Downsizing of devices opens the question of how to tune not only their electronic properties, but also of how to influence 'mechanical' degrees of freedom such as translational and rotational motions. Experimentally, this has been meanwhile demonstrated by manipulating individual molecules with e.g. current pulses from a Scanning Tunneling Microscope tip. Here, we propose a rotational version of the well-known Anderson-Holstein model to address the coupling between collective rotational variables and the molecular electronic system with the goal of exploring conditions for unidirectional rotation. Our approach is based on a quantum-classical description leading to effective Langevin equations for the mechanical degrees of freedom of the molecular rotor. By introducing a timedependent gate to mimic the influence of current pulses on the molecule, we show that unidirectional rotations can be achieved by fine tuning the time-dependence of the gate as well as by changing the relative position of the potential energy surfaces involved in the rotational process. idea by going beyond the linear coupling regime and, more importantly, by considering a non-harmonic, periodic potential energy surfaces associated with a collective rotational degree of freedom rather than with the linear displacement of the standard AHM. Our basic assumption is that the movement of the tip of a Scanning Tunneling Microscope (STM) can act as an effective time-dependent electrical gate for a molecule deposited on the substrate, being able to generate a current-induce rotation. The setup we are envisioning is displayed in figure 1: a single molecule adsorbed on a metallic substrate is electrically addressed by the STM tip. This gate is able to change the average occupation of the relevant electronic state coupled to the collective rotational variable (s) and it may thus trigger a (possibly) unidirectional rotation of the molecule. Specifically, we can design two PESs with a given separation of minima and choose an appropriate switching of the gate to make the molecule rotate one-way. To address this problem, we use a quantum-classical approach to the problem, by considering the rotational degrees of freedom as classical variables, whose dynamics is governed by a generalized Langevin equation, while, on the other hand, the electronic system is treated within the nonequilibrium Green function (NEGF) technique exploiting methods developed in the context of current-induced forces [39][40][41][42][43][44][45].The outline of the article is as follows: in section 2, the rotational analogy of the AHM Hamiltonian is formulated and the corresponding equation of motion and the reduced density matrix are discussed. In section 3, a simple example of a planar molecule with N-fold symmetry is considered. By performing an adiabatic expansion in the reduced density matrix, we derive an equation of motion in the adiabatic limit, which allows simplifying the problem and leading to the concept of mean torque, damping, and external-driving torque. Consequently, it e...

Manipulating and coupling molecule gears is the first step towards realizing molecular-scale mechanical machines. Here, we theoretically investigate the behavior of such gears using molecular dynamics simulations. Within a nearly rigid-body approximation we reduce the dynamics of the gears to the rotational motion around the orientation vector. This allows us to study their behavior based on a few collective variables. Specifically, for a single hexa (4-tert-butylphenyl) benzene molecule we show that the rotational-angle dynamics corresponds to the one of a Brownian rotor. For two such coupled gears, we extract the effective interaction potential and find that it is strongly dependent on the center of mass distance. Finally, we study the collective motion of a train of gears. We demonstrate the existence of three different regimes depending on the magnitude of the driving-torque of the first gear: underdriving, driving and overdriving, which correspond, respectively, to no collective rotation, collective rotation and only single gear rotation. This behavior can be understood in terms of a simplified interaction potential. arXiv:1910.06644v2 [cond-mat.soft]