice orientation with respect to the substrates and thus can be used for a wide range of applications including hydrogen storage.

Transport properties of monolayer MoS2 grown by chemical vapor deposition.

Recent success in the growth of monolayer MoS2 via chemical vapor deposition (CVD) has opened up prospects for the implementation of these materials into thin film electronic and optoelectronic devices. Here, we investigate the electronic transport properties of individual crystallites of high quality CVD-grown monolayer MoS2. The devices show low temperature mobilities up to 500 cm(2) V(-1) s(-1) and a clear signature of metallic conduction at high doping densities. These characteristics are comparable to the electronic properties of the best mechanically exfoliated monolayers in literature, verifying the high electronic quality of the CVD-grown materials. We analyze the different scattering mechanisms and show that the short-range scattering plays a dominant role in the highly conducting regime at low temperatures. Additionally, the influence of optical phonons as a limiting factor is discussed.

Disorder-induced magnetoresistance in a two-dimensional electron system.

We predict and demonstrate that a disorder-induced carrier density inhomogeneity causes magnetoresistance (MR) in a two-dimensional electron system. Our experiments on graphene show a quadratic MR persisting far from the charge neutrality point. Effective medium calculations show that for charged impurity disorder, the low-field MR is a universal function of the ratio of carrier density to fluctuations in carrier density, a power law when this ratio is large, in excellent agreement with experiment. The MR is generic and should occur in other materials with large carrier density inhomogeneity.

Direct imaging of charged impurity density in common graphene substrates.

Kelvin probe microscopy in ultrahigh vacuum is used to image the local electrostatic potential fluctuations above hexagonal boron nitride (h-BN) and SiO2, common substrates for graphene. Results are compared to a model of randomly distributed charges in a two-dimensional (2D) plane. For SiO2, the results are well modeled by 2D charge densities ranging from 0.24 to 2.7 × 10(11) cm(-2), while h-BN displays potential fluctuations 1-2 orders of magnitude lower than SiO2, consistent with the improvement in charge carrier mobility for graphene on h-BN compared to SiO2. Electron beam exposure of SiO2 increases the charge density fluctuations, creating long-lived metastable charge populations of ~2 × 10(11) cm(-2) at room temperature, which can be reversed by heating.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures.

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.

Dissipation-enabled hydrodynamic conductivity in a tunable bandgap semiconductor.

Electronic transport in the regime where carrier-carrier collisions are the dominant scattering mechanism has taken on new relevance with the advent of ultraclean two-dimensional materials. Here, we present a combined theoretical and experimental study of ambipolar hydrodynamic transport in bilayer graphene demonstrating that the conductivity is given by the sum of two Drude-like terms that describe relative motion between electrons and holes, and the collective motion of the electron-hole plasma. As predicted, the measured conductivity of gapless, charge-neutral bilayer graphene is sample- and temperature-independent over a wide range. Away from neutrality, the electron-hole conductivity collapses to a single curve, and a set of just four fitting parameters provides quantitative agreement between theory and experiment at all densities, temperatures, and gaps measured. This work validates recent theories for dissipation-enabled hydrodynamic conductivity and creates a link between semiconductor physics and the emerging field of viscous electronics.

Carrier transport theory for twisted bilayer graphene in the metallic regime.

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.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material.

Trisodium bismuthide (Na3 Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na3 Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na3 Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.