Kinks and antikinks of the classical φ 4 field model are topological solutions connecting its two distinct ground states. Here we establish an analogy between the excitations of a long graphene nanoribbon buckled in the transverse direction and φ 4 model results. Using molecular dynamics simulations, we investigated the dynamics of a buckled graphene nanoribbon with a single kink and with a kink-antikink pair. Several features of φ 4 model have been observed including the kink-antikink capture at low energies, kink-antikink reflection at high energies, and a bounce resonance. Our results pave the way towards the experimental observation of a rich variety of φ 4 model predictions based on graphene.
PACS numbers:Currently, there is strong interest in suspended graphene (the graphene above a trench) from both fundamental and application points of view. Fundamentally, the advantages of graphene suspension include the elimination of substrate-induced carrier scattering, dopants and phonon leakage. This provides an access to intrinsic properties of graphene such as the intrinsic carrier mobility Here, we consider a buckled graphene over a trench in a non-standard geometry in which the trench length is much longer than its width. It is assumed that the graphene is relaxed in the direction along the trench and compressed in the transverse direction. Using classical molecular dynamics (MD) simulations we demonstrate the existence of kinks (see Fig. 1) and antikinks in such buckled graphene -the solutions connecting two minima of potential energy -and investigate some of their properties. To the best of our knowledge, this Letter is the first study of buckled graphene in such configuration.
FIG. 1: Graphene kink.Furthermore, we argue that such buckled graphene provides (to the certain extent) an experimental realization of the classical φ 4 field model [12][13][14] in 1+1 dimensions, having applications in the areas of ferroelectrics [15][16][17], linear polymeric chains [18], quantum field theory [19,20], and even nuclear physics [21,22]. This model is based on the dimensionless Lagrangianthat leads to the Euler-Lagrange equation of motion of the formThere are two stable constant solutions of Eq. (2), φ = ±1, and one unstable trivial, φ = 0. Moreover, Eq. (2) has a topologically non-trivial solutionswhere ± signs correspond to the kink and antikink, respectively, V is the velocity, and x 0 is the position of the kink/antikink center at the initial moment of time t = 0.In what follows, we present the details and results of our MD simulations and discuss the similarity between the graphene kinks (exemplified in Fig. 1) and the solutions (3) of Eq. (2). MD simulations are frequently employed to model various physical aspects of graphene, carbone nanotubes and other nanoscale structures [23][24][25][26][27][28][29][30][31][32]. In this study, we used NAMD2 [33], a highly scalable massively parallel classical MD code [40]. Specifically, we investigated the dynamics of a graphene nanoribbon (membrane) of L = 425Å length and w ...