Magnetomotive instability and generation of mechanical vibrations in suspended semiconducting carbon nanotubes

Abstract

We have theoretically investigated the electromechanical properties of a freely suspended carbon nanotube that is connected to a constant-current source and subjected to an external magnetic field. We show that self-excitation of mechanical vibrations of the nanotube can occur if the magnetic field H exceeds a dissipation-dependent critical value Hc, which we find to be of the order of 10-100 mT for realistic parameters. The instability develops into a stationary regime characterized by time periodic oscillations in the fundamental bending mode amplitude. We find that for nanotubes with large quality factors and a magnetic-field strength just above Hc the frequency of the stationary vibrations is very close to the eigenfrequency of the fundamental mode. We also demonstrate that the magnetic field dependence of the time averaged voltage drop across the nanotube has a singularity at H = Hc. We discuss the possibility of using this phenomenon for the detection of nanotube vibrations.Nanoelectromechanical systems (NEMS) containing a suspended carbon nanotube (CNT) vibrating at radio frequencies (RF) have received increasing attention recently. Advantages of CNT mechanical resonators include their high resonance frequencies -up to the GHz range --their low dissipative losses 1 and the possibility to tune the resonance frequency by adjusting the tension in the tube 2,3 . CNT based NEMS devices have already shown a great potential for a plethora of technological applications including mass sensing 4,5 and tunable high frequency electronics 2,3,6,7 . However, most of the devices which have been realized thus far are passive resonators which perform frequency filtering of the incoming RFsignal 2,3,6,7 . Here we propose an active oscillator based on an current biased doubly-clamped CNT for which the conductance depends monotonically on the nanotube deflection. Such a deflection sensitive resistance has been demonstrated for a semiconducting single-walled CNT suspended over a gate electrode 2,3,8 . The active feedback is provided by a Lorentz force induced by a constant magnetic field directed perpendicular to the direction of the current and parallel to the gate electrode. We show that , by applying a constant external current in a sufficiently high magnetic field, we obtain mechanical instability and self-sustained mechanical oscillations at a frequency close to the mechanical resonance frequency. Furthermore, we show that the mechanical instability results in oscillations of the voltage drop across the nanotube accompanied by a deviation of the time averaged voltage from its static time-independent value.

Magnetomotive cooling and excitation of carbon nanotube oscillations under voltage bias

“…The same phenomenon, but expressed in terms of a rise (or drop) in the time averaged voltage, was derived in our previous paper [10].…”

“…[10]. Obviously, one can equally well consider other causes of the coupling such as the effect of pure mechanical strain [17][18][19] and the considerations below remain valid given any deflectionsensitive resistance.…”

“…On the other hand, today there are numerous different schemes for cooling of nanotubes, many of which utilize a magnetic field [6][7][8][9]. In a recent paper [10] we proposed a constant-current biased oscillator device whose feedback mechanisms consisted of the nanotube's displacement-sensitive resistance and a Lorentz force induced by a uniform magnetic field. A major advantage with this scheme is that a displacement-sensing resistance can be implemented using a gate electrode which can be placed at a relatively large distance from the nanotube [11][12][13][14][15].…”

Self-sustained oscillations in nanoelectromechanical systems induced by Kondo resonance

“…These mechanical systems include long cantilever nanorelay [15], atomic force microscopy with a tip [16,17] and a nanoisland attached either to the cantilever [18] or to one of the leads [16,17]. A basic understanding of the NEM/NSM has been achieved in both theoretical [19][20][21][22][23][24][25] and experimental [26,27] studies of single-electron shuttling. Alternatively, the mechanical system can itself play the role of one of the contacts when the quantum dot (impurity) is deposited on top of the metallic cantilever [18].…”

Kondo Force in Shuttling Devices: Dynamical Probe for a Kondo Cloud

“…Recent progress in fabrication of nanoelectromechanical systems (NEMS) based on suspended carbon nanotubes [1] as well as on suspended Si [2] and SiN [3] nanowires vibrating at radio frequencies (RF) resulted in rapidly growing amount of theoretical works [4]- [8] addressing the issues of interplay between spin/charge transport and nano-mechanics [9]. The observation of Coulomb Blockade [2] in NEMS opened a possibility to consider the influence of strongly correlated and resonance effects on a behaviour of nano-oscillators.…”