Transport theory through single molecules : Jahn-Teller effect: breakdown of Born-Oppenheimer picture and adiabatic time-dependent driving out of equilibrium

摘要

In this thesis, we theoretically investigate the interplay of the vibrational, charge and spin degrees of freedom characteristic of complex dimer molecules. The influence of the pseudo Jahn-Teller effect, well known in molecular chemistry, is investigated in the new situation where an electric current is driven through a molecule. Furthermore, we present a new theory to describe time-dependent adiabatic transport through such type of molecular quantum dot systems, accounting for strong intra-molecular interactions, adiabatic driving and non-equilibrium bias. Based on this, we propose a new tool for spectroscopy of such complex quantum dots using the periodic modulation of external electric fields. A molecular quantum dot device consists of a quantum dot or single molecule connected to two metallic contacts such that a current can be driven through the system. One reason for the great experimental as well as theoretical interest in such devices is the hope to make the next step in the miniaturization of informational technology devices, since molecules are only a few nanometers small. Besides the aspect of size reduction, molecules exhibit a rich spectrum of quantized degrees of freedom such as charge, vibrations and spin. These and even their interplay can be used to manipulate the charge flow through the device. At present, the purpose of experiments and theories is to understand how such molecular quantum dot systems behave in transport setups. Experiments need to overcome the difficulties in attaching nanometer-sized systems to macroscopic metallic leads in a controllable and reproducible way. Here, theory can provide crucial clues about the origin of observed features in the current and to predict how special, intrinsic properties of the studied molecule influence the transport current in a particular way. This motivates the study undertaken in this thesis. We develop a theory which allows us to describe the transport current through such systems in the presence of non-equilibrium bias and even time-dependent modulations of externally controllable parameters. The driving of the latter induces a retarded response of the molecule, which crucially depends on the characteristic details of the molecule and its coupling to the leads and can therefore be used e.g. as a spectroscopic tool. The method used and further developed in this thesis is the generalized master or kinetic equation approach for the reduced density operator of the dot, explicitly eliminating the degrees of freedom in the metallic leads to which it is weakly coupled. In comparison to other approaches, it has several advantages. For instance, interactions on the dot are taken into account non-perturbatively. Apart from electron-electron interaction, also non-trivial electron-vibration interaction (e.g., anharmonic and (pseudo) Jahn-Teller coupling) is correctly treated, which is very hard to do otherwise. Furthermore, the method goes beyond the linear response, which is mandatory since the experimentally applied electric fields can drive the system far from equilibrium. The coupling to the leads is taken into account using a systematic expansion in the tunnel amplitudes using the real-time diagrammatic approach combined with the technique of Liouville superoperators. This yields general yet compact expressions for the contributions of the expansion. One of the major theoretical advances made in this work is the explicit generalization of this transport theory to adiabatically slow modulations of external parameters for arbitrary molecular models. To this end, we perform a systematic "adiabatic expansion" of the transport rates in orders of the modulation frequency. We present diagram rules to write down the transport kernels and show that the resulting integral expressions can be obtained by additional rules from those already known from the stationary case. This transport theory is then applied to two specific molecular models. First, we consider a rather complex model of a dimer molecule and calculate the transport current through this system in the absence of time-dependent modulations. In particular, we investigate the influence of the interplay of vibrational, charge and, if the molecule exhibits a finite spin moment, spin degrees of freedom on the transport current. We show that this interplay leads to characteristic fingerprints in the current, from which one can extract valuable information about the molecular device, and even allows us to control molecular properties. Recently, some of these predicted results have also been confirmed experimentally. In a second system we consider only a single electronic level but allow for adiabatically slow time-dependent modulations of the applied electric fields. We show that the corrections due to the system's retardation carry valuable information about the molecular device and propose a new spectroscopic tool for transport through devices on the nanometer scale.