Molecular junctions far from equilibrium: Insights from real-time TDDFT

Time-dependent density functional theory (TDDFT) is used to simulate electronic transport through single molecules or atomic wires, sandwiched between semi-infinite metallic leads. The basic idea is to propagate the time-dependent Kohn-Sham equations upon ramping up a bias between the metallic leads. In this way, genuinely time-dependent phenomena, not accessible in the standard Landauer approach, can be addressed. The following generic features are found in the simulations: (a) After switching-on a dc bias, the current first shows some transient oscillations and then converges to the Landauer steady-state value if the junction has a smooth density of states. (b) If the long-time limit of the Hamiltonian supports two or more bound states, then undamped oscillations of the current occur whose amplitude is history-dependent. (c) Coulomb blockade manifests itself in the time-domain as a periodic charging and discharging of the central quantum dot. In all of these simulations, only electronic degrees of freedom were considered while the nuclei are clamped. To include nuclear motion in the description, current-induced forces on the nuclei need to be dealt with and, at the same time, electronic friction must be accounted for, so that the actual nuclear motion is the result of a subtle interplay between these two forces. To analyze this interplay in a sufficiently simple situation, we study the translational, vibrational, and rotational motion of a diatomic molecule immersed in a current-carrying electron liquid [1]. The approach is a combination of Ehrenfest dynamics combined with linear-response TDDFT. The electronic viscosity is accounted for by the frequency-dependence of the xc kernel. Starting from the nuclear equilibrium distance and applying a current pulse, we observe three phases of the nuclear motion: (i) acceleration due to the initial dominance of the current-induced force, (ii) stabilization upon balancing of the two forces, and (iii) deceleration caused by the friction after the end of the pulse.

[1] V.U. Nazarov, T.N. Todorov, E.K.U. Gross, PRL 133, 026301 (2024).