The remarkable properties of carbon nanotubes (CNTs) have allowed the proposition, design and exploitation of nanomechanical devices. One example is the CNT oscillator proposed by Zheng and Jiang [1] based upon the experimental realization of low-friction nanoscale linear bearings [2]. Linear nanomotors based on coupled CNTs have also been experimentally realized [3, 4]. CNT oscillators, in their simplest form, consist of a double- walled CNT where the inner tube can move inside the outer tube in an oscillatory low-friction motion of high frequency. This motion is induced and maintained by van der Waals interac- tions between the inner and the outer tubes. Many works have contributed to understand the characteristics of CNT oscillators such as their oscillation frequency dependence upon CNT parameters [5], stability [6–8], friction [9–11], energy dissipation [12–15], and chaotic behavior [16]. Key issues regarding these devices are how to initialize them and how to sustain the motion in a controllable way. Different strategies have been proposed to start the oscillatory motion, e.g., by applying magnetic and electrical fields [6, 17], by accelerating encapsulated charged elements located inside the inner tube [18], and by thermal expansion of encapsulated gases [19]. 

In this letter we propose an alternative way to start, maintain, and control the oscillatory motion, based on thermophoresis, i.e., the use of thermal gradients to induce mass transport. In this case, the thermal gradient is imposed on the outer tube by external agents such as electrical currents. This approach was inspired on the recent findings that demonstrated the possibility of producing nanoscale thermal motors based on CNTs [20]. Thermophoretic mass transport through CNTs has been theoretically investigated for solid gold nanoparticles [21] and water nanodroplets [22], but not yet for CNT-based oscillators. 

The concept of the thermophoretically driven device is presented in Fig. 1. A CNT containing a “X”-like junction and a movable internal CNT is placed between two contacts. An electrical current I can be injected through the contacts to create thermal gradients along the outer tube, with temperatures T$_{1}$ and T$_{2}$ ( T$_{1}$ > T$_{2}$ ). The Joule heating will create a hotter region at the junction producing a heat flux along the x -direction. As will demonstrate below suitable choices of periodic electrical current pulses provide ways to start, tune and control the oscillatory behavior of the inner tube. It is important to mention that the configurations of tubes on the device of Fig. 1 are feasible to be obtained with current technological capabilities [23]. 

In order to investigate the dynamics of the device shown in Fig. 1 we have used analytical 

