The isolation of graphene in 2004 from graphite was a defining moment for the "birth" of a field: two-dimensional (2D) materials. In recent years, there has been a rapidly increasing number of papers focusing on non-graphene layered materials, including transition-metal dichalcogenides (TMDs), because of the new properties and applications that emerge upon 2D confinement. Here, we review significant recent advances and important new developments in 2D materials "beyond graphene". We provide insight into the theoretical modeling and understanding of the van der Waals (vdW) forces that hold together the 2D layers in bulk solids, as well as their excitonic properties and growth morphologies. Additionally, we highlight recent breakthroughs in TMD synthesis and characterization and discuss the newest families of 2D materials, including monoelement 2D materials (i.e., silicene, phosphorene, etc.) and transition metal carbide- and carbon nitride-based MXenes. We then discuss the doping and functionalization of 2D materials beyond graphene that enable device applications, followed by advances in electronic, optoelectronic, and magnetic devices and theory. Finally, we provide perspectives on the future of 2D materials beyond graphene.

With the advent of atomically thin and flat layers of conducting materials such as graphene, new designs for thin film energy storage devices with good performance have become possible. Here, we report an "in-plane" fabrication approach for ultrathin supercapacitors based on electrodes comprised of pristine graphene and multilayer reduced graphene oxide. The in-plane design is straightforward to implement and exploits efficiently the surface of each graphene layer for energy storage. The open architecture and the effect of graphene edges enable even the thinnest of devices, made from as grown 1-2 graphene layers, to reach specific capacities up to 80 μFcm(-2), while much higher (394 μFcm(-2)) specific capacities are observed multilayer reduced graphene oxide electrodes. The performances of devices with pristine as well as thicker graphene-based structures are examined using a combination of experiments and model calculations. The demonstrated all solid-state supercapacitors provide a prototype for a broad range of thin-film based energy storage devices.

Most studied two-dimensional (2D) materials exhibit isotropic behavior due to high lattice symmetry; however, lower-symmetry 2D materials such as phosphorene and other elemental 2D materials exhibit very interesting anisotropic properties. In this work, we report the atomic structure, electronic properties, and vibrational modes of few-layered PdSe exfoliated from bulk crystals, a pentagonal 2D layered noble transition metal dichalcogenide with a puckered morphology that is air-stable. Micro-absorption optical spectroscopy and first-principles calculations reveal a wide band gap variation in this material from 0 (bulk) to 1.3 eV (monolayer). The Raman-active vibrational modes of PdSe were identified using polarized Raman spectroscopy, and a strong interlayer interaction was revealed from large, thickness-dependent Raman peak shifts, agreeing with first-principles Raman simulations. Field-effect transistors made from the few-layer PdSe display tunable ambipolar charge carrier conduction with a high electron field-effect mobility of ∼158 cm V s, indicating the promise of this anisotropic, air-stable, pentagonal 2D material for 2D electronics.

Graphene nanoribbons can exhibit either quasi-metallic or semiconducting behavior, depending on the atomic structure of their edges. Thus, it is important to control the morphology and crystallinity of these edges for practical purposes. We demonstrated an efficient edge-reconstruction process, at the atomic scale, for graphitic nanoribbons by Joule heating. During Joule heating and electron beam irradiation, carbon atoms are vaporized, and subsequently sharp edges and step-edge arrays are stabilized, mostly with either zigzag- or armchair-edge configurations. Model calculations show that the dominant annealing mechanisms involve point defect annealing and edge reconstruction.

A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein-ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 - 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 - 0.38 kcal/mol.

Single-layer black phosphorus (BP), or phosphorene, is a highly anisotropic two-dimensional elemental material possessing promising semiconductor properties for flexible electronics. However, the direct bandgap of single-layer black phosphorus predicted theoretically has not been directly measured, and the properties of its edges have not been considered in detail. Here we report atomic scale electronic variation related to strain-induced anisotropic deformation of the puckered honeycomb structure of freshly cleaved black phosphorus using a high-resolution scanning tunneling spectroscopy (STS) survey along the light (x) and heavy (y) effective mass directions. Through a combination of STS measurements and first-principles calculations, a model for edge reconstruction is also determined. The reconstruction is shown to self-passivate most dangling bonds by switching the coordination number of phosphorus from 3 to 5 or 3 to 4.

Orthorhombic black phosphorus (BP) and other layered materials, such as gallium telluride (GaTe) and tin selenide (SnSe), stand out among two-dimensional (2D) materials owing to their anisotropic in-plane structure. This anisotropy adds a new dimension to the properties of 2D materials and stimulates the development of angle-resolved photonics and electronics. However, understanding the effect of anisotropy has remained unsatisfactory to date, as shown by a number of inconsistencies in the recent literature. We use angle-resolved absorption and Raman spectroscopies to investigate the role of anisotropy on the electron-photon and electron-phonon interactions in BP. We highlight, both experimentally and theoretically, a nontrivial dependence between anisotropy and flake thickness and photon and phonon energies. We show that once understood, the anisotropic optical absorption appears to be a reliable and simple way to identify the crystalline orientation of BP, which cannot be determined from Raman spectroscopy without the explicit consideration of excitation wavelength and flake thickness, as commonly used previously.

Supercapacitors, commonly called electric double-layer capacitors (EDLCs), are emerging as a novel type of energy-storage device with the potential to substitute batteries in applications that require high power densities. In response to the latest experimental breakthrough in nanoporous carbon supercapacitors, we propose a heuristic theoretical model that takes pore curvature into account as a replacement for the EDLC model, which is based on a traditional parallel-plate capacitor. When the pore size is in the mesopore regime (2-50 nm), counterions enter mesoporous carbon materials and approach the pore wall to form an electric double-cylinder capacitor (EDCC); in the micropore regime (<2 nm), solvated/desolvated counterions line up along the pore axis to form an electric wire-in-cylinder capacitor (EWCC). In the macropore regime (>50 nm) at which pores are large enough so that pore curvature is no longer significant, the EDCC model can be reduced naturally to the EDLC model. We present density functional theory calculations and detailed analyses of available experimental data in various pore regimes, which show the significant effects of pore curvature on the supercapacitor properties of nanoporous carbon materials. It is shown that the EDCC/EWCC model is universal for carbon supercapacitors with diverse carbon materials, including activated carbon materials, template carbon materials, and novel carbide-derived carbon materials, and with diverse electrolytes, including organic electrolytes, such as tetraethylammonium tetrafluoroborate (TEABF(4)) and tetraethylammonium methylsulfonate (TEAMS) in acetonitrile, aqueous H(2)SO(4) and KOH electrolytes, and even an ionic liquid electrolyte, such as 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide (EMI-TFSI). The EDCC/EWCC model allows the supercapacitor properties to be correlated with pore size, specific surface area, Debye length, electrolyte concentration and dielectric constant, and solute ion size It may lend support for the systematic optimization of the properties of carbon supercapacitors through experiments. On the basis of the insight obtained from the new model, we also discuss the effects of the kinetic solvation/desolvation process, multimodal (versus unimodal) pore size distribution, and exohedral (versus endohedral) capacitors on the electrochemical properties of supercapacitors.