Phonon Rabi-assisted tunneling in diatomic molecules

We study electronic transport in diatomic molecules connected to metallic contacts in the regime where both electron-electron and electron-phonon interactions are important. We find that the competition between these interactions results in unique resonant conditions for interlevel transitions and polaron formation: the Coulomb repulsion requires additional energy when electrons attempt phonon-assisted interlevel jumps between fully or partially occupied levels. We apply the equations of motion approach to calculate the electronic Green’s functions. The density of states and conductance through the system are shown to exhibit interesting Rabi-like splitting of Coulomb blockade peaks and strong temperature dependence under the interacting resonant conditions.

Figure 1

Schematic representation of the model system. The electron-phonon interaction connects the local sites $({ϵ}_{\alpha }<{ϵ}_{\beta })$ via phonons of frequency ${\omega }_0$ with coupling constant $\lambda$.

Figure 2

(Color online) Total density of states (DOS) vs energy and gate voltage for a two-site molecule as in Fig. 1. In units of $\Delta ϵ$, the parameters are: $\lambda =0.2$, $k_{B}T=0.015$, $t_{\alpha }=t_{\beta }=0.1$, $U=0.4$, and $\hslash {\omega }_0=0.6$. The Fermi level is set at zero energy; ${ϵ}_{\alpha }=1$ and ${ϵ}_{\beta }=2$ for $V_g=0$. For $V_g\approx 1.6–2.4$, the DOS exhibits a clearly split feature at $\omega -{ϵ}_{\alpha }\approx 1$ produced by the strong phonon-assisted level coupling. The inset shows the DOS at $V_g=2$, indicated by the dashed line in the main figure.

Figure 3

(Color online) Conductance vs gate voltage for $k_{B}T∕\Delta ϵ=0.015$, 0.10, and 0.15. Temperature has a strong effect on the resonance condition, enhancing the Rabi splitting of the third Coulomb blockade peak $(V_g-{ϵ}_{\alpha }\simeq 1)$ at higher $T$ and exposing the shoulder in second peak. The inset shows inelastic contributions for the conductance. The highest peak is due to phonon emission. The dashed line shows results for $U=0$ and ${\omega }_0=1$. Curves offset for clarity.

Figure 4

(Color online) Conductance through the molecule at around the third Coulomb blockade peak as a function of interaction $U$ and gate voltage $V_g$ for $k_{B}T=0.015\Delta ϵ$. The inset indicates phonon emission and absorption processes involved.