Substrate Interference and Strain in the Second-Harmonic Generation from MoSe2 Monolayers.

Nonlinear optical materials of atomic thickness, such as non-centrosymmetric 2H transition metal dichalcogenide monolayers, have a second-order nonlinear susceptibility (χ(2)) whose intensity can be tuned by strain. However, whether χ(2) is enhanced or reduced by tensile strain is a subject of conflicting reports. Here, we grow high-quality MoSe2 monolayers under controlled biaxial strain created by two different substrates and study their linear and nonlinear optical responses with a combination of experimental and theoretical approaches. Up to a 15-fold overall enhancement in second-harmonic generation (SHG) intensity is observed from MoSe2 monolayers grown on SiO2 when compared to its value on a Si3N4 substrate. By considering an interference contribution from different dielectrics and their thicknesses, a factor of 2 enhancement of χ(2) was attributed to the biaxial strain: substrate interference and strain are independent handles to engineer the SHG strength of non-centrosymmetric 2D materials.

Synthesis and Polymorph Manipulation of FeSe2 Monolayers.

Polymorph engineering involves the manipulation of material properties through controlled structural modification and is a candidate technique for creating unique two-dimensional transition metal dichalcogenide (TMDC) nanodevices. Despite its promise, polymorph engineering of magnetic TMDC monolayers has not yet been demonstrated. Here we grow FeSe2 monolayers via molecular beam epitaxy and find that they have great promise for magnetic polymorph engineering. Using scanning tunneling microscopy (STM) and spectroscopy (STS), we find that FeSe2 monolayers predominantly display a 1T' structural polymorph at 5 K. Application of voltage pulses from an STM tip causes a local, reversible transition from the 1T' phase to the 1T phase. Density functional theory calculations suggest that this single-layer structural phase transition is accompanied by a magnetic transition from an antiferromagnetic to a ferromagnetic configuration. These results open new possibilities for creating functional magnetic devices with TMDC monolayers via polymorph engineering.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update.

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Slippery Paraelectric Transition-Metal Dichalcogenide Bilayers.

Traditional ferroelectrics undergo thermally induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed paraelectric. Ferroelectric transition-metal dichalcogenide bilayers have been recently shown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison.

Microscopic Manipulation of Ferroelectric Domains in SnSe Monolayers at Room Temperature.

Two-dimensional (2D) van der Waals ferroelectrics provide an unprecedented architectural freedom for the creation of artificial multiferroics and nonvolatile electronic devices based on vertical and coplanar heterojunctions of 2D ferroic materials. Nevertheless, controlled microscopic manipulation of ferroelectric domains is still rare in monolayer-thick 2D ferroelectrics with in-plane polarization. Here we report the discovery of robust ferroelectricity with a critical temperature close to 400 K in SnSe monolayer plates grown on graphene and the demonstration of controlled room-temperature ferroelectric domain manipulation by applying appropriate bias voltage pulses to the tip of a scanning tunneling microscope (STM). This study shows that STM is a powerful tool for detecting and manipulating the microscopic domain structures in 2D ferroelectric monolayers, which are difficult for conventional approaches such as piezoresponse force microscopy, thus facilitating the hunt for other 2D ferroelectric monolayers with in-plane polarization with important technological applications.

Quantum Paraelastic Two-Dimensional Materials.

We study the elastic energy landscape of two-dimensional tin oxide (SnO) monolayers and demonstrate a transition temperature of T_{c}=8.5±1.8 K using ab initio molecular dynamics (MD) that is close to the value of the elastic energy barrier J derived from T=0 K density functional theory calculations. The power spectra of the velocity autocorrelation throughout the MD evolution permit identifying soft phonon modes likely responsible for the structural transformation. The mean atomic displacements obtained from a Bose-Einstein occupation of the phonon modes suggest the existence of a quantum paraelastic phase that could be tuned with charge doping: SnO monolayers could be 2D quantum paraelastic materials with a charge-tunable quantum phase transition.

Standing Waves Induced by Valley-Mismatched Domains in Ferroelectric SnTe Monolayers.

Two-dimensional (2D) quasiparticle standing waves originate from the interference of coherent quantum states and are usually created by the scattering off edges, atomic steps, or adatoms that induce large potential barriers. We report standing waves close to the valence band maximum (E_{V}), confined by electrically neutral domain walls of newly discovered ferroelectric SnTe monolayers, as revealed by spatially resolved scanning tunneling spectroscopy. Ab initio calculations show that this novel confinement arises from the polarization lifted hole valley degeneracy and a ∼90° rotation of the Brillouin zones that render holes' momentum mismatched across neighboring domains. These results show a potential for polarization-tuned valleytronics in 2D ferroelectrics.

Strain and the optoelectronic properties of nonplanar phosphorene monolayers.

Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene--a new 2D atomic material--in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum.

Electronic and optical properties of strained graphene and other strained 2D materials: a review.

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Photostrictive Two-Dimensional Materials in the Monochalcogenide Family.

Photostriction is predicted for group-IV monochalcogenide monolayers, two-dimensional ferroelectrics with rectangular unit cells (the lattice vector a_{1} is larger than a_{2}) and an intrinsic dipole moment parallel to a_{1}. Photostriction is found to be related to the structural change induced by a screened electric polarization (i.e., a converse piezoelectric effect) in photoexcited electronic states with either p_{x} or p_{y} (in-plane) orbital symmetry that leads to a compression of a_{1} and a comparatively smaller increase of a_{2} for a reduced unit cell area. The structural change documented here is 10 times larger than that observed in BiFeO_{3}, making monochalcogenide monolayers an ultimate platform for this effect. This structural modification should be observable under experimentally feasible densities of photexcited carriers on samples that have been grown already, having a potential usefulness for light-induced, remote mechano-optoelectronic applications.

Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers.

Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale EC (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm is a given material's melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order-disorder transition and melt directly. All other monochalcogenide monolayers with EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order-disorder transition. The order-disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.

Structural Phase Transition and Material Properties of Few-Layer Monochalcogenides.

GeSe and SnSe monochalcogenide monolayers and bilayers undergo a two-dimensional phase transition from a rectangular unit cell to a square unit cell at a critical temperature T_{c} well below the melting point. Its consequences on material properties are studied within the framework of Car-Parrinello molecular dynamics and density-functional theory. No in-gap states develop as the structural transition takes place, so that these phase-change materials remain semiconducting below and above T_{c}. As the in-plane lattice transforms from a rectangle into a square at T_{c}, the electronic, spin, optical, and piezoelectric properties dramatically depart from earlier predictions. Indeed, the Y and X points in the Brillouin zone become effectively equivalent at T_{c}, leading to a symmetric electronic structure. The spin polarization at the conduction valley edge vanishes, and the hole conductivity must display an anomalous thermal increase at T_{c}. The linear optical absorption band edge must change its polarization as well, making this structural and electronic evolution verifiable by optical means. Much excitement is drawn by theoretical predictions of giant piezoelectricity and ferroelectricity in these materials, and we estimate a pyroelectric response of about 3×10^{-12} C/K m here. These results uncover the fundamental role of temperature as a control knob for the physical properties of few-layer group-IV monochalcogenides.

Defect-Free Nanowelding of Bilayer SnSe Nanoplates.

Nanowelding is a bottom-up technique to create custom-designed nanostructures and devices beyond the precision of lithographic methods. Here, a new technique is reported based on anisotropic lubricity at the van der Waals interface between monolayer and bilayer SnSe nanoplates and a graphene substrate to achieve precise control of the crystal orientation and the interface during the welding process. As-grown SnSe monolayer and bilayer nanoplates are commensurate with graphene's armchair direction but lack commensuration along graphene's zigzag direction, resulting in a reduced friction along that direction and a rail-like, 1D movement that permits joining nanoplates with high precision. This way, molecular beam epitaxially grown SnSe nanoplates of lateral sizes 30-100 nm are manipulated by the tip of a scanning tunneling microscope at room temperature. In situ annealing is applied afterward to weld contacting nanoplates without atomic defects at the interface. This technique can be generalized to any van der Waals interfaces with anisotropic lubricity and is highly promising for the construction of complex quantum devices, such as field effect transistors, quantum interference devices, lateral tunneling junctions, and solid-state qubits.

Charge transport through graphene junctions with wetting metal leads.

Graphene is believed to be an excellent candidate material for next-generation electronic devices. However, one needs to take into account the nontrivial effect of metal contacts in order to precisely control the charge injection and extraction processes. We have performed transport calculations for graphene junctions with wetting metal leads (metal leads that bind covalently to graphene) using nonequilibrium Green's functions and density functional theory. Quantitative information is provided on the increased resistance with respect to ideal contacts and on the statistics of current fluctuations. We find that charge transport through the studied two-terminal graphene junction with Ti contacts is pseudo-diffusive up to surprisingly high energies.

Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry.

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal (C4in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries-furnishing topological protection-are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective two-fold energy degeneracies taking place at few discretek-points away from zero energy in the bulk Hamiltonian-that are topologically protected-persist at the u.c. thickness limit. The chiral nature of the bulk TCI Hamiltonian permits creating a2×2square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c. thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions.

Separation-dependent electronic transparency of monolayer graphene membranes on III-V semiconductor substrates.

Ultrahigh vacuum scanning tunneling microscopy and first-principles calculations have been carried out to study monolayer graphene nanomembranes deposited in situ onto UHV-cleaved GaAs(110) and InAs(110) surfaces. A bias-dependent semitransparency effect is observed in which the substrate atomic structure is clearly visible through the graphene monolayer. Statistical data analysis and density functional theory calculations suggest that this semitransparency phenomenon is due to the scanning tunneling microscope tip pushing the graphene membrane away from its equilibrium location and closer to the substrate surface, causing their electronic states to intermix.

Vortex-Oriented Ferroelectric Domains in SnTe/PbTe Monolayer Lateral Heterostructures.

Heterostructures formed from interfaces between materials with complementary properties often display unconventional physics. Of especial interest are heterostructures formed with ferroelectric materials. These are mostly formed by combining thin layers in vertical stacks. Here the first in situ molecular beam epitaxial growth and scanning tunneling microscopy characterization of atomically sharp lateral heterostructures between a ferroelectric SnTe monolayer and a paraelectric PbTe monolayer are reported. The bias voltage dependence of the apparent heights of SnTe and PbTe monolayers, which are closely related to the type-II band alignment of the heterostructure, is investigated. Remarkably, it is discovered that the ferroelectric domains in the SnTe surrounding a PbTe core form either clockwise or counterclockwise vortex-oriented quadrant configurations. In addition, when there is a finite angle between the polarization and the interface, the perpendicular component of the polarization always points from SnTe to PbTe. Supported by first-principles calculation, the mechanism of vortex formation and preferred polarization direction is identified in the interaction between the polarization, the space charge, and the strain effect at the horizontal heterointerface. The studies bring the application of 2D group-IV monochalcogenides on in-plane ferroelectric heterostructures a step closer.

Effects of metallic contacts on electron transport through graphene.

We report on a first-principles study of the conductance through graphene suspended between Al contacts as a function of junction length, width, and orientation. The charge transfer at the leads and into the freestanding section gives rise to an electron-hole asymmetry in the conductance and in sufficiently long junctions induces two conductance minima at the energies of the Dirac points for suspended and clamped regions, respectively. We obtain the potential profile along a junction caused by doping and provide parameters for effective model calculations of the junction conductance with weakly interacting metallic leads.

Enhanced Spontaneous Polarization in Ultrathin SnTe Films with Layered Antipolar Structure.

2D SnTe films with a thickness of as little as 2 atomic layers (ALs) have recently been shown to be ferroelectric with in-plane polarization. Remarkably, they exhibit transition temperatures (Tc ) much higher than that of bulk SnTe. Here, combining molecular beam epitaxy, variable temperature scanning tunneling microscopy, and ab initio calculations, the underlying mechanism of the Tc enhancement is unveiled, which relies on the formation of γ-SnTe, a van der Waals orthorhombic phase with antipolar inter-layer coupling in few-AL thick SnTe films. In this phase, 4n - 2 AL (n = 1, 2, 3…) thick films are found to possess finite in-plane polarization (space group Pmn21 ), while 4n AL thick films have zero total polarization (space group Pnma). Above 8 AL, the γ-SnTe phase becomes metastable, and can convert irreversibly to the bulk rock salt phase as the temperature is increased. This finding unambiguously bridges experiments on ultrathin SnTe films with predictions of robust ferroelectricity in GeS-type monochalcogenide monolayers. The observed high transition temperature, together with the strong spin-orbit coupling and van der Waals structure, underlines the potential of atomically thin γ-SnTe films for the development of novel spontaneous polarization-based devices.

Water Splits To Degrade Two-Dimensional Group-IV Monochalcogenides in Nanoseconds.

The experimental exfoliation of layered group-IV monochalcogenides-semiconductors isostructural to black phosphorus-using processes similar to those followed in the production of graphene or phosphorene has turned out unsuccessful thus far, as if the chemical degradation observed in black phosphorus was aggravated in these monochalcogenides. Here, we document a facile dissociation of water by these materials within 10 ns from room-temperature Car-Parrinello molecular dynamics calculations under standard temperature and pressure conditions. These results suggest that humidity must be fully eradicated to exfoliate monolayers successfully, for instance, by placing samples in a hydrophobic solution during mechanical exfoliation. From another materials perspective, these two-dimensional materials that create individual hydrogen ions out of water without illumination may become relevant for applications in hydrogen production and storage.