TUD

In recent years considerable progress has been made in the fabrication of quasi one dimensional nanostructures. Such quantum wires are ideal tools for studying the interplay of impurity and interaction effects. It is even possible to form one dimensional quantum dots coupled to one channel quantum wires [1] and probe their transport properties in the linear and non-linear regime where the latter gives insight in the spectral properties of the system. The mutual Coulomb interaction is often treated phenomenologically - as in classical Coulomb blockade theory in terms of a capacitance assigned to the dot. In one dimension however interactions can be accounted for microscopically by employing bosonisation. Then one usually resorts to the long wave length zero range limit of the interaction and can use Luttinger liquid theory. These treatments disguise effects due to the long range nature of Coulomb interaction. On the one hand the microscopic charging energy of the quantum dot between the links is underestimated in the zero range interaction. On the other hand one cannot treat leads and dot as separate systems when the interaction intermediates through barriers between all parts of the system. Basically this leads to an ``open'' quantum dot. We use Luttinger liquid theory and a particular form of finite range interaction to investigate its impact on the charging effects and spectral properties of a system consisting of a double barrier structure in a quantum wire and compare to the usual zero range interaction case. We provide a microscopic description of Coulomb blockade and single electron tunneling and compare our results with recent experiments.

[1] O.M. Auslaender et al., Phys. Rev. Lett 84, 1764 (2000).