Nonequilibrium electron transport in strongly correlated molecular junctions

We investigate minimal molecular junction models to account for zero-bias anomaly and the inelastic transport by discrete molecular phonons. Nonlinear transport calculations with the imaginary-time nonequilibrium formalism shows that (highest-occupied-molecular-orbital)–(lowest-unoccupied-molecular-orbital) model with Anderson-Holstein interaction produces significant cotunneling conductance peaks in the vicinity of Kondo resonance, mediated by many-body resonance assisted by phonons at bias equal to the phonon frequency. Destruction of the resonance leads to negative-differential resistance in the sequential tunneling regime.

Figure 1

Schematic energy diagrams for isolated molecular configurations with respect to source/drain reservoirs under bias $\Phi$. (a) Single-orbital model with one electron occupying the level at energy ${ϵ}_d$. Phonon excitation level is marked by a dashed line. (b) With an extra electron, the energy level is pushed up ${ϵ}_d+U\sim U/2$ by Coulomb repulsion. (c) HOMO-LUMO model with the level spacing $\Delta$. (d) Charge-excited state. With $\Delta ⪢U/2$, the LUMO level is nearly empty.

Figure 2

(Color online) Differential conductance in single-orbital Anderson-Holstein model. (a) Conductance with large el-ph coupling $\left(2g_{\text{ep}}^2/{\omega }_{\text{ph}}>U\right)$ in the charge-Kondo regime. With increasing $U$ the mass-renormalization is reduced. (b) Spin-Kondo regime recovered with large $U$. (c) Larger phonon frequency at fixed $g_{\text{ep}}^2/{\omega }_{\text{ph}}=1$. (d) Comparison of the $g_{\text{ep}}=0$ limit to Ref. 14 and the negative $U$ model.

Figure 3

Differential conductance in the HOMO-LUMO model with Anderson-(Jahn-Teller) Holstein model. (a) Conductance peaks for the Kondo anomaly and inelastic cotunneling at $\Phi ={\omega }_{\text{ph}}$. Dashed line $\left(g_{\text{ep}}=0\right)$ confirms that the large bias structures are due to phonon. (b) Spectral functions for bias $\Phi =0,\dots ,1$ with the interval 0.2. Curves are shifted for clarity. With increasing $\Phi$, the Kondo peak disappears and the Coulomb peak (peak $A$) shifts to phonon excitation energy (peak $B$). As $\Phi \to {\omega }_{\text{ph}}$, new resonance (peak $C$) emerges inside the voltage window and contributes to the cotunneling conductance peak at $\Phi \approx {\omega }_{\text{ph}}$. Dashed line is for $\beta =20$. (c) Conductance in pure el-ph limit. A strong negative-differential-resistance effect appears at $\Phi /2={\omega }_{\text{ph}}$ in the sequential tunneling regime. (d) Disappearance of the resonance (dashed line at $\Phi /2={\omega }_{\text{ph}}$) leads to the NDR.

Figure 4

(a) Phonon spectral function of HOMO/LUMO model for parameters of Fig. 3a. With increasing $\Phi$, higher phonon quanta are created by absorbing the chemical potential difference in the electron reservoirs. (b) Similar results for Fig. 3b.