Nonlinear Vibration And Its Effect On The Electronic Transport In Graphene Nano-resonators

Nanoelectromechanical resonators based on two dimensional material,such as graphene,have attracted extensive attention due to their low mass and high quality factors.The Fermi-Pasta-Ulam-Tsingou(FPU)physics plays an impor-tant role in the performance of graphene resonator as the dissipation of funda-mental mode due to coupling with other modes intrinsically limits the quality factors of the device.In this dissertation,we focus on the nonlinear vibration in graphene resonators,and have developed a mode coupling methods to calculate the coupling strength between normal modes,which has been used to analyse the energy flow pathways due to the dissipation of fundamental mode,and to cal-culate the timescale for equipartition in graphene resonators.Furthermore,the transport behaviors subject to the nonlinear vibrations has also been investigated in this dissertation.In the first chapter,the flexural modes and its effects on the mechanical,thermal and transport properties is introduced,and then we briefly summarize the simple history and main results of FPU problem.The basic theory about molecular dynamics(MD)simulation is presented in the end of this chapter.In the second chapter,the VFF model and its simplified expression,used in MD simulations,are firstly presented,which have been used to calculate the normal modes,eigen-frequency and dispersion relation of the graphene system.Specially,due to the symmetry of displacement profile,all the normal modes can be grouped into four different classes.The initiatory result of MD simulations shows that the nonlinearity in VFF model results in the energy flow from the first normal mode to the other modes with higher frequency,and results in the fact that the frequency of vibration is approximately proportional to the relative deformation.In the third chapter,we examine solely the mode coupling between flexural modes and identify their energy flow pathway during thermalization process.The key is the development of a universal scheme that numerically characterizes the strength of nonlinear interactions between normal modes.In particular,for our square graphene system,the modes are grouped into four classes by their distinct symmetries.The couplings are significantly larger within a class than between classes.As a result,the equations for the normal modes in the same class as the initially excited one can be approximated by driven harmonic oscillators,therefore they get energy almost instantaneously.Because of the hierarchical organization of the mode coupling,the energy distribution among the modes will arrive at a stable profile,where most of the energy is localized on a few modes,leading to the formation of "natural package" and metastable states.The dynamics for modes in other symmetry classes follow a Mathieu type of equation,thus inter-class energy flow starts typically when there is a mode lies in the unstable region in the parameter space of Mathieu equation.Due to strong coupling of the modes inside the class,the whole class will get energy and be lifted up by the unstable mode.In the fourth chapter,the timescale to the equipartition for the graphene flexural modes has been investigated with MD simulations.The computation unveils that the modes belonging to the same symmetry class as the initially excited one can be easily excited,while it takes much longer time for the modes in different symmetry class to get energy due to the existence of symmetry block-ade.The equipartition time follows the stretched exponential law ?? exp(?-?):1)in the small energy limit,higher modes are more difficult to arrive energy equipartition,while the higher modes are easier to reach equipartition for larger initial excitation energy;2)larger system has a smaller equipartition time for the same initial excitation energy.As the size increases,the data points collapse to a single curve,indicating the convergence of the scaling in the large size limit.Furthermore,the exponent ? decreases to a stable value when the system size is lager than 8 nm.In the fifth chapter,the effects of mechanical vibrations on electronic trans-port through graphene quantum dots has been investigated with MD simulation and tight-binding methods.If only consider the linear interaction in the MD simulations,the motion of the system will be periodic,which will result in peri-odic oscillation in the quantum transmission at the same frequency.Specifically,for small-amplitude vibrations,each transmission peak for the static graphene is extended into a transmission band or plateaus,leading to transmission enhance-ment;for large deformation amplitude,resonant scattering can occur,leading to sharp fluctuations in the transmission.With nonlinear interactions,the dis-placement profile of motion can be very complex,which results in more complex transmission patterns and the nets from intertwined transmission bands,leading to spurious higher-frequency modes in the current.The conclusion of this dissertation and some prospects for the future works in this field is given in the last chapter.