Lindblad theory for incoherently-driven electron transport in molecular nanojunctions

TL;DR

The paper tackles electron transport in nanojunctions driven by incoherent light, incorporating Coulomb interactions and radiative processes. It develops a Lindblad quantum master equation framework under the Born–Markov and secular approximations to derive general expressions for transient and stationary electron and photon currents, analyzed for single-site and two-site configurations with driving rate $W$, spontaneous emission $\gamma_r$, and Coulomb interaction $U$; bias enters through $\mu_L=\varepsilon_F+V_b/2$ and $\mu_R=\varepsilon_F-V_b/2$. Key contributions include showing that the Lindblad model reproduces negative differential conductance, current-induced light emission, and light-assisted transport, and it predicts light-driven currents when $W$ is comparable to lead rates $\Gamma_L$, $\Gamma_R$, with clear physical interpretation in terms of population dynamics between ground and excited states. The work also outlines extensions to include coherent light–matter interactions and other degrees of freedom, offering a simple, positivity-preserving platform for exploring optoelectronic effects in molecular nanojunctions with potential applications in light-controlled electronic devices.

Abstract

We study electron transport in molecular nanojunctions that are driven by incoherent radiation using Markovian quantum dynamics based on the Lindblad quantum master equation. General expressions for the transient electron and photon currents between system and reservoir are derived. For experimentally relevant nanojunction configurations that include on-site Coulomb repulsion, electron tunneling, spontaneous photon emission, and incoherent driving, we show that Lindblad theory can reproduce stationary conductance features reported in the literature such as negative differential conductance, Coulomb blockade, and current-induced light emission. Light-induced currents are predicted for two-site configurations with ground-level tunneling when the incoherent driving rate is comparable with the transfer rate to contact electrodes. Model extensions to include coherent light-matter interaction are suggested.

Figures (4)

• Figure 1: Driven single-site conductance. (a) Nanojunction scheme with a two-level single site incoherently pumped at rate $W$ and spontaneously emitting photons with flux $j_r$. (b) System energybasis $\{ \ket{\epsilon},\omega_\epsilon \}$. (c) Conductance $G$ as a function of bias voltage $V_b$ for the driven (green line $W=\Gamma_L$) and undriven (black line $W=0$) system. (d) Emitted photon flux $j_{\rm r}$ for the same conditions as in panel (c). Vertical lines represent resonances $\mu_l = \omega_{\epsilon,\epsilon'}$. System parameters are $\{ \varepsilon_F, \varepsilon_g,\varepsilon_e,U \} = \{ 0.5,0.5,1.5,0.1 \}$ eV, $T_0 = 300$ K and $\{ \gamma_r, \Gamma_L, \Gamma_R \} = \{ 1, 10^3,10^3\}$ GHz.
• Figure 2: Scaling of driving effect. Difference of conductance peak $\Delta G$ induced by incoherent driving with respect to the undriven value for the two-level single-site. Conductance peaks associated to transition frequencies $\omega_{2,1}$ (solid lines) and $\omega_{4,3}$ (dashed lines) for different value of Coulomb repulsion $U$. The rest of parameters are the same as in Fig. \ref{['fig:single_site']}.
• Figure 3: Negative conductance. (a) Nanojunction scheme of two-sites system with coherent tunneling $t_g$ between the left and the right ground levels, separated in energy by $\lambda V_b$. (b) Current $I$ as a function of the bias voltage $V_b$. Solid curves show Lindblad predictions for $\lambda =0$ (black curve) and $\lambda = 0.4$ (green curve). Experimental results taken from Ref. perrin2014large are shown in circles, normalized to $\lambda = 0.4$ theory curve. $t_g=0.02$ eV, $T_0= 80\,{\rm K}$ with other parameters as in Fig. \ref{['fig:single_site']}.
• Figure 4: Incoherent driving suppresses Coulomb blockade. (a) Nanojunction scheme of a driven two-sites system with coherent tunneling rate $t_g$ between the ground orbitals under pumping. Conductance $G$ as a function of bias $V_b$ and Coulomb energy $U$ when the system is (b) undriven and (c) driven at rate $W=\Gamma_L$. Parameters are $t_g=0.01$ eV with other parameters as in Fig. \ref{['fig:single_site']}.