Vibrational Sidebands and the Kondo Effect in Molecular Transistors

Electron transport through molecular quantum dots coupled to a single vibrational mode is studied in the Kondo regime. We apply a generalized Schrieffer-Wolff transformation to determine the effective low-energy spin-spin-vibron interaction. From this model we calculate the nonlinear conductance and find Kondo sidebands located at bias voltages equal to multiples of the vibron frequency. Because of selection rules, the side peaks are found to have strong gate-voltage dependences, which can be tested experimentally. In the limit of weak electron-vibron coupling, we employ a perturbative renormalization group scheme to calculate analytically the nonlinear conductance.

Figure 1

Upper panel: ${\partial }^{2}I/\partial V^2$ vs bias and gate voltage, for ${\lambda }^2=3$, $N(0)|t_L{|}^2=0.1{\omega }_0$, $D=E_C=8{\omega }_0$, and $T=0.01{\omega }_0$. Black (white) indicates large negative (positive) values. Lower panel: conductance vs bias voltage for three values of $V_g$ corresponding to the vertical black lines ($a$, $b$, $c$) in the upper panel. The lower curve ($a$) corresponds to the PH-symmetric point $\mathcal{N}=1-{\lambda }^2{\omega }_0/E_C$.

Figure 2

Conductance vs bias voltage using perturbatively renormalized couplings. Gate voltage is tuned to the PH-symmetric point and $\alpha =4.30$, $\delta =7.54$, $T_K=1.51\times {10}^{-4}{\omega }_0$, $T^{*}=7.18\times {10}^{-8}{\omega }_0$, and $T=0.05{\omega }_0$, i.e., $\alpha /\ln (T/T^{*})=0.32$ and $\delta /\ln (T/T^{*})=0.56$, corresponding to bare parameters: ${\lambda }^2=4.5$, $N(0)|t_L{|}^2=0.1{\omega }_0$, and $D=E_C=8{\omega }_0$. Insets show the renormalized couplings $g_{00}(\omega )$ and $g_{20}(\omega )$, as well as a zoom in the conductance curve showing the satellite peak on a separate conductance scale but on the same voltage scale.