Axel Martin Eriksson

Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.

Energy-dependent path of dissipation in nanomechanical resonators

Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multilayer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay changes abruptly to a lower value. This finding can be explained by a model where the measured mode hybridizes with other modes of the resonator at high energy. Below a threshold energy, modes are decoupled, resulting in comparatively low decay rates and giant quality factors exceeding 1 million. Our work opens up new possibilities to manipulate vibrational states, engineer hybrid states with mechanical modes at completely different frequencies, and to study the collective motion of this highly tunable system.

Nonresonant high frequency excitation of mechanical vibrations in a graphene based nanoresonator

We theoretically analyze the dynamics of a suspended graphene membrane which is in tunnel contact with grounded metallic electrodes and subjected to ac-electrostatic potential induced by a gate electrode. It is shown that for such a system the retardation effects in the electronic subsystem generate an effective pumping for the relatively slow mechanical vibrations if the driving frequency exceeds the inverse charge relaxation time. Under this condition there is a critical value of the driving voltage amplitude above which the pumping overcomes the intrinsic damping of the mechanical resonator, leading to a mechanical instability. This nonresonant instability is saturated by nonlinear damping and the system exhibits self-sustained oscillations of relatively large amplitude.

Zero-Phase-Difference Josephson Current Based on Spontaneous Symmetry Breaking via Parametric Excitation of a Movable Superconducting Dot

Recent advances have attracted attention to nonstandard Josephson junctions in which a supercurrent can flow despite zero phase difference between the constituent superconducting leads. Here, we propose a zero-phase-difference nanoelectromechanical junction which, in contrast to other considered systems, exhibits symmetry between leftward and rightward tunneling through the junction. We show that a supercurrent is, nevertheless, possible as a result of spontaneous symmetry breaking. In the suggested junction, the supercurrent is mediated by tunneling via a superconducting Cooper-pair box on a mechanical resonator. An alternating electric potential parametrically excites mechanical oscillations which are synchronized with charge oscillations of the box. This leads to coherent transfer of Cooper pairs through the junction. The direction of the supercurrent is a result of spontaneous symmetry breaking and thus it can be reversed without changing the parameters.

Corrigendum: Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators (2013 Nanotechnology 24 395702)

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Nanoelectromechanical Heat Engine Based on Electron-Electron Interaction

We theoretically show that a nanoelectromechanical system can be mechanically actuated by a heat flow through it via an electron-electron interaction. In contrast to most known actuation mechanisms in similar systems, this new mechanism does not involve an electronic current nor external ac fields. Instead, the mechanism relies on deflection-dependent tunneling rates and a heat flow which is mediated by an electron-electron interaction while an electronic current through the device is prohibited by, for instance, a spin-valve effect. Therefore, the system resembles a nanoelectromechanical heat engine. We derive a criterion for the mechanical instability and estimate the amplitude of the resulting self-sustained oscillations. Estimations show that the suggested phenomenon can be studied using available experimental techniques.

Selective nonresonant excitation of vibrational modes in suspended graphene via vibron–plasmon interaction

We theoretically study a doped graphene ribbon suspended over a trench and subject to an ac-electrical field polarized perpendicularly to the graphene plane. In such a system, the external ac-field is coupled to the relatively slow mechanical vibrations via plasmonic oscillations in the isolated graphene sheet. We show that the electrical field generates an effective pumping of the mechanical modes. It is demonstrated that in the case of underdamped plasma oscillation, a peculiar kind of geometrical resonance of the mechanical and plasma oscillations appear. Namely the efficiency of pumping significantly increases when the wave number of the mechanical mode is in close agreement with the wave number of the plasma waves. The intensity of the pumping increases with the wave number of the mode. This phenomenon allows selective actuation of different mechanical modes although the driving field is homogeneous.

Nonresonant high-frequency excitation of mechanical vibrations in a movable quantum dot

Nonresonant high-frequency electrostatic actuation of a movable quantum dot (QD) is investigated analytically. The electronic dot state is in tunneling contact with a continuum of electronic states in bulk electrodes. Gate electrodes induce an electric ac-field at the dot. Absorbtion of the field is accompanied by increment or decrement of one vibrational quantum in the QD. It is shown that the rate of increment overcomes the rate of decrement of vibrational quanta when the driving frequency exceeds the inverse tunneling time between the bulk electrodes and the QD. This results in a mechanical instability, leading to relatively large amplitude oscillations of the QD, which are saturated by nonlinear dissipation.