Negative Electronic Friction and Non-Markovianity in Nonequilibrium Systems

Abstract

We address the connection between negative electronic friction and non-Markovian effects in the nonadiabatic vibrational dynamics of molecules interacting with metal surfaces under nonequilibrium conditions. We show that a generic nonequilibrium mechanism leading to negative Markovian electronic friction, where molecular vibrations couple directly to inelastic electronic transitions, also introduces significant non-Markovian contributions to the electronic friction. To demonstrate these ideas, we investigate nonequilibrium charge transport through a molecular nanojunction containing a vibrationally coupled donor-acceptor model, where negative electronic friction reflects driving of the vibrational mode beyond standard Joule heating. By comparison to numerically exact, fully quantum hierarchical equations of motion simulations, we verify that these non-Markovian effects have a significant impact on the nonequilibrium dynamics and even on the stability of the resulting Langevin equation.

Figures (4)

• Figure 1: Three different energetic configurations of the donor-acceptor model: (a) $\Delta > 0$, (b) $\Delta <0$, and (c) $\Delta = 0$.
• Figure 2: Steady-state average vibrational excitation, $\langle N_{\text{vib}} \rangle$, as a function of bias voltage. Inset: $\langle N_{\text{vib}} \rangle$ at higher voltages for $\Delta = 100\text{ meV}$. Parameters: $\Gamma = 100$ meV, $\lambda = 10$ meV, $\Omega = 30$ meV, and $k_{B}T = 0.0258 \text{ meV}$. The solid lines are calculated fully quantum mechanically with HEOM, while the dashed, dotted, and dash-dot lines refer to results obtained from Markovian electronic friction and Langevin dynamics (EFLD), Markovian electronic friction without the stochastic force (EF), and the Ehrenfest approach (Ehr), respectively.
• Figure 3: (a) Equilibrium and nonequilibrium contributions of the Markovian friction coefficient as a function of $x$ and (b) total Markovian friction coefficient, computed at $\Phi = 0.4$ V. Other parameters are the same as in Fig. (\ref{['fig: quantum results']}). Schematics of equilibrium and nonequilibrium EHP creation processes are shown in (c) and (d), respectively.
• Figure 4: Real part of the Fourier transform of the friction, $\text{Re}\left\{\tilde{\gamma}\right\}$ and corresponding relation to the correlation function of the stochastic force with $\Phi = 0.4$ V at three different vibrational coordinates: (a) $x= 0$, (b) $x = 5$, (c) $x = 10$. Other parameters are the same as in Fig. (\ref{['fig: quantum results']}).