Chaotic dynamics of graphene and graphene nanoribbons

Abstract

We study the chaotic dynamics of graphene structures, considering both a periodic, defect free, graphene sheet and graphene nanoribbons (GNRs) of various widths. By numerically calculating the maximum Lyapunov exponent, we quantify the chaoticity for a spectrum of energies in both systems. We find that for all cases, the chaotic strength increases with the energy density and that the onset of chaos in graphene is slow, becoming evident after more than 104 natural oscillations of the system. For the GNRs, we also investigate the impact of the width and chirality (armchair or zigzag edges) on their chaotic behavior. Our results suggest that due to the free edges, the chaoticity of GNRs is stronger than the periodic graphene sheet and decreases by increasing width, tending asymptotically to the bulk value. In addition, the chaotic strength of armchair GNRs is higher than a zigzag ribbon of the same width. Furthermore, we show that the composition of 12C and 13C carbon isotopes in graphene has a minor impact on its chaotic strength.

Triple-Band Surface Plasmon Resonance Metamaterial Absorber Based on Open-Ended Prohibited Sign Type Monolayer Graphene

“…Among these materials, graphene stands out due to its extremely high conductivity and carrier mobility, which provides a full-spectrum response to terahertz waves and strong surface plasmon resonance [ 21 , 22 , 23 ]. Moreover, the Fermi level of graphene can be precisely controlled through external voltage [ 24 ], while materials such as VO 2 are difficult and expensive to control due to their abrupt phase transitions [ 25 ]. Furthermore, graphene exhibits a fast response throughout the entire terahertz range [ 26 ], enabling graphene materials to achieve multiple perfect absorption peaks in the terahertz range with improved spacing between resonant frequencies and modulation bandwidth.…”

Complex dynamics, released energy, and multistability in a single-layered graphene sheet under periodic loads

“…Furthermore, several works have addressed the analysis of the nonlinear dynamical behavior of graphene, with chaos being the main nonlinear behavior discovered [11][12][13][14][15][16][17]. In [14], they investigated the nonlinear dynamics of some graphene structures. Graphene sheets and graphene nanoribbons were some of those structures.…”

“…0 and T f stand for temporal parameters chosen in the manner of avoiding transient modes of oscillation, T tot is the running time. The mean values of the energy function in equation(21) are based on the energy function obtained in equation(14). When the damping coefficient e and the nonlocal parameter m are both varied, figure 7 is obtained.…”

Width Dependent Elastic Properties of Graphene Nanoribbons

“…From the theoretical perspective, several force fields have been designed [ 20 , 34 , 35 , 36 , 37 , 38 ] that are able to sufficiently describe particular features of this nanomaterial or, more generally, of carbon condensed phases. Various dynamical and structural properties of graphene have been examined [ 39 , 40 , 41 , 42 ], as well as the influence of different kinds of defects [ 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ]. Graphene has been used in a number of devices and applications, for example, in integrated circuits [ 53 ], sensors/biosensors [ 54 , 55 , 56 ], detectors [ 57 , 58 ], etc.…”