Taylor series of Landauer conductance: Towards closed-form solutions

We present a novel method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in mesoscopic systems [1]. The method is based on the recursive scattering matrix method, that permits us to find the scattering matrix of a system from the scattering matrices of its subsystems [2]. By extending this study to the complex domain, we find 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 method to find the closed-form expression for the transmission function in general systems [3].

[1] C. Ramírez, M.J. Rodríguez and B.D. Gomez, Physica E 124, 114213 (2020).
[2] C. Ramírez, Ann. Phys. (Berlin) 530, 1700170 (2018).
[3] M.J. Rodríguez and B.D. Gomez, C. Ramírez, arXiv:2008.01923.