Nanomechanical Phenomena in Low-Dimensional Structures

Doctoral thesis, 2017

This is a compilation thesis which investigates various mechanical phenomena in different low-dimensional nanoscale systems. In the first part, we consider a purely mechanical phenomenon: the sensitivity of the dispersion of a Love-type surface acoustic wave (SAW) to geometry and material parameters. We model a SAW sensor as a three-layer system with elastic, viscous, or viscoelastic layers. We find that viscoelasticity can remove the support for Love waves. We also derive analytic expressions for the wave velocity and attenuation in the limit of a thin middle layer. In the second part, we consider the interaction of SAWs with an electronic subsystem. We model a flat semi-infinite graphene sheet using 2D elasticity theory and consider Rayleigh-type SAWs. We investigate the resonant interaction of such SAWs with electronic edge states induced by a transverse magnetic field. When electronic relaxation is much faster than phonon absorption, we find that the SAWs attenuate. In the opposite limit, we show that nonlinear effects can lead to the formation of hypersonic solitons. In the third part, we demonstrate how interaction with an electronic subsystem can actuate nanomechanical vibrations. We study two different systems composed of a movable quantum dot (QD) in position dependent tunneling contact with two leads. In the first system, the leads are held at different temperatures and a spin-valve effect prevents electron exchange between them. We show that electron-electron interaction can mediate a heat flow which can actuate the QD position via a capacitive coupling. In the second system, both the leads and the QD are superconducting and the system has mirror symmetry. We find that an applied ac field can induce charge oscillations in the QD and parametrically excite vibrations of its position. The automatic synchronization of the oscillations in charge and position generates a supercurrent, the direction of which is a result of spontaneous symmetry breaking.