PhD defense by Freja Schou Guttesen

Title: Chiral Molecular Motors

Abstract: Archimedes' screws have been widely used both for pumping water, and, later in hydroelectric power stations ever since the Egyptians developed the first pump prior to 200 BCE. In the 1950s, the idea of molecular electronics was first suggested, and the field of nanomachines has developed rapidly since then.

This thesis describes a theoretical study that has been developed in close collaboration with experimentalists who have realized a molecular Archimedean screw. For the first time, 100\% unidirectional rotational motion in a synthetic molecular motor is observed along with an increase in the current that deviates drastically from the expected cubic voltage dependence.

This nanomachine, consisting of a chiral molecule in a break junction, functions both as an electric current turbine and a mechanical current booster. The presence of a current-induced non-conservative torque, the "wind force", in atomic wires was first derived by Dundas et al. (2009). Using a classical stochastic approach together with a quantum mechanical scattering approach, we propose a theoretical framework that provides a unified understanding of the electronic mechanisms at play.

Assuming that the molecular rotation is much slower than the electronic motion, an adiabatic expansion of the time evolution is employed. Using the Non-Equilibrium Green Function formalism in a scattering picture, expressions for the relevant operators of the system are studied, including the non-conservative wind force. Using a simple two-level model (representing the molecule), coupled to two leads, the system is numerically modeled.

A semi-classical Langevin equation for a rotating system, including relevant stochastic forces, is used to simulate the voltage dependent current of the system, and a current enhancement of one order of magnitude is obtained. The significant jump in current is found to be related to the point at which the molecule starts to rotate unhindered, leading to a rotation-induced resonance effect.

Both experimental and theoretical observations reveal a U-shaped behavior in the efficiency of the molecular motor, establishing a direct correlation between the two.