Real-time diagrammatic approach to current-induced forces: Application to quantum-dot based nanomotors

Abstract

During the last years there has been an increasing excitement in nanomotors and particularly in current-driven nanomotors. Despite the broad variety of stimulating results found, the regime of strong Coulomb interactions has not been fully explored for this application. Here we consider nanoelectromechanical devices composed by a set of coupled quantum dots interacting with mechanical degrees of freedom taken in the adiabatic limit and weakly coupled to electronic reservoirs. We use a real-time diagrammatic approach to derive general expressions for the current-induced forces, friction coefficients, and zero-frequency force noise in the Coulomb blockade regime of transport. We prove our expressions accomplish with Onsager's reciprocity relations and the fluctuation-dissipation theorem for the energy dissipation of the mechanical modes. The obtained results are illustrated in a nanomotor consisting of a double quantum dot capacitively coupled to some rotating charges. We analyze the dynamics and performance of the motor as function of the applied voltage and loading force for trajectories encircling different triple points in the charge stability diagram.

Thermodynamics and Steady State of Quantum Motors and Pumps Far from Equilibrium

“…In recent years, there has been a sustained growth in the interest in different forms of nanomachines. This was boosted by seminal experiments [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ], the blooming of new theoretical proposals [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], and the latest developments towards the understanding of the fundamental physics underlying such systems [ 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. Quantum mechanics has proven to be crucial in the description of a broad family of nanomachines, which can be put together under the generic name of “quantum motors” and “quantum pumps” [ 13 , 46 , 47 , 48 , 49 , 50 , ...…”

“…Remarkably, some systems operate solely due to quantum interference, e.g., quantum pumps and motors based on chaotic quantum dots [ 13 , 39 , 54 ], Thouless quantum pumps and motors [ 13 , 22 , 55 ], or Anderson quantum motors [ 56 ], among others. On the other hand, the strong Coulomb repulsion between electrons in quantum-dot-based pumps and motors has shown to enhance the performance (or even induce the activation) of these nanodevices [ 26 , 42 , 57 , 58 , 59 ]. The effect of decoherence has also been addressed [ 22 , 39 , 54 , 60 ], as well as the influence of the friction forces and the system-lead coupling in the dynamics of quantum motors and pumps [ 22 ].…”

“…A typical problem is that when these devices are coupled to nonequilibrium sources, nonconservative current-induced forces (CIFs) appear. These CIFs come, in the first place, by assuming a type of Born–Oppenheimer approximation where the electronic and mechanical degrees of freedom can be treated separately and, secondly, by evaluating the mean value of the force operator [ 10 , 11 , 22 , 24 , 26 , 34 , 35 , 37 , 39 , 42 , 44 , 49 , 50 , 51 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 ]. Because of the delayed response of the electronic degrees of freedom to the mechanical motion, one should include the so-called nonadiabatic corrections with the CIFs.…”

“…This phenomenon is translated into a possible complex dependency of the CIFs on the velocity of the mechanical degrees of freedom. When the effect of the mechanical velocities on CIFs can be treated in linear response, it is clear whether it is adequate or not to assume a constant terminal velocity [ 22 , 39 , 42 ]. However, in far-from-equilibrium conditions, this subject has not been fully addressed.…”

Current-induced rotations of molecular gears

“…However, the underlying physical mechanisms leading to unidirectional molecular rotation are not well understood, since they involve in general terms a delicate interplay between collective mechanical and electronic degrees of freedom. On the theoretical side, a combination of model-based approaches [28][29][30][31][32][33][34], catching the basic physics of the problem with more advanced first-principles methodologies able to provide atomistic, system-specific information is required. Some of the problems here include, e.g.…”