Distribution of residence times as a marker to distinguish different pathways for quantum transport

Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunneling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper we use the quantum master equation to consider the following questions. (i) Given that an electron has tunneled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events (the tunneling path)? (ii) Given that an electron tunneled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events ($a$ tunneling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between the electron tunneling path and an electron tunneling path.

Figure 1

Residence time distributions $w\left(\tau \right)=\left({\tilde{J}}_{10}^D\right|e^{{\mathcal{L}}_0\tau }\left|J_{01}^S\right)$ for an electron and the electron. The parameters used in the calculations are $\epsilon =-0.3\mathrm{\Gamma },U=0.5\mathrm{\Gamma },{\mu }_{S/D}=\pm 0.5\mathrm{\Gamma }$, and $T=2.585\mathrm{\Gamma }$.

Figure 2

Temperature dependence of the average residence time computed for various values of electron-electron repulsion $U$. The parameters used in the calculation are $\epsilon =-0.3\mathrm{\Gamma }$ and ${\mu }_{S/D}=\pm 0.5\mathrm{\Gamma }$.