School of Chemistry, Faculty of Exact Sciences

E-mail: gcohen@tau.ac.il

Phone: +972-3-6406583

*E-mail: **odedhod@tau.ac.il*

*Cell phone number: 050-5311972*

**Non-Equilibrium Electron Dynamics in Open Quantum Systems **

Over the past decade, the study of electron dynamics in open quantum systems out of equilibrium has gained growing attention within the molecular electronics community. Many important aspects of molecular junctions have been addressed including the characterization of transient current dynamics, dynamical response to time-dependent bias voltages, optically induced current variations and non-equilibrium thermodynamics in externally driven systems. Despite the many developments made in the field, understanding dynamical effects in molecular junctions remains a major theoretical, computational, and experimental challenge. This challenge needs to be addressed at a fundamental level to enable the future design of molecular-based electronic components with fast response times.

During the past five years our group has been developing the driven Liouville-von Neumann (DLvN) equation of motion (EOM) for simulating time-dependent electron transport in molecular junctions. Within this approach the junction is represented by a fully atomistic finite model system consisting of two (or more) sufficiently large lead sections bridged by an (extended-) molecule. Open boundary conditions are enforced by augmenting the Liouville-von Neumann EOM with an appropriate non-unitary source/sink term. The latter continuously drives the leads state occupations toward the equilibrium Fermi-Dirac distribution of the (implicit) electronic reservoir to which each lead is coupled. With appropriate choices for the chemical potential and the electronic temperature of the various reservoirs a non-equilibrium charge-polarized state, characterized by charge accumulation and depletion near the corresponding junction model edges, is achieved. This, in turn, results in well-defined voltage and electronic temperature gradients that induce dynamic current flow through the system. Recently, we have replaced the single driving rate serving as a fitting parameter in the original theory by a set of single-particle lead state broadening factors that are extracted explicitly from the self-energy of the corresponding reservoir. This eliminates the need for any fitting procedure, resulting in an autonomous methodology that can be readily implemented within existing packages in a "black box" fashion.

The performance of the DLvN approach was demonstrated for simple molecular junctions based on tight-binding (TB) Hamiltonian models as well as for explicit non-orthogonal basis-set representations based on extended-Hückel (EH) theory. The dynamics obtained by the DLvN EOM was shown to conserve density matrix positivity and to obey Pauli's exclusion principle. Furthermore, the method was shown to accurately describe dynamic currents in junctions subjected to time-dependent perturbations.

The success of the DLvN approach suggests that it offers a computationally efficient and physically motivated methodology for time-dependent charge transport in molecular junctions. Furthermore, the simplicity of the underlying theory implies transferability to advanced density functional theory-based electronic structure descriptions that will provide higher accuracy predictions. Our future work in this field will focus on the implementation of the developed methodology within density functional theory and density functional tight-binding based computational codes and its application to the study of time-dependent transport phenomena in realistic molecular junctions. Furthermore, we will use it to study non-equilibrium thermodynamics in open quantum systems.

This project is performed in collaboration with Prof. Leeor Kronik (Weizmann), Prof. Abraham Nitzan (TAU, U. Penn), Prof. Thomas Frauenheim (BCCMS), Prof. Thorsten Hansen (U. Copenhagen), and Prof. Jeffrey B. Neaton (Berkeley).

**Coherent Electronic Transport in Molecular Interferometers **

In recent years, the flourishing field of molecular electronics has demonstrated many breakthroughs in the ability to control the electronic transport through individual molecules. As the size of the active molecular components becomes comparable to the coherence length of the transported electrons quantum interference effects may dictate the conductance properties of the molecular junction. This allows for the design of novel electronic components based on carefully tailored molecular junctions, where the geometry of the molecule as well as external perturbations may be used to manipulate the relative phases of the current carrying electrons resulting in unique transport characteristics.

Of special interest are molecular rings, which may be viewed as nanoscale counterparts of mesoscale interferometers. Nevertheless, due to the unrealistically large magnetic fields required to fulfill even a single Aharonov-Bohm period, it is commonly believed that magnetic fields cannot be used as practical controls for the transport properties of molecular rings. With this respect, we have been able to identify conditions under which high sensitivity of the electronic transmittance through molecular rings can be obtained as a response to realistic magnetic fields. These include: (i) low coupling between the ring and the leads; (ii) asymmetric coupling geometry; (iii) the existence of degenerate electronic states carrying opposite angular momentum; and (iv) low temperature to assure small dephasing. We have demonstrated this concept on several molecular rings showing how various junction geometries may result in distinctive transport properties. Furthermore, by relating the circular component of the current flowing through a molecular ring to the corresponding induced magnetic field we have given a unique definition of the circular currents developing in quantum ring structures under external bias voltages. Using this definition we have been able to show how different parts of multi-ring molecular systems may present opposing circular currents of magnitudes far exceeding the total. Current traversing the ring thus opening the way for magnetic field control of molecular transport and geometry.