Landauer conductance in the complex domain: A path to find closed-form solutions

The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems connected to semi-infinite atomic chains. This reveals the presence of complex-conjugated pairs of simple poles that are responsible for transmission peaks in the real-domain evaluations. This leads us to formulate a closed-form expression for the transmission function.