ABSTRACT
Electronic transport through molecular wires and junctions has been attracting much attention in past years due to remarkable experimental and theoretical advances. Statistically reliable measurements of single molecule junctions at steady state are being performed and analyzed, revealing a wealth of unique physical characteristics of non-equilibrium transport through molecules. Much less is known about the transient dynamics in molecular junctions following excitation by external time dependent fields. Anticipation for new physical phenomena as well as technological breakthroughs associated with electronic devices operation at fast intra-molecular (terahertz) frequencies drives experimental efforts along this direction, based on irradiation of the junctions with periodic sequences of pulses. In this chapter, we address one of the important challenges in the theory of field-driven
molecular junctions, which is the need to account for direct excitations of the leads (plasmons, e-h pairs, phonons) and to unveil their role in the charge transport processes. First we consider the long range nature of excitations in the leads and map them onto finite range time-dependent interactions between the molecule and the leads. Then we focus on implementation of quantum scattering theory to calculations of steady state currents in the presence of transient driving fields of general shape and intensity. Generalized transport equations are rigorously derived and approximations to these equations are shown to lead to simpler formulas (generalized Tien-Gordon formulas) for photo-assisted currents. Applications to analytically solvable models are given, demonstrating the basic principles of current enhancement or suppression by time-periodic, but otherwise general, driving fields. 7.1 IntroductionElectronic transport through molecular wires and junctions has been attracting much attention in past years due to remarkable experimental and theoretical advances [1-18]. The field has reached a level where statistically reliable measurements of single molecule junctions can be performed in order to explore the effect of various parameters on their conductance properties [19-25]. Along with advances in the theoretical understanding and the modeling of these systems [26], the unique physics of non-equilibrium transport through molecules is revealed. Yet, our current understanding of molecular junctions is primarily based on steady state measurements under a fixed bias potential, where the intricate many-body electronic and nuclear dynamics is essentially averaged by the measurement process. The dynamical response of molecular junctions to transient perturbations leading to charge and energy transfer within the molecule or the leads, or between the molecule and the leads, is much less explored. The main reasons for this gap of knowledge have been experimental difficulties to perform controlled time resolved measurements at the single junction level. The anticipation is that once the ultrafast quantum dynamics in molecular junctions could be experimentally probed, new and useful phenomena can be discovered. Indeed, while the prime interest in theoretical understanding of these systems is derived from their challenging complexity (being open many body
quantum systems, out of equilibrium), an essential motivation to understand the transient behavior of molecular junctions is technological. Standard fast electronic components are operating in the gigahertz frequency regime. Molecular components with their characteristic electronic resonances and vibronic coupling time scales, are expected to be switchable on a much shorter (sub-picoseconds) time scale. Hence molecular based devices could in principle operate in the terahertz regime, with an expected improvement of three orders of magnitude in the speed of operation.Phenomena associated with irradiation of tunneling junctions have been studied experimentally for several decades, primarily for continuous wave (ac) and in the microwave regime. Photo-assisted transport [26] was identified and analyzed in superconductors [27, 28] semiconductors [29], STM junctions [30], and carbon nanotube quantum dots [31]. In recent years, experimental efforts were focused on laser excitations of nano-junctions in the optical frequencies regime [32-42], and the role of field enhancement by surface plasmons excitations at the metallic nano-contacts was elucidated [35-40]. However, in single molecule junctions the signatures of specific molecular electronic and vibronic excitations, as well as specific local excitations at the lead near the molecule-lead contacts were not yet characterized experimentally. Indeed, such studies require an uncommon combination of molecular electronics setups along with ultra-fast laser optical tools, and the need to overcome or filter out effects of local heating [43-48] which may obscure transient dynamical effects. Yet, it is very likely that attempts to realize such experiments would appear [49], motivated by the scientific and technological interest in detecting features of the combined molecule-leads dynamical response to transient excitations with femtosecond laser pulses.
