Mixing of moiré-surface and bulk states in graphite.

Van der Waals assembly enables the design of electronic states in two-dimensional (2D) materials, often by superimposing a long-wavelength periodic potential on a crystal lattice using moiré superlattices1-9. This twistronics approach has resulted in numerous previously undescribed physics, including strong correlations and superconductivity in twisted bilayer graphene10-12, resonant excitons, charge ordering and Wigner crystallization in transition-metal chalcogenide moiré structures13-18 and Hofstadter's butterfly spectra and Brown-Zak quantum oscillations in graphene superlattices19-22. Moreover, twistronics has been used to modify near-surface states at the interface between van der Waals crystals23,24. Here we show that electronic states in three-dimensional (3D) crystals such as graphite can be tuned by a superlattice potential occurring at the interface with another crystal-namely, crystallographically aligned hexagonal boron nitride. This alignment results in several Lifshitz transitions and Brown-Zak oscillations arising from near-surface states, whereas, in high magnetic fields, fractal states of Hofstadter's butterfly draw deep into the bulk of graphite. Our work shows a way in which 3D spectra can be controlled using the approach of 2D twistronics.

Ferroelectric Switching at Symmetry-Broken Interfaces by Local Control of Dislocations Networks.

Semiconducting ferroelectric materials with low energy polarization switching offer a platform for next-generation electronics such as ferroelectric field-effect transistors. Recently discovered interfacial ferroelectricity in bilayers of transition metal dichalcogenide films provides an opportunity to combine the potential of semiconducting ferroelectrics with the design flexibility of 2D material devices. Here, local control of ferroelectric domains in a marginally twisted WS2 bilayer is demonstrated with a scanning tunneling microscope at room temperature, and their observed reversible evolution is understood using a string-like model of the domain wall network (DWN). Two characteristic regimes of DWN evolution are identified: (i) elastic bending of partial screw dislocations separating smaller domains with twin stackings due to mutual sliding of monolayers at domain boundaries and (ii) merging of primary domain walls into perfect screw dislocations, which become the seeds for the recovery of the initial domain structure upon reversing electric field. These results open the possibility to achieve full control over atomically thin semiconducting ferroelectric domains using local electric fields, which is a critical step towards their technological use.

Mixed-Stacking Few-Layer Graphene as an Elemental Weak Ferroelectric Material.

Ferroelectricity (Valasek, J. Phys. Rev. 1921, 17, 475), a spontaneous formation of electric polarization, is a solid state phenomenon, usually, associated with ionic compounds or complex materials. Here we show that, atypically for elemental solids, few-layer graphenes can host an equilibrium out-of-plane electric polarization, switchable by sliding the constituent graphene sheets. The systems hosting such effect include mixed-stacking tetralayers and thicker (5-9 layers) rhombohedral graphitic films with a twin boundary in the middle of a flake. The predicted electric polarization would also appear in marginally (small-angle) twisted few-layer flakes, where lattice reconstruction would give rise to networks of mesoscale domains with alternating value and sign of out-of-plane polarization.

ARPES Signatures of Few-Layer Twistronic Graphenes.

Diverse emergent correlated electron phenomena have been observed in twisted-graphene layers. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. We use angle-resolved photoemission spectroscopy to study the twist-dependent (1° < θ < 8°) band structure of twisted-bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid k·p model for interlayer coupling. Quantitative agreement is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing field-induced gaps in twisted graphenes. However, for tDBG at θ = 1.5 ± 0.2°, close to the magic angle θ = 1.3°, a flat band is found near the Fermi level with measured bandwidth Ew = 31 ± 5 meV. An analysis of the gap between the flat band and the next valence band shows deviations between experiment (Δh = 46 ± 5 meV) and theory (Δh = 5 meV), indicative of lattice relaxation in this regime.

Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules.

Materials such as graphene and topological insulators host massless Dirac fermions that enable the study of relativistic quantum phenomena. Single quantum dots and coupled quantum dots formed with massless Dirac fermions can be viewed as artificial relativistic atoms and molecules, respectively. Such structures offer a unique testbed to study atomic and molecular physics in the ultrarelativistic regime (particle speed close to the speed of light). Here we use a scanning tunnelling microscope to create and probe single and coupled electrostatically defined graphene quantum dots to unravel the magnetic-field responses of artificial relativistic nanostructures. We observe a giant orbital Zeeman splitting and orbital magnetic moment up to ~70 meV T-1 and ~600µB (µB, Bohr magneton) in single graphene quantum dots. For coupled graphene quantum dots, Aharonov-Bohm oscillations and a strong Van Vleck paramagnetic shift of ~20 meV T-2 are observed. Our findings provide fundamental insights into relativistic quantum dot states, which can be potentially leveraged for use in quantum information science.

Moiré modulation of charge density waves.

Here we investigate how charge density waves (CDWs), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For3×3CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for2×2CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For3×3CDWs with twist angles close to 180∘, moiré-scale triangular structures can form; while close to 0∘, moiré-scale dimer domains occur. The star-of-David CDW (13×13) is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to the2×2CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré superlattice and CDW phases intrinsic to the comprising 2D materials.

Band Gap Opening in Bilayer Graphene-CrCl3/CrBr3/CrI3 van der Waals Interfaces.

We report experimental investigations of transport through bilayer graphene (BLG)/chromium trihalide (CrX3; X = Cl, Br, I) van der Waals interfaces. In all cases, a large charge transfer from BLG to CrX3 takes place (reaching densities in excess of 1013 cm-2), and generates an electric field perpendicular to the interface that opens a band gap in BLG. We determine the gap from the activation energy of the conductivity and find excellent agreement with the latest theory accounting for the contribution of the σ bands to the BLG dielectric susceptibility. We further show that for BLG/CrCl3 and BLG/CrBr3 the band gap can be extracted from the gate voltage dependence of the low-temperature conductivity, and use this finding to refine the gap dependence on the magnetic field. Our results allow a quantitative comparison of the electronic properties of BLG with theoretical predictions and indicate that electrons occupying the CrX3 conduction band are correlated.

Light sources with bias tunable spectrum based on van der Waals interface transistors.

Light-emitting electronic devices are ubiquitous in key areas of current technology, such as data communications, solid-state lighting, displays, and optical interconnects. Controlling the spectrum of the emitted light electrically, by simply acting on the device bias conditions, is an important goal with potential technological repercussions. However, identifying a material platform enabling broad electrical tuning of the spectrum of electroluminescent devices remains challenging. Here, we propose light-emitting field-effect transistors based on van der Waals interfaces of atomically thin semiconductors as a promising class of devices to achieve this goal. We demonstrate that large spectral changes in room-temperature electroluminescence can be controlled both at the device assembly stage -by suitably selecting the material forming the interfaces- and on-chip, by changing the bias to modify the device operation point. Even though the precise relation between device bias and kinetics of the radiative transitions remains to be understood, our experiments show that the physical mechanism responsible for light emission is robust, making these devices compatible with simple large areas device production methods.

Scattering between Minivalleys in Twisted Double Bilayer Graphene.

A unique feature of the complex band structures of moiré materials is the presence of minivalleys, their hybridization, and scattering between them. Here, we investigate magnetotransport oscillations caused by scattering between minivalleys-a phenomenon analogous to magnetointersubband oscillations-in a twisted double bilayer graphene sample with a twist angle of 1.94°. We study and discuss the potential scattering mechanisms and find an electron-phonon mechanism and valley conserving scattering to be likely. Finally, we discuss the relevance of our findings for different materials and twist angles.

A Scalable Network Model for Electrically Tunable Ferroelectric Domain Structure in Twistronic Bilayers of Two-Dimensional Semiconductors.

Moiré structures in small-angle-twisted bilayers of two-dimensional (2D) semiconductors with a broken-symmetry interface form arrays of ferroelectric (FE) domains with periodically alternating out-of-plane polarization. Here, we propose a network theory for the tunability of such FE domain structure by applying an electric field perpendicular to the 2D crystal. Using multiscale analysis, we derive a fully parametrized string-theory-like description of the domain wall network (DWN) and show that it undergoes a qualitative change, after the arcs of partial dislocation (PD) like domain walls merge (near the network nodes) into streaks of perfect screw dislocations (PSD), which happens at a threshold displacement field dependent on the DWN period.

Interfacial ferroelectricity in marginally twisted 2D semiconductors.

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new metamaterials. Here we demonstrate a room temperature ferroelectric semiconductor that is assembled using mono- or few-layer MoS2. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarization arranged into a twist-controlled network. The last can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The observed interfacial charge transfer, movement of domain walls and their bending rigidity agree well with theoretical calculations. Furthermore, we demonstrate proof-of-principle field-effect transistors, where the channel resistance exhibits a pronounced hysteresis governed by pinning of ferroelectric domain walls. Our results show a potential avenue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions.

Kondo effect and spin-orbit coupling in graphene quantum dots.

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin-orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin-orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin-orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin-orbit interaction.

Coherent Jetting from a Gate-Defined Channel in Bilayer Graphene.

Graphene has evolved as a platform for quantum transport that can compete with the best and cleanest semiconductor systems. Here, we report on the observation of distinct electronic jets emanating from a narrow split-gate-defined channel in bilayer graphene. We find that these jets, which are visible via their interference patterns, occur predominantly with an angle of 60° between each other. This observation is related to the trigonal warping in the band structure of bilayer graphene, which, in conjunction with electron injection through a constriction, leads to a valley-dependent selection of momenta. This experimental observation of electron jetting has consequences for carrier transport in two-dimensional materials with a trigonally warped band structure in general, as well as for devices relying on ballistic and valley-selective transport.

Multispectral Graphene-Based Electro-Optical Surfaces with Reversible Tunability from Visible to Microwave Wavelengths.

Optical materials with colour-changing abilities have been explored for display devices1, smart windows2,3, or modulation of visual appearance4-6. The efficiency of these materials, however, has strong wavelength dependence, which limits their functionality to a specific spectral range. Here, we report graphene-based electro-optical devices with unprecedented optical tunability covering the entire electromagnetic spectrum from the visible to microwave. We achieve this non-volatile and reversible tunability by electro-intercalation of lithium into graphene layers in an optically accessible device structure. This unique colour-changing capability, together with area-selective intercalation, inspires fabrication of new multispectral devices, including display devices and electro-optical camouflage coating. We anticipate that these results provide realistic approaches for programmable smart optical surfaces with a potential utility in many scientific and engineering fields such as active plasmonics and adaptive thermal management.

Out-of-Plane Dielectric Susceptibility of Graphene in Twistronic and Bernal Bilayers.

We describe how the out-of-plane dielectric polarizability of monolayer graphene influences the electrostatics of bilayer graphene-both Bernal (BLG) and twisted (tBLG). We compare the polarizability value computed using density functional theory with the output from previously published experimental data on the electrostatically controlled interlayer asymmetry potential in BLG and data on the on-layer density distribution in tBLG. We show that monolayers in tBLG are described well by polarizability αexp = 10.8 Å3 and effective out-of-plane dielectric susceptibility ϵz = 2.5, including their on-layer electron density distribution at zero magnetic field and the interlayer Landau level pinning at quantizing magnetic fields.

Weak ferroelectric charge transfer in layer-asymmetric bilayers of 2D semiconductors.

In bilayers of two-dimensional semiconductors with stacking arrangements which lack inversion symmetry charge transfer between the layers due to layer-asymmetric interband hybridisation can generate a potential difference between the layers. We analyse bilayers of transition metal dichalcogenides (TMDs)-in particular, [Formula: see text]-for which we find a substantial stacking-dependent charge transfer, and InSe, for which the charge transfer is found to be negligibly small. The information obtained about TMDs is then used to map potentials generated by the interlayer charge transfer across the moiré superlattice in twistronic bilayers.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene.

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Tunable Valley Splitting and Bipolar Operation in Graphene Quantum Dots.

Quantum states in graphene are 2-fold degenerate in spins, and 2-fold in valleys. Both degrees of freedom can be utilized for qubit preparations. In our bilayer graphene quantum dots, we demonstrate that the valley g-factor gv, defined analogously to the spin g-factor gs for valley splitting in a perpendicular magnetic field, is tunable by over a factor of 4 from 20 to 90, by gate voltage adjustments only. Larger gv results from larger electronic dot sizes, determined from the charging energy. On our versatile device, bipolar operation, charging our quantum dot with charge carriers of the same or the opposite polarity as the leads, can be performed. Dots of both polarities are tunable to the first charge carrier, such that the transition from an electron to a hole dot by the action of the plunger gate can be observed. Addition of gates easily extends the system to host tunable double dots.

Raman spectroscopy of GaSe and InSe post-transition metal chalcogenides layers.

III-VI post-transition metal chalcogenides (InSe and GaSe) are a new class of layered semiconductors, which feature a strong variation of size and type of their band gaps as a function of number of layers (N). Here, we investigate exfoliated layers of InSe and GaSe ranging from bulk crystals down to monolayer, encapsulated in hexagonal boron nitride, using Raman spectroscopy. We present the N-dependence of both intralayer vibrations within each atomic layer, as well as of the interlayer shear and layer breathing modes. A linear chain model can be used to describe the evolution of the peak positions as a function of N, consistent with first principles calculations.

Electronic phase separation in multilayer rhombohedral graphite.

Of the two stable forms of graphite, hexagonal and rhombohedral, the former is more common and has been studied extensively. The latter is less stable, which has so far precluded its detailed investigation, despite many theoretical predictions about the abundance of exotic interaction-induced physics1-6. Advances in van der Waals heterostructure technology7 have now allowed us to make high-quality rhombohedral graphite films up to 50 graphene layers thick and study their transport properties. Here we show that the bulk electronic states in such rhombohedral graphite are gapped8 and, at low temperatures, electron transport is dominated by surface states. Because of their proposed topological nature, the surface states are of sufficiently high quality to observe the quantum Hall effect, whereby rhombohedral graphite exhibits phase transitions between a gapless semimetallic phase and a gapped quantum spin Hall phase with giant Berry curvature. We find that an energy gap can also be opened in the surface states by breaking their inversion symmetry by applying a perpendicular electric field. Moreover, in rhombohedral graphite thinner than four nanometres, a gap is present even without an external electric field. This spontaneous gap opening shows pronounced hysteresis and other signatures characteristic of electronic phase separation, which we attribute to emergence of strongly correlated electronic surface states.