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.

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.

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.

Quantum Transport in Air-Stable Na3Bi Thin Films.

Na3Bi has attracted significant interest in both bulk form as a three-dimensional topological Dirac semimetal and ultrathin form as a wide-band gap two-dimensional topological insulator. Its extreme air sensitivity has limited experimental efforts on thin and ultrathin films grown via molecular beam epitaxy to ultrahigh vacuum environments. Here, we demonstrate air-stable Na3Bi thin films passivated with magnesium difluoride (MgF2) or silicon (Si) capping layers. Electrical measurements show that deposition of MgF2 or Si has minimal impact on the transport properties of Na3Bi while in ultrahigh vacuum. Importantly, the MgF2-passivated Na3Bi films are air-stable and remain metallic for over 100 h after exposure to air, as compared to near instantaneous degradation when they are unpassivated. Air stability enables transfer of films to a conventional high-magnetic field cryostat, enabling quantum transport measurements, which verify that the Dirac semimetal character of Na3Bi films is retained after air exposure.

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.

Polaronic Trions at the MoS2 /SrTiO3 Interface.

The reduced electrical screening in 2D materials provides an ideal platform for realization of exotic quasiparticles, that are robust and whose functionalities can be exploited for future electronic, optoelectronic, and valleytronic applications. Recent examples include an interlayer exciton, where an electron from one layer binds with a hole from another, and a Holstein polaron, formed by an electron dressed by a sea of phonons. Here, a new quasiparticle is reported, "polaronic trion" in a heterostructure of MoS2 /SrTiO3 (STO). This emerges as the Fröhlich bound state of the trion in the atomically thin monolayer of MoS2 and the very unique low energy soft phonon mode (≤7 meV, which is temperature and field tunable) in the quantum paraelectric substrate STO, arising below its structural antiferrodistortive (AFD) phase transition temperature. This dressing of the trion with soft phonons manifests in an anomalous temperature dependence of photoluminescence emission leading to a huge enhancement of the trion binding energy (≈70 meV). The soft phonons in STO are sensitive to electric field, which enables field control of the interfacial trion-phonon coupling and resultant polaronic trion binding energy. Polaronic trions could provide a platform to realize quasiparticle-based tunable optoelectronic applications driven by many body effects.

Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor.

Understanding the remarkable excitonic effects and controlling the exciton binding energies in two-dimensional (2D) semiconductors are crucial in unlocking their full potential for use in future photonic and optoelectronic devices. Here, we demonstrate large excitonic effects and gate-tunable exciton binding energies in single-layer rhenium diselenide (ReSe2) on a back-gated graphene device. We used scanning tunneling spectroscopy and differential reflectance spectroscopy to measure the quasiparticle electronic and optical bandgap of single-layer ReSe2, respectively, yielding a large exciton binding energy of 520 meV. Further, we achieved continuous tuning of the electronic bandgap and exciton binding energy of monolayer ReSe2 by hundreds of milli-electron volts through electrostatic gating, attributed to tunable Coulomb interactions arising from the gate-controlled free carriers in graphene. Our findings open a new avenue for controlling the bandgap renormalization and exciton binding energies in 2D semiconductors for a wide range of technological applications.

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.

Tailoring sample-wide pseudo-magnetic fields on a graphene-black phosphorus heterostructure.

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.

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.

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.

Tuning magnetoresistance in molybdenum disulphide and graphene using a molecular spin transition.

Coupling spins of molecular magnets to two-dimensional (2D) materials provides a framework to manipulate the magneto-conductance of 2D materials. However, with most molecules, the spin coupling is usually weak and devices fabricated from these require operation at low temperatures, which prevents practical applications. Here, we demonstrate field-effect transistors based on the coupling of a magnetic molecule quinoidal dithienyl perylenequinodimethane (QDTP) to 2D materials. Uniquely, QDTP switches from a spin-singlet state at low temperature to a spin-triplet state above 370 K, and the spin transition can be electrically transduced by both graphene and molybdenum disulphide. Graphene-QDTP shows hole-doping and a large positive magnetoresistance ( ~ 50%), while molybdenum disulphide-QDTP demonstrates electron-doping and a switch to large negative magnetoresistance ( ~ 100%) above the magnetic transition. Our work shows the promise of spin detection at high temperature by coupling 2D materials and molecular magnets.Engineering a coupling between magnetic molecules and conducting materials at room temperature could help the development of spintronic devices. Loh et al. show that the spin state of QDTP molecules deposited on graphene and MoS2 couples to their electronic structure, affecting magnetotransport.

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.

Spatial charge inhomogeneity and defect states in topological Dirac semimetal thin films of Na3Bi.

Topological Dirac semimetals (TDSs) are three-dimensional analogs of graphene, with carriers behaving like massless Dirac fermions in three dimensions. In graphene, substrate disorder drives fluctuations in Fermi energy, necessitating construction of heterostructures of graphene and hexagonal boron nitride (h-BN) to minimize the fluctuations. Three-dimensional TDSs obviate the substrate and should show reduced EF fluctuations due to better metallic screening and higher dielectric constants. We map the potential fluctuations in TDS Na3Bi using a scanning tunneling microscope. The rms potential fluctuations are significantly smaller than the thermal energy room temperature (ΔEF,rms = 4 to 6 meV = 40 to 70 K) and comparable to the highest-quality graphene on h-BN. Surface Na vacancies produce a novel resonance close to the Dirac point with surprisingly large spatial extent and provide a unique way to tune the surface density of states in a TDS thin-film material. Sparse defect clusters show bound states whose occupation may be changed by applying a bias to the scanning tunneling microscope tip, offering an opportunity to study a quantum dot connected to a TDS reservoir.

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.