Transport of interacting electrons in arrays of quantum dots and diffusive wires

We develop a detailed theoretical investigation of the effect of Coulomb interaction on electron transport in arrays of chaotic quantum dots and diffusive metallic wires. Employing the real time path integral technique we formulate a new Langevin-type of approach which exploits a direct relation between shot noise and interaction effects in mesoscopic conductors. With the aid of this approach we establish a general expression for the Fano factor of 1D quantum dot arrays and derive a complete formula for the interaction correction to the current which embraces all perturbative results previously obtained for various quasi-0D and quasi-1D disordered conductors and extends these results to yet unexplored regimes.

Figure 1

1D array of chaotic quantum dots. The array consists of $N-1$ dots and $N$ barriers. The $n\text{th}$ dot is characterized by mean level spacing ${\delta }_n$ and gate capacitance $C_{\mathit{gn}}$. The $n\text{th}$ barrier is described by its Landauer conductance $1∕R_n$, capacitance $C_n$ and Fano factor ${\beta }_n$. The array is placed between two big metallic reservoirs which are connected to the voltage source via Ohmic resistor $R_S$.

Figure 2

The linear conductance $G$ (solid lines) as a function of temperature $T$ together with the differential conductance $dI∕dV$ (dashed lines) as a function of the applied voltage $V$ at $T=0$. The results are obtained from Eq. (63) for $g=1000$, $\beta =1∕3$, ${\tau }_D∕RC={10}^4$, $C_g∕C=2.5$, and for three different numbers of barriers: $N=2$, 10, and 50. We identify four different regimes (the boundaries between them are shown by dotted lines): (I) saturation regime $eV$, $T\lesssim {\pi }^2∕2N^2{\tau }_D$, Eq. (69); (II) diffusive regime ${\pi }^2∕2N^2{\tau }_D\lesssim eV$, $T\lesssim 1∕{\tau }_D$, Eqs. (68, 70); (III) logarithmic regime of almost independent barriers $1∕{\tau }_D\lesssim eV$, $T\lesssim 1∕RC$, Eqs. (67, 71); and (IV) high temperature (classical) regime $eV$, $T\lesssim 1∕RC$, Eq. (66).