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.

Printable two-dimensional superconducting monolayers.

Two-dimensional superconductor (2DSC) monolayers with non-centrosymmetry exhibit unconventional Ising pair superconductivity and an enhanced upper critical field beyond the Pauli paramagnetic limit, driving intense research interest. However, they are often susceptible to structural disorder and environmental oxidation, which destroy electronic coherence and provide technical challenges in the creation of artificial van der Waals heterostructures (vdWHs) for devices. Herein, we report a general and scalable synthesis of highly crystalline 2DSC monolayers via a mild electrochemical exfoliation method using flexible organic ammonium cations solvated with neutral solvent molecules as co-intercalants. Using NbSe2 as a model system, we achieved a high yield (>75%) of large-sized single-crystal monolayers up to 300 µm. The as-fabricated, twisted NbSe2 vdWHs demonstrate high stability, good interfacial properties and a critical current that is modulated by magnetic field when one flux quantum fits to an integer number of moiré cells. Additionally, formulated 2DSC inks can be exploited to fabricate wafer-scale 2D superconducting wire arrays and three-dimensional superconducting composites with desirable morphologies.

Controlling many-body states by the electric-field effect in a two-dimensional material.

To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity.

Computational methods for 2D materials modelling.

Materials with thickness ranging from a few nanometers to a single atomic layer present unprecedented opportunities to investigate new phases of matter constrained to the two-dimensional plane. Particle-particle Coulomb interaction is dramatically affected and shaped by the dimensionality reduction, driving well-established solid state theoretical approaches to their limit of applicability. Methodological developments in theoretical modelling and computational algorithms, in close interaction with experiments, led to the discovery of the extraordinary properties of two-dimensional materials, such as high carrier mobility, Dirac cone dispersion and bright exciton luminescence, and inspired new device design paradigms. This review aims to describe the computational techniques used to simulate and predict the optical, electronic and mechanical properties of two-dimensional materials, and to interpret experimental observations. In particular, we discuss in detail the particular challenges arising in the simulation of two-dimensional constrained fermions and quasiparticles, and we offer our perspective on the future directions in this field.

Stability of a Rolled-Up Conformation State for Two-Dimensional Materials in Aqueous Solutions.

Two-dimensional (2D) materials can roll up, forming stable scrolls under suitable conditions. However, the great diversity of materials and fabrication techniques has resulted in a huge parameter space significantly complicating the theoretical description of scrolls. In this Letter, we describe a universal binding energy of scrolls determined solely by their material parameters, the bending stiffness, and the Hamaker coefficient. Aiming to predict the stability of functionalized scrolls in water solutions, we consider the electrostatic double-layer repulsion force that may overcome the binding energy and flatten the scrolls. Our predictions are represented as comprehensive maps indicating the stable and unstable regions of a rolled-up conformation state in the space of material and external parameters. While focusing mostly on functionalized graphene in this work, our approach is applicable to the whole range of 2D materials able to form scrolls.

Polyelectrolyte-Graphene Oxide Multilayer Composites for Array of Microchambers which are Mechanically Robust and Responsive to NIR Light.

Development of composite polymer/graphene oxide (GO) materials attracts significant attention due to their unique properties. In this work, highly ordered arrays of hollow microchambers made of composite polyelectrolyte/GO multilayers (PEGOMs) are successfully fabricated via layer-by-layer assembly on sacrificial or sustainable templates having imprinted patterns of microwells on their surface. Mechanical and optical properties of PEGOMs are studied by nanoindentation and near-infrared (NIR) absorption spectroscopy. Incorporation of three GO layers in between the polyelectrolyte multilayer stacks increases Young's modulus and critical stress of the microchambers by a factor of 5.6 and 2.6, respectively. Optical density of this PEGOM film is found to decrease gradually from 0.14 at λ = 800 nm to 0.06 at λ = 1500 nm. Remote opening of PEGOM microchambers with NIR laser beam is also demonstrated. One of the possible applications of the developed structures includes micropackaging and delivery systems in biological tissues with remote triggering.

Gate-tuning of graphene plasmons revealed by infrared nano-imaging.

Surface plasmons are collective oscillations of electrons in metals or semiconductors that enable confinement and control of electromagnetic energy at subwavelength scales. Rapid progress in plasmonics has largely relied on advances in device nano-fabrication, whereas less attention has been paid to the tunable properties of plasmonic media. One such medium--graphene--is amenable to convenient tuning of its electronic and optical properties by varying the applied voltage. Here, using infrared nano-imaging, we show that common graphene/SiO(2)/Si back-gated structures support propagating surface plasmons. The wavelength of graphene plasmons is of the order of 200 nanometres at technologically relevant infrared frequencies, and they can propagate several times this distance. We have succeeded in altering both the amplitude and the wavelength of these plasmons by varying the gate voltage. Using plasmon interferometry, we investigated losses in graphene by exploring real-space profiles of plasmon standing waves formed between the tip of our nano-probe and the edges of the samples. Plasmon dissipation quantified through this analysis is linked to the exotic electrodynamics of graphene. Standard plasmonic figures of merit of our tunable graphene devices surpass those of common metal-based structures.

Resolving the Spatial Structures of Bound Hole States in Black Phosphorus.

Understanding the local electronic properties of individual defects and dopants in black phosphorus (BP) is of great importance for both fundamental research and technological applications. Here, we employ low-temperature scanning tunnelling microscope (LT-STM) to probe the local electronic structures of single acceptors in BP. We demonstrate that the charge state of individual acceptors can be reversibly switched by controlling the tip-induced band bending. In addition, acceptor-related resonance features in the tunnelling spectra can be attributed to the formation of Rydberg-like bound hole states. The spatial mapping of the quantum bound states shows two distinct shapes evolving from an extended ellipse shape for the 1s ground state to a dumbbell shape for the 2px excited state. The wave functions of bound hole states can be well-described using the hydrogen-like model with anisotropic effective mass, corroborated by our theoretical calculations. Our findings not only provide new insight into the many-body interactions around single dopants in this anisotropic two-dimensional material but also pave the way to the design of novel quantum devices.

Gate-Tunable Giant Stark Effect in Few-Layer Black Phosphorus.

Two-dimensional black phosphorus (BP) has sparked enormous research interest due to its high carrier mobility, layer-dependent direct bandgap and outstanding in-plane anisotropic properties. BP is one of the few two-dimensional materials where it is possible to tune the bandgap over a wide energy range from the visible up to the infrared. In this article, we report the observation of a giant Stark effect in electrostatically gated few-layer BP. Using low-temperature scanning tunnelling microscopy, we observed that in few-layer BP, when electrons are injected, a monotonic reduction of the bandgap occurs. The injected electrons compensate the existing defect-induced holes and achieve up to 35.5% bandgap modulation in the light-doping regime. When probed by tunnelling spectroscopy, the local density of states in few-layer BP shows characteristic resonance features arising from layer-dependent sub-band structures due to quantum confinement effects. The demonstration of an electrical gate-controlled giant Stark effect in BP paves the way to designing electro-optic modulators and photodetector devices that can be operated in a wide electromagnetic spectral range.

Evidence for Fast Interlayer Energy Transfer in MoSe2/WS2 Heterostructures.

Strongly bound excitons confined in two-dimensional (2D) semiconductors are dipoles with a perfect in-plane orientation. In a vertical stack of semiconducting 2D crystals, such in-plane excitonic dipoles are expected to efficiently couple across van der Waals gap due to strong interlayer Coulomb interaction and exchange their energy. However, previous studies on heterobilayers of group 6 transition metal dichalcogenides (TMDs) found that the exciton decay dynamics is dominated by interlayer charge transfer (CT) processes. Here, we report an experimental observation of fast interlayer energy transfer (ET) in MoSe2/WS2 heterostructures using photoluminescence excitation (PLE) spectroscopy. The temperature dependence of the transfer rates suggests that the ET is Förster-type involving excitons in the WS2 layer resonantly exciting higher-order excitons in the MoSe2 layer. The estimated ET time of the order of 1 ps is among the fastest compared to those reported for other nanostructure hybrid systems such as carbon nanotube bundles. Efficient ET in these systems offers prospects for optical amplification and energy harvesting through intelligent layer engineering.

Plasmons in graphene moiré superlattices.

Moiré patterns are periodic superlattice structures that appear when two crystals with a minor lattice mismatch are superimposed. A prominent recent example is that of monolayer graphene placed on a crystal of hexagonal boron nitride. As a result of the moiré pattern superlattice created by this stacking, the electronic band structure of graphene is radically altered, acquiring satellite sub-Dirac cones at the superlattice zone boundaries. To probe the dynamical response of the moiré graphene, we use infrared (IR) nano-imaging to explore propagation of surface plasmons, collective oscillations of electrons coupled to IR light. We show that interband transitions associated with the superlattice mini-bands in concert with free electrons in the Dirac bands produce two additive contributions to composite IR plasmons in graphene moiré superstructures. This novel form of collective modes is likely to be generic to other forms of moiré-forming superlattices, including van der Waals heterostructures.

Multiferroic Two-Dimensional Materials.

The relation between unusual Mexican-hat band dispersion, ferromagnetism, and ferroelasticity is investigated using a combination of analytical, first-principles, and phenomenological methods. The class of material with Mexican-hat band edge is studied using the α-SnO monolayer as a prototype. Such a band edge causes a van Hove singularity diverging with 1/sqrt[E], and a charge doping in these bands can lead to time-reversal symmetry breaking. Herein, we show that a material with Mexican-hat band dispersion, α-SnO, can be ferroelastic or paraelastic depending on the number of layers. Also, an unexpected multiferroic phase is obtained in a range of hole density for which the material presents ferromagnetism and ferroelasticity simultaneously.

Quantum Transport and Observation of Dyakonov-Perel Spin-Orbit Scattering in Monolayer MoS_{2}.

Monolayers of group 6 transition metal dichalcogenides are promising candidates for future spin-, valley-, and charge-based applications. Quantum transport in these materials reflects a complex interplay between real spin and pseudospin (valley) relaxation processes, which leads to either positive or negative quantum correction to the classical conductivity. Here we report experimental observation of a crossover from weak localization to weak antilocalization in highly n-doped monolayer MoS_{2}. We show that the crossover can be explained by a single parameter associated with electron spin lifetime of the system. At low temperatures and high carrier densities, the spin lifetime is inversely proportional to momentum relaxation time; this indicates that spin relaxation occurs via a Dyakonov-Perel mechanism.

Atomic healing of defects in transition metal dichalcogenides.

As-grown transition metal dichalcogenides are usually chalcogen deficient and therefore contain a high density of chalcogen vacancies, deep electron traps which can act as charged scattering centers, reducing the electron mobility. However, we show that chalcogen vacancies can be effectively passivated by oxygen, healing the electronic structure of the material. We proposed that this can be achieved by means of surface laser modification and demonstrate the efficiency of this processing technique, which can enhance the conductivity of monolayer WSe2 by ∼400 times and its photoconductivity by ∼150 times.

Tunneling Plasmonics in Bilayer Graphene.

We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At subnanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nanoimaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tunneling. Moreover, we were able to shut off plasmons in bilayer graphene through gating within a wide voltage range. Theoretical modeling indicates that such a plasmon-off region is directly linked to a gapped insulating state of bilayer graphene, yet another implication of interlayer tunneling. Our work uncovers essential plasmonic properties in bilayer graphene and suggests a possibility to achieve novel plasmonic functionalities in graphene few-layers.

Oxygen defects in phosphorene.

Surface reactions with oxygen are a fundamental cause of the degradation of phosphorene. Using first-principles calculations, we show that for each oxygen atom adsorbed onto phosphorene there is an energy release of about 2 eV. Although the most stable oxygen adsorbed forms are electrically inactive and lead only to minor distortions of the lattice, there are low energy metastable forms which introduce deep donor and/or acceptor levels in the gap. We also propose a mechanism for phosphorene oxidation involving reactive dangling oxygen atoms and we suggest that dangling oxygen atoms increase the hydrophilicity of phosphorene.

Lattice relaxation at the interface of two-dimensional crystals: graphene and hexagonal boron-nitride.

Heteroepitaxy of two-dimensional (2D) crystals, such as hexagonal boron nitride (BN) on graphene (G), can occur at the edge of an existing heterointerface. Understanding strain relaxation at such 2D laterally fused interface is useful in fabricating heterointerfaces with a high degree of atomic coherency and structural stability. We use in situ scanning tunneling microscopy to study the 2D heteroepitaxy of BN on graphene edges on a Ru(0001) surface with the aim of understanding the propagation of interfacial strain. We found that defect-free, pseudomorphic growth of BN on a graphene edge "substrate" occurs only for a short distance (<1.29 nm) perpendicular to the interface, beyond which misfit zero-dimensional dislocations occur to reduce the elastic strain energy. Boundary states originating from a coherent zigzag-linked G/BN boundary are observed to greatly enhance the local conductivity, thus affording a new avenue to construct one-dimensional transport channels in G/BN hybrid interface.

Strain-induced gap modification in black phosphorus.

The band structure of single-layer black phosphorus and the effect of strain are predicted using density functional theory and tight-binding models. Having determined the localized orbital composition of the individual bands from first principles, we use the system symmetry to write down the effective low-energy Hamiltonian at the Γ point. From numerical calculations and arguments based on the crystal structure of the material, we show that the deformation in the direction normal to the plane can be used to change the gap size and induce a semiconductor-metal transition.

Extrinsic spin Hall effect induced by resonant skew scattering in graphene.

We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.

Origin of indirect optical transitions in few-layer MoS2, WS2, and WSe2.

It has been well-established that single layer MX2 (M = Mo, W and X = S, Se) are direct gap semiconductors with band edges coinciding at the K point in contrast to their indirect gap multilayer counterparts. In few-layer MX2, there are two valleys along the Γ-K line with similar energy. There is little understanding on which of the two valleys forms the conduction band minimum (CBM) in this thickness regime. We investigate the conduction band valley structure in few-layer MX2 by examining the temperature-dependent shift of indirect exciton photoluminescence peak. Highly anisotropic thermal expansion of the lattice and the corresponding evolution of the band structure result in a distinct peak shift for indirect transitions involving the K and Λ (midpoint along Γ-K) valleys. We identify the origin of the indirect emission and concurrently determine the relative energy of these valleys.