Quantum transport in interacting nanodevices: from quantum dots to single-molecule transistors

Unprecedented control over the manufacture of electronic devices on nanometer scale has allowed to perform highly controllable and fine-tuned experiments in the quantum regime where exotic effects can nowadays be measured. In quantum dot devices, enhanced conductance below a characteristic energy scale is the signature of Kondo singlet formation. Precise predictions of quantum transport properties in similar nanoelectronics devices are desired to design optimal functionality and control. Standard transport methods suffer from limitations in nanostructure specifics, set-up design, temperature and voltage regime of applicability. To overcome these issues, such that we obtain modelling flexibility and accurate conductance predictions, in this thesis we analytically derive alternative and improved quantum transport formulations having as their starting point scattering theory in the Landauer-B\"uttiker formula, linear response theory in the Kubo formula, nonequilibrium Keldysh theory in the Meir-Wingreen formula and Fermi liquid theory in the Oguri formula. We perform a systematic benchmark of our exact expressions, comparing with the standard approaches using numerical renormalization group techniques. The new formulations not only reproduce literature results, but also show higher accuracy and computational efficiency, as well as a wider applicability under regimes and conditions out of reach by existing methods. We also derive generalized effective models for multi-orbital two-lead interacting nanostructures in both Coulomb blockade and mixed-valence regime, which yield reusable conductance predictions directly in terms of the effective model parameters. We conclude by applying our novel formulations to complex nanoelectronics systems, including a single-molecule benzene transistor, a charge-Kondo quantum dot made from graphene and semiconductor triple quantum dot.