T. Damker

Spin Hall-effect in two-dimensional hopping systems

A two-dimensional hopping system with Rashba spin-orbit interaction is considered. Our main interest is concerned with the evolution of the spin degree of freedom of the electrons. We derive the rate equations governing the evolution of the charge density and spin polarization of this system in the Markovian limit in one-particle approximation. If only two-site hopping events are taken into account, the evolution of the charge density and of the spin polarization is found to be decoupled. A critical electric field is found, above which oscillations are superimposed on the temporal decay of the total polarization. A coupling between charge density and spin polarization occurs on the level of three-site hopping events. The coupling terms are identified as the anomalous Hall-effect and the recently proposed spin Hall-effect. Thus, an unpolarized charge current through a sheet of finite width leads to a transversal spin accumulation in our model system.

Phonon hopping in disordered systems

Abstract Anharmonic interactions between localised vibrational states and extended low-energy phonons can lead to thermally activated hopping of the localized states. Such a mechanism has been proposed to explain the thermal conductivity behaviour of dielectric glasses and amorphous films above the so-called “plateau temperature”. We derive rate equations for the occupation numbers of the localized states using the anharmonic coupling constant as an expansion parameter. The calculated localized state life times increase with the energy of the state, in accordance with recent experiments, as well as with the fracton hopping model (the functional form differs though). This is in contrast to another model, namely the model of diffusive transport by extended but non-propagating modes of Allen and Feldman. Our model, furthermore, predicts an increase of the conductivity with increasing frequency of an AC temperature gradient, again in contrast to the diffusive transport model.

Spin transport in disordered two-dimensional hopping systems with Rashba spin-orbit interaction

The influence of Rashba spin-orbit interaction on the spin dynamics of a topologically disordered hopping system is studied in this paper. This is a significant generalization of a previous investigation, where an ordered (polaronic) hopping system has been considered instead. It is found, that in the limit, where the Rashba length is large compared to the typical hopping length, the spin dynamics of a disordered system can still be described by the expressions derived for an ordered system, under the provision that one takes into account the frequency dependence of the diffusion constant and the mobility (which are determined by charge transport and are independent of spin). With these results we are able to make explicit the influence of disorder on spin related quantities as, e.g., the spin life-time in hopping systems.

Heat conduction in disordered anharmonic systems

Abstract The heat transport of (2D) disordered dielectric model systems in the high-temperature regime is studied in two respects. Firstly, we find that the heat conductivity due to hopping of localized phonons increases linearly with the temperature up to a “saturated” value, which emerges at certain strengths of the coupling with the extended phonons. Secondly, third- or fourth-order anharmonicity is shown to lower or enhance the conductivity, respectively, which can be understood by weakening or strengthening of the stiffness of the bonds in the system.

Replica-trick approach to percolation networks with central and bond-bending forces

For the first time, a self-consistent effective medium is set up for central-force percolation networks with bond-bending forces, which do not allow the standard technique, the HCPA, to be used. By means of the replica trick, for two-dimensional bond-dilute triangular lattices with central and bond-bending forces, an effective lattice potential with complex, frequency dependent force constants is derived. The density of vibrational states is calculated and compared with corresponding results obtained by means of other methods.