There's Plenty of Room in Higher Dimensions - Nonlinear Dynamics of Nanoelectromechanical Systems

Abstract: Nanoelectromechanical systems (NEMS) couple the dynamics of electrons to vibrating nanostructures such as suspended beams or membranes. These resonators can be used in for instance nanoelectronics and sensor applications. NEMS are also of fundamental interest since electrons exhibit strong quantum effects when confined in nanoobjects. Furthermore, NEMS such as graphene resonators are strongly nonlinear, which opens the door for complex dynamical response. The operation of nanoresonators often rely on actuation of mechanical vibrations driven by an electric ac-field. The first part of this thesis theoretically investigates high-frequency nonresonant actuation relying on electromechanical back action (Papers I-II). The nonresonant phenomenon can be utilized to study nonlinear dissipation and to selectively actuate different vibrational modes, also asymmetric ones, even though the driving field is homogeneous (Paper III). Another nonresonant actuation mechanism converts heat into mechanical energy and relies on electron-electron interaction in a movable quantum dot (Paper IV).Furthermore, parametric actuation of a nanoresonator can be used to generate a supercurrent through a superconducting weak link even though the superconducting phase difference across the link is zero (Paper V). The excitation leads to a spontaneous symmetry breaking, which allows for a new possibility to switch between the two current directions.Actuation of mechanical vibrations is also used to study nonlinear dynamics and mode coupling in nanoresonators. The strength of nonlinearities and vibrational frequencies can be tuned by electrostatic means (Paper VI). This tunability and the low dissipation in nanoresonators make it possible to selectively address individual or combinations of modes. Coupled modes allow for much richer nonlinear dynamics, such as internal resonances (Paper VII), due to the increased dimensionality of the relevant phase space. Furthermore, exotic dynamical regions may be hidden and not observed in standard experiments. However, bifurcation theory can help to construct maps which reveal the hidden regions. A lot more is therefore to be expected from coupled mode dynamics, since there’s plenty of room in higher dimensions.