For machine learning of interatomic potentials a scalable sparse Gaussian process regression formalism is introduced with a data-efficient on-the-fly adaptive sampling algorithm. With this approach, the computational cost is effectively reduced to those of the Bayesian linear regression methods while maintaining the appealing characteristics of the exact Gaussian process regression. As a showcase, experimental melting and glass-crystallization temperatures are reproduced for ${\mathrm{Li}}_7{\mathrm{P}}_3{\mathrm{S}}_{11}$, Li diffusivity is simulated, and an unchartered phase is revealed with much lower Li diffusivity which should be circumvented.

This spotlight discusses intriguing properties and diverse applications of graphene (Gr) and Gr analogs. Gr has brought us two-dimensional (2D) chemistry with its exotic 2D features of density of states. Yet, some of the 2D or 2D-like features can be seen on surfaces and at interfaces of bulk materials. The substrate on Gr and functionalization of Gr (including metal decoration, intercalation, doping, and hybridization) modify the unique 2D features of Gr. Despite abundant literature on physical properties and well-known applications of Gr, spotlight works based on the conceptual understanding of the 2D physical and chemical nature of Gr toward vast-ranging applications are hardly found. Here we focus on applications of Gr, based on conceptual understanding of 2D phenomena toward 2D chemistry. Thus, 2D features, defects, edges, and substrate effects of Gr are discussed first. Then, to pattern Gr electronic circuits, insight into differentiating conducting and nonconducting regions is introduced. By utilizing the unique ballistic electron transport properties and edge spin states of Gr, Gr nanoribbons (GNRs) are exploited for the design of ultrasensitive molecular sensing electronic devices (including molecular fingerprinting) and spintronic devices. The highly stable nature of Gr can be utilized for protection of corrosive metals, moisture-sensitive perovskite solar cells, and highly environment-susceptible topological insulators (TIs). Gr analogs have become new types of 2D materials having novel features such as half-metals, TIs, and nonlinear optical properties. The key insights into the functionalized Gr hybrid materials lead to the applications for not only energy storage and electrochemical catalysis, green chemistry, and electronic/spintronic devices but also biosensing and medical applications. All these topics are discussed here with the focus on conceptual understanding. Further possible applications of Gr, GNRs, and Gr analogs are also addressed in a section on outlook and future challenges.

In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density $\rho \sim 0.893$ and temperature $T\sim 1.1$, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: $\xi \approx exp\left(b|T-T_c{|}^{-\nu }\right)$. Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the $r^{-12}$ potential and that melting of the $r^{-n}$ potential is KTHNY-like for $n\le 12$ but melting of the $r^{-64}$ potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range $12<n<64$.