Delocalized nonlinear vibrational modes in graphene: second harmonic generation and negative pressure

With the help of molecular dynamics simulations, delocalized nonlinear vibrational modes (DNVM) in graphene are analyzed. Such modes are dictated by the lattice symmetry, they are exact solutions to the atomic equations of motion, regardless the employed interatomic potential and for any mode amplitude (though for large amplitudes they are typically unstable). In this study, only one‐ and two‐component DNVM are analyzed, they are reducible to the dynamical systems with one and two degrees of freedom, respectively. There exist 4 one‐component and 12 two‐component DNVM with in‐plane atomic displacements. Any two‐component mode includes one of the one‐component modes. If the amplitudes of the modes constituting a two‐component mode are properly chosen, periodic in time vibrations are observed for the two degrees of freedom at frequencies ω and 2ω, that is, second harmonic generation takes place. For particular DNVM, the higher harmonic can have frequency nearly two times larger than the maximal frequency of the phonon spectrum of graphene. Excitation of some of DNVM results in the appearance of negative in‐plane pressure in graphene. This counterintuitive result is explained by the rotational motion of carbon hexagons. Our results contribute to the understanding of nonlinear dynamics of the graphene lattice

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

Delocalized nonlinear vibrational modes (DNVMs) supported in crystal lattices are exact solutions to the equations of motion of particles that are determined by the symmetry of the lattices. DNVMs exist for any vibration amplitudes and for any interparticle potentials. It is important to know how the properties of DNVMs depend on the parameters of interparticle potentials. In this work, we analyze the effect of the Morse potential stiffness on the properties of one-component DNVMs in a face-centered cubic (fcc) lattice. In particular, the frequencies, kinetic and potential energy, mechanical stress, and elastic constants of DNVMs in a large range of vibration amplitudes are considered. Frequency-amplitude dependency obtained for the Morse crystal is compared with that obtained earlier for copper by using the potentials of the many-body embedded atom method. The properties of DNVMs are mainly dictated by their symmetry and are less influenced by the interparticle potentials. It is revealed that at low and high stiffness of interparticle bonds, different sets of DNVMs have frequencies above the phonon band. This is important to predict the possible types of discrete breathers supported by the fcc lattice. The results obtained in the work enrich the understanding of the influence of interparticle potentials on the properties of the studied family of exact dynamic solutions.Published versionThe work of S.S. (derivation of DNVMs) and S.D. (discussion, writing the manuscript) is funded by the Russian Science Foundation (Grant Reference No. 21-12-00229). E.K. (discussion of the results) is grateful for the financial support of Council on Grants of the President of the Russian Federation (Grant Reference No. NSh 4320.2022.1.2). The work is also supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the state assignment of Ufa State Aviation Technical University, the youth research laboratory ”Metals and Alloys under Extreme Impacts” (Agreement No. 075-03-2022-318/1)

Two-dimensional black phosphorus carbide:rippling and formation of nanotubes

Abstract The allotropes of a new layered material, phosphorus carbide (PC), have been predicted recently, and a few of these predicted structures have already been successfully fabricated. Herein, by using first-principles calculations, we investigate the effects of rippling an α-PC monolayer, one of the most stable modifications of layered PC, under large compressive strains. Similar to phosphorene, layered PC is found to have the extraordinary ability to bend and form ripples with large curvatures under a sufficiently large strain applied along its armchair direction. The band gap, work function, and Young’s modulus of a rippled α-PC monolayer are predicted to be highly tunable by strain engineering. Moreover, a direct-indirect band gap transition is observed under compressive strains in the range from 6% to 11%. Another important feature of the α-PC monolayer rippled along the armchair direction is the possibility of its rolling to a PC nanotube (PCNT) under an extreme compressive strain. These tubes of different sizes exhibit high thermal stability, possess a comparably high Young’s modulus, and a well tunable band gap which can vary from 0 to 0.95 eV. In addition, for both structures, rippled α-PC and PCNTs, the changes of their properties under compressive strain are explained in terms of the modification of their structural parameters