Pair Tunneling through Single Molecules

By a polaronic energy shift, the effective charging energy of molecules can become negative, favoring ground states with even numbers of electrons. Here we show that charge transport through such molecules near ground-state degeneracies is dominated by tunneling of electron pairs which coexists with (featureless) single-electron cotunneling. Because of the restricted phase space for pair tunneling, the current-voltage characteristics exhibit striking differences from the conventional Coulomb blockade. In asymmetric junctions, pair tunneling can be used for gate-controlled current rectification and switching.

Figure 1

(a) Level configuration of the negative-$U$ model. Shown are the one-particle energies for the singly occupied dot (${\epsilon }_d$), the doubly occupied dot (${\epsilon }_d+U/2$), and the energy for which holes can propagate through the doubly occupied dot (${\epsilon }_d+U$). The right panel illustrates the relevant types of processes: (b) cotunneling, (c),(d) pair tunneling.

Figure 2

Conductance as a function of gate voltage, based on our analytical results. (a) Linear conductance $G$ for several temperatures. The conductance curve exhibits a featureless background due to cotunneling and a distinct peak of constant height and width $\sim T$ due to pair tunneling. (b) Conductance for several bias voltages at $T=1.0\times {10}^{-3}|U|$ for a symmetric junction. With bias voltages $eV\gg k_{B}T$, the width of the double peak is given by $eV$.

Figure 3

Current as a function of bias and gate voltage for (a) a symmetric junction with ${\Gamma }_L={\Gamma }_R=k_{B}T$, (b) an asymmetric junction with ${\Gamma }_L=0.1k_{B}T$, ${\Gamma }_R=10k_{B}T$, and with $k_{B}T=0.5\times {10}^{-3}|U|$. For asymmetric junctions, one observes the rectification effect due to pair tunneling.

Figure 4

Stability diagram for the ground-state occupation $n_d$ and dominant transport modes as a function of gate and bias voltages for a symmetric device with negative $U$.