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Unprecedented control over the manufacture of electronic devices on nanometerscale has allowed to perform highly controllable and fine-tuned experiments inthe quantum regime where exotic effects can nowadays be measured. In quantumdot devices, enhanced conductance below a characteristic energy scale is thesignature of Kondo singlet formation. Precise predictions of quantum transportproperties in similar nanoelectronics devices are desired to design optimalfunctionality and control. Standard transport methods suffer from limitationsin nanostructure specifics, set-up design, temperature and voltage regime ofapplicability. To overcome these issues, such that we obtain modellingflexibility and accurate conductance predictions, in this thesis weanalytically derive alternative and improved quantum transport formulationshaving as their starting point scattering theory in the Landauer-B\"uttikerformula, linear response theory in the Kubo formula, nonequilibrium Keldyshtheory in the Meir-Wingreen formula and Fermi liquid theory in the Oguriformula. We perform a systematic benchmark of our exact expressions, comparingwith the standard approaches using numerical renormalization group techniques.The new formulations not only reproduce literature results, but also showhigher accuracy and computational efficiency, as well as a wider applicabilityunder regimes and conditions out of reach by existing methods. We also derivegeneralized effective models for multi-orbital two-lead interactingnanostructures in both Coulomb blockade and mixed-valence regime, which yieldreusable conductance predictions directly in terms of the effective modelparameters. We conclude by applying our novel formulations to complexnanoelectronics systems, including a single-molecule benzene transistor, acharge-Kondo quantum dot made from graphene and semiconductor triple quantumdot.

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