Charging ratchets: Coulomb blockade and rectification

Discrete ratchets describe directed motion of a ‘reaction coordinate’ through a cycle of states in response to some varying external parameter. Such systems, in the simple, history-independent case, are described by a Markov process which in turn leads to a master equation with a transition matrix. Thus the ratchet property is reduced to a characteristic of the parameter-dependent symmetry of matrices. In the standard model of tunneling through a set of quantum dots in the Coulomb-blockade regime, a master equation is also used to describe the evolution through states in ‘dot-occupancy space’, leading to transport of electrons from a source to a drain. The symmetry of the transition matrix in this case is also a function of external parameters, notably the applied gate voltages and source–drain voltage, as well as depending on the configuration of dots and their tunnel couplings. We show that rectification and other ratchet behavior is a common feature of tunneling transport in the Coulomb-blockade regime. We also show that specific arrangements of dots and their tunnel couplings can be designed to enhance the ratchet effect. Finally, we show that the strong rectification of Coulomb-blockaded systems results from the reduction in phase space accessible to the system as it traverses the states in the reaction cycle.