Orbital fluctuations and strong correlations in quantum dots

Abstract

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.

Acknowledgements

I would like to thank all my collaborators, especially Laszló Borda, Walter Hofstetter, and A. Zawadowski for valuable discussions. This research has been supported by Hungarian Grants No. OTKA T038162, T046267, and T046303, and the European ‘Spintronics’ RTN HPRN-CT-2002-00302.

Notes

¹ The Friedel sum rule can only be applied in our case at temperature T=0, where the impurity spin is screened and disappears from the problem, and conduction electrons at the Fermi surface experience only some residual scattering. The Friedel sum rule has rigorously been derived only for the Anderson Hamiltonian, where it relates the number of electrons on the dot to the phase shifts – see 25. In the case of the Kondo problem, there seems to be an ambiguity modulo π in the phase shift's definition.