There's Plenty of Room in Higher Dimensions - Nonlinear Dynamics of Nanoelectromechanical Systems
Doctoral thesis, 2017

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.

nonresonant actuation

quantum dots


internal resonance


nonlinear dynamics

PJ-salen, Origo, Fysikgården 1
Opponent: Prof. Wolfgang Belzig, Department of Physics, University of Konstanz, Germany


Martin Eriksson

Chalmers, Physics, Condensed Matter Theory

Mathematical modeling can be used to understand different dynamical phenomena in nature. The dynamical response of a system can be drastically altered even for tiny changes of the system parameters due to so called nonlinearities. The general framework of nonlinear dynamics is widely applicable for instance in predator-prey dynamics in biology, reaction of substances in chemistry, collective behavior in social media and interacting neurons in the brain.

This thesis uses analytical methods from nonlinear dynamics in order to understand the response of nanoelectromechanical systems (NEMS). These systems are typically made of tiny suspended beams or membranes which are about one nanometer thick, a 100'000 times smaller than a human hair. NEMS can be utilized for instance for sensor applications and nanoelectronics.

In NEMS, researchers take advantage of the interaction between mechanical motion of the suspended structure and the flow of electrons. The suspended structure can be forced to vibrate by pulling electrons in and out of the structure by means of electric fields. These vibrations are similar to the vibrations of a guitar string or a drum. There are several ways to actuate mechanical oscillations. One option is direct resonance which is what we utilize when we push a child on a swing.

In the research presented in this thesis, we investigated how NEMS can be mechanically actuated by nonresonant techniques. In particular, actuation can be achieved if the electric field is so fast that there is a pronounced delay in the electron response. We also studied how heat can be converted to mechanical energy by utilizing the interaction between electrons, and how mechanical actuation can be used to generate super­conducting currents.

Furthermore, exotic nonlinear response can be observed in NEMS if they are properly tuned. Different kinds of vibrations (modes) will then be strongly coupled and combinations of modes can be selectively addressed thanks to the extraordinary parameters of the systems. Especially when two or more modes are coupled, the complexity of the dynamics drastically increases because of the increased dimensionality of the corresponding mathematical equations. One aim of nonlinear nanomechanics is to understand and utilize this complex dynamical response.

An important conclusion of this thesis is that interesting dynamical regions might not be observed by standard experiments. However, nonlinear modeling can provide maps which reveal ''hidden'' regions. Such maps can guide researchers to experimentally find the hidden regions.

The famous physicist Richard Feynman stated that ''There's plenty of room at the bottom'' referring to the forthcoming field of nanoscience. From the advances in coupled nanoresonators, it can be concluded that there's also plenty of room in higher dimensions.

Areas of Advance

Nanoscience and Nanotechnology (SO 2010-2017, EI 2018-)

Subject Categories

Physical Sciences

Other Physics Topics

Condensed Matter Physics


Basic sciences



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4294



PJ-salen, Origo, Fysikgården 1

Opponent: Prof. Wolfgang Belzig, Department of Physics, University of Konstanz, Germany

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