Orbital fluctuations and strong correlations in quantum dots

In this paper we focus our attention on quantum dot systems where exotic strongly correlated behaviour develops due to the presence of orbital or charge degrees of freedom. After giving a concise overview of the theory of transport and the Kondo effect through a single-electron transistor, we discuss how the SU(4) Kondo effect develops in dots having orbitally degenerate states and in double dot systems, and then study the singlet–triplet transition in lateral quantum dots. Charge fluctuations and Matveev's mapping to the two-channel Kondo model in the vicinity of a charge degeneracy point are also discussed.