Thermoelectric properties of a series of Landauer barriers

The thermoelectric effect in a disordered one-dimensional (1D) mesoscopic wire is analyzed within the Landauer picture. A definition that distinguishes between the transport coefficients of the entire system (including reservoirs) and the coefficients of a Landauer barrier is suggested. As a result the transport coefficients of the barrier satisfy the Onsager relations. The multichannel case is shown to be a simple generalization. The thermopower is calculated as a function of the length of the system. This is done by calculating the thermopower of a series of Landauer barriers. The barriers are randomly separated and an ensemble average over the disorder is carried out. We find that the thermopower increases linearly with the length of the system as localization occurs (while the resistance increases exponentially). The efficiency of the thermoelectric effect also increases with the length of the system.