Coulomb Blockade distribution for a disordered ensemble of Quantum Dots

Techniques for synthesizing quantum dots (QDs) result in an assembly in which a certain amount of disorder is inevitable. Experimental probes often record the collective properties of an assembly of QDs and not exclusively that of a single QD. On the other hand, theoretical calculations often limit themselves to an analysis of a single QD. In the present work we present a mean field theory for Coulomb Blockade (CB) in an assembly of QDs. We consider two types of disorder: (i) Size disorder; e.g QDs have a distribution of sizes which could be a unimodal or bimodal in nature, (ii) Potential disorder with the confining potential assuming a variety of shapes depending on growth condition and external fields. We illustrate our methodology assuming a gaussian distribution in disorder in both size and potential. However our theoretical framework can accommodate an experimentally provided distribution in disorder. To do this we rely on the scaling laws for CB (also termed as Hubbard U) obtained for an isolated QD. We observe that CB is partially suppressed by the disorder. Further, the distribution in U is a skewed gaussian with enhanced broadening.