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Effects of vibration on charge transport through molecular bridges

M. Hartung

Diplom (equiv. Master) Thesis, University of Regensburg, August 2004

Just before the turn of the century the first measurement of an electrical current through a single molecule has been reported [1]. This experiment brought to extreme actuality the vision of scaling the size of transistors, building blocks of every electronic device, down to the molecular scale. However, it is the fundamental implication opened by molecular scale devices which triggered a number of new experiments aiming at understanding to which extent single molecules with their internal quantum complexity could be accessed via a macroscopic investigation, as it is the case for electric currents (see Chapter 1). Theory is not less challenged. A current of few a μA flowing through a nanometer size device would classically imply enormous electric fields (∼ 108 V/m) and large amounts of dissipated power (104 W/cm2). The solution to this puzzle has its roots in the 1957 paper by Rolf Landauer describing quantum transport as a scattering process [2]. Many groups have thus applied this idea to single molecules sandwiched between two metallic leads by merging (i) electronic structure calculations for the molecular region (obtainable e.g. with density functional theory accuracy), and (ii) the machinery of functions (in the spirit of the mesoscopic electron system theory).
It is however widely realized that molecules, in contrast to solid state devices or even mesoscopic scale devices, do have mechanical degrees of freedom which are definitely excited in transport processes even at very low temperatures. This results in an enrichment of the electronic quantum spectrum of a certain molecular device and opens the door to completely new phenomena. The idea of fully accounting for the effect of vibrations and molecular charge transport is a field in its infancy which has proven itself as a multidisciplinary challenge at the border between physics and chemistry.
This thesis tackles with full quantum accuracy the simplest model capturing the physics of a vibrating molecular bridge, namely a single level atom in between two metallic leads (Fig. 2.2 illustrates a sketch of the problem at hand). The full apparatus of the nonequilibrium Keldysh functions has been implemented to account for the following experimentally relevant physical conditions:

  1. Finite bias voltages
    The case of a finite bias potential at the ends of a molecular conductor (via the contact with two metallic pads) has been studied. The full non-linear response regime has been investigated with the help of the powerful tools of Keldysh functions (Chapter 3). Such techniques have been reviewed and applied to the determination of physical quantities such as the current, the differential conductance, the shot noise, and the dissipated power (Chapter 5).
  2. Self-consistent calculations
    Both, electron and phonon dynamics have been calculated self-consistently to the leading order of the self-energy functional (Chapter 4). Already existing approaches for the electronic self-consistency [3] and the phononic one [4] have been formulated for the case of bond-stretching electron-phonon coupling (implementing the idea that ionic motion not only alters the ion onsite energy but the overlap of neighboring atomic orbitals; Chapter 2).
  3. Environmental effects
    In order to simulate the loss of energy in the scattering region a bosonic bath has been connected to the phonon mode (Chapter 2). This bath influences not only the phonon mode, but can be recognized in the electronic degrees of freedom.
Our results are then obtained within a numerical approach presented in Chapter 6. We discuss in Chapter 7 the influence of different lead-molecule coupling regimes: strong, weak and asymmetric coupling. The weak coupling regime is however limited to cases in which correlation effects like Coulomb blockade and Kondo physics can be excluded. Furthermore, we point out the differences between the above mentioned bond-stretching and the onsite electron-phonon coupling mechanisms. We also show the effects caused by the heated phonon mode, due to the applied bias, back onto the electronic degrees of freedom. Finally we characterize the noise spectrum and show the different implication given by the electron and phonon dynamics.

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