Charge Transport at Atomic Scales in 1D-Semiconductors: A Quantum Statistical Model Allowing Rigorous Numerical Studies

There has been a recent surge of interest in understanding charge transport at atomic scales. The motivations are myriad, including understanding the conductance properties of peptides measured experimentally. In this study, we propose a model of quantum statistical mechanics which aims to investigate the transport properties of 1D-semiconductor at nanoscales. The model is a two-band Hamiltonian in which electrons are assumed to be quasi-free. It allows us to investigate the behaviour of current and quantum fluctuations under the influence of numerous parameters, showing the response with respect to varying voltage, temperature and length. We compute the current observable at each site and demonstrate the local behaviour generating the current.