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Register a new userThe influence of constriction on the motion of graphene kinks
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Graphene kinks are topological states of buckled graphene membranes. We show that when a moving kink encounters a constriction, there are three general classes of behavior: reflection, trapping, and transmission. Overall, constriction is characterized by an attractive potential. In the case of a simple symmetric constriction, the kink potential energy has a relatively deep minimum surrounded by energy barriers. However, the potential energy alone does not fully define the class of behavior: the effect of a resonant reflection was observed in our simulations. Moreover, we demonstrate that asymmetric constrictions can transform kinks from one type into another. MD simulation results are compared with predictions of the classical $phi^4$ model.
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In this Chapter we provide a review of the main results obtained in the modeling of graphene kinks and antikinks, which are elementary topological excitations of buckled graphene membranes. We introduce the classification of kinks, as well as discuss kink-antikink scattering, and radiation-kink interaction. We also report some new findings including i) the evidence that the kinetic energy of graphene kinks is described by a relativistic expression, and ii) demonstration of damped dynamics of kinks in membranes compressed in the longitudinal direction. Special attention is paid to highlight the similarities and differences between the graphene kinks and kinks in the classical scalar $phi^4$ theory. The unique properties of graphene kinks discussed in this Chapter may find applications in nanoscale motion.
The problem of the Klein tunneling across a potential barrier in bi-layer graphene is addressed. The electron wave functions are treated as massive chiral particles. This treatment allows us to compute the statistical complexity and Fisher-Shannon information for each angle of incidence. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. The role played by the evanescent waves on these magnitudes is disclosed. Due to the influence of these waves, it is found that the statistical measures take their minimum values not only in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in bi-layer graphene.
Angle-resolved photoemission spectroscopy reveals pronounced kinks in the dispersion of the sigma band of graphene. Such kinks are usually caused by the combination of a strong electron-boson interaction and the cut-off in the Fermi-Dirac distribution. They are therefore not expected for the $sigma$ band of graphene that has a binding energy of more than 3.5 eV. We argue that the observed kinks are indeed caused by the electron-phonon interaction, but the role of the Fermi-Dirac distribution cutoff is assumed by a cut-off in the density of $sigma$ states. The existence of the effect suggests a very weak coupling of holes in the $sigma$ band not only to the $pi$ electrons of graphene but also to the substrate electronic states. This is confirmed by the presence of such kinks for graphene on several different substrates that all show a strong coupling constant of lambda=1.
Membranes of suspended two-dimensional materials show a large variability in mechanical properties, in part due to static and dynamic wrinkles. As a consequence, experiments typically show a multitude of nanomechanical resonance peaks, which makes an unambiguous identification of the vibrational modes difficult. Here, we probe the motion of graphene nanodrum resonators with spatial resolution using a phase-sensitive interferometer. By simultaneously visualizing the local phase and amplitude of the driven motion, we show that unexplained spectral features represent split degenerate modes. When taking these into account, the resonance frequencies up to the eighth vibrational mode agree with theory. The corresponding displacement profiles however, are remarkably different from theory, as small imperfections increasingly deform the nodal lines for the higher modes. The Brownian motion, which is used to calibrate the local displacement, exhibits a similar mode pattern. The experiments clarify the complicated dynamic behaviour of suspended two-dimensional materials, which is crucial for reproducible fabrication and applications.
The motion of a C60 molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a C60 molecule near a graphene sheet is found to be diffusive in the lateral directions. While, in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the C60 molecule. We also examine the rotational diffusion of C60 and show that its motion over the graphene sheet is not a rolling motion.
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