Light-induced current in molecular junctions: Local field and non-Markov effects

We consider a two-level system coupled to contacts as a model for a charge pump under external laser pulse. The model represents a charge-transfer molecule in a junction and is a generalization of previously published results [B. D. Fainberg, M. Jouravlev, and A. Nitzan, Phys. Rev. B 76, 245329 (2007)]. Effects of local field for realistic junction geometries and non-Markov response of the molecule are taken into account within finite-difference time-domain and on-the-contour equation-of-motion formulations, respectively. We find that contrary to the symmetric behavior of the pump relative to the chirp sign, the duration of the corresponding local-field pulse does depend on the chirp sign, which results in an asymmetric charge pumping. The most effective charge-pump regime is found at positive bias, contrary to Markov consideration of the previous study.

Figure 1

A sketch of local field-driven-molecular-charge pump.

Figure 2

Results of FDTD simulations for chirped pulses exciting the bowtie antenna schematically depicted in the inset of panel (a). Panel (a) shows the enhancement of the local intensity $\left|\mathrm{E⃗}\right|{}^2$ detected in the gap of the bowtie antenna as a function of the incident frequency. Panel (b) presents a local field component of the electric field along the axis of symmetry of the structure, $E_x$, as a function of time for two chirp rates at the plasmon resonance, ${\omega }_0=2.057$ eV: black solid line for ${\Phi }^{\text{'}\text{'}}({\nu }_0)=-3000$ fs${}^2$ and red dashed line for ${\Phi }^{\text{'}\text{'}}({\nu }_0)=3000$ fs${}^2$. Panel (c) shows the amplitude of the local field in the frequency domain (note that it is independent of the phase rate). Panel (d) represents the phase of the local field in the frequency domain at two chirped rates: black solid line for ${\Phi }^{\text{'}\text{'}}({\nu }_0)=-3000$ fs${}^2$ and red dashed line for ${\Phi }^{\text{'}\text{'}}({\nu }_0)=3000$ fs${}^2$.

Figure 3

Time dependence of charge pumped through the junction, Q(t), see Eq. (12) for several chirp rates. Shown are results for (a) ${\Phi }^{\text{'}\text{'}}=2000$ and $-2000$ fs${}^2$ without energy transfer, $B({\varepsilon }_{21})=0$ (red solid line and blue dashed line, respectively), and taking into account energy transfer term, $B({\varepsilon }_{21})=0.1$ eV (red dash-dotted line and blue dotted line, respectively) and (b) ${\Phi }^{\text{'}\text{'}}=10\hspace{0.5em}000$ and $-10\hspace{0.5em}000$ fs${}^2$ for $B({\varepsilon }_{21})=0.1$ eV and $\mu {\mathcal{E}}_0=0.03$ (red solid line and blue dashed line, respectively) and $\mu {\mathcal{E}}_0=0.003$ eV (red dash-dotted line and blue dotted line, respectively).

Figure 4

Charge pumped through the junction during a pulse vs. chirp rate: (a) total charge, i.e., the integral of Q(t), see Eq. (12), over the local-field-pulse duration and (b) asymmetry in charge transfer between positively and negatively chirped incoming laser pulses, $\Delta Q\equiv Q(|{\Phi }^{\text{'}\text{'}}|)-Q(-|{\Phi }^{\text{'}\text{'}}|)$. Shown are results with $B({\varepsilon }_{21})=0.1$ eV, blue dashed line with triangles, and without energy transfer, $B({\varepsilon }_{21})=0$, red solid line with circles.

Figure 5

Dependence of charge pumping on the molecule-contact states hybridization at $\mu {\mathcal{E}}_0=0.03$ eV. Shown are (a) charge pumped through the junction during a pulse vs. electronic escape rate for chirp rate ${\Phi }^{\text{'}\text{'}}=10\hspace{0.5em}000$ fs${}^2$ (red solid line) and $-10\hspace{0.5em}000$ fs${}^2$ (blue dashed line) and (b) normalized transferred charge buildup (i.e., charge normalized to the total charge transferred during a pulse) vs. time for chirp rate ${\Phi }^{\text{'}\text{'}}=10\hspace{0.5em}000$ fs${}^2$ and ${\Gamma }_{11}^L={\Gamma }_{22}^R=0.1$ eV (red solid line) and $1$ eV (blue dashed line). The red line in panel (b) is the same as the solid red line in Fig. 3b.

Figure 6

Dependence of charge pumping on bias. (a) Total excess charge pumped through the junction during a pulse vs. bias for chirp rate ${\Phi }^{\text{'}\text{'}}=10\hspace{0.5em}000$ fs${}^2$ (red solid line) and $-10\hspace{0.5em}000$ fs${}^2$ (blue dashed line). (b) Excess charge buildup (normalized to the total excess charge transferred during a pulse) vs. time at chirp rate ${\Phi }^{\text{'}\text{'}}=10\hspace{0.5em}000$ fs${}^2$ for $V_{\mathrm{sd}}=-1$ V (blue dashed line), $0$ V (red solid line), and $1$ V (black dotted line). Here, ${\Gamma }_{11}^L={\Gamma }_{22}^R=0.5$ eV. The red line in panel (b) is the same as the solid red line in Fig. 3b.