Weak Coulomb Blockade Effect in Quantum Dots

We develop the general nonequilibrium theory of transport through a quantum dot, including Coulomb blockade effects via a $1/N$ expansion, where $N$ is the number of scattering channels. At lowest order we recover the Landauer formula for the current plus a self-consistent equation for the dot potential. We obtain the leading corrections and compare with earlier approaches. Finally, we show that to leading and to next leading order in $1/N$ there is no interaction correction to the weak localization, in contrast to previous theories, but consistent with experiments by Huibers et al. [Phys. Rev. Lett. 81, 1917 (1998)], where $N=4$.

Figure 1

Left: schematic drawing of a quantum dot coupled to source and drain leads via point contacts. Top right: a fictitious lead is side coupled to electrons leaving the dot as a mathematical trick. The scattering Hamiltonian $H_1$, when included to all orders, decouples the fictitious leads, as illustrated in the bottom right panel.

Figure 2

(a) At leading order in $1/N$, we retain only tree diagrams. (b) The one-loop diagrams.