H. Böttger

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.

On the use of separation of scales in the solution of hopping transport problems

Abstract In the paper we show how separation of scales can be used for the calculation of the critical hopping length and its dispersion in the whole range of frequencies. The separation of scales that we use is already present in the pair approximation of Pollak and Geballe. In fact, with decreasing frequency the hopping length increases compared with the localization length. If we use this fact, we obtain a general method that can be applied to systems with and without inelastic scattering both close to and far from equilibrium. We demoiistrate the applicability of the method for several examples and discuss the relation of the method to our previous effective-medium method.

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.

Non-diffusive heat transport and chaos in non-linear dielectric lattices

Deviations from Fouriers law emerge from numerical simulations of various lattices modelling solids. Non-integrability and moreover chaotic motion are considered to be conditions of normal heat conduction. However, these are not sufficient conditions. Using a simple model as an example, we show that non-diffusive transport could occur even in the presence of disorder in the lattice and completely chaotic dynamics. We conclude that diffusive and non-diffusive transport can coexist, while the system is moving along a chaotic trajectory in the phase space.

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.

Random-resistor network description for hopping transport in the presence of Hubbard interaction

On the basis of the linearized rate equations for hopping electrons in the presence of Hubbard interaction we derive a random resistor network analogue of the transport equations. In contrast to the ordinary Miller–Abraham network our network has two nodes per site. The occurrence of the second node is related to the capability of the system to propagate excitations, and thus is characteristic for the interacting situation. Our random resistor network can be used for the investigation of the transport properties in alternating electric fields and for the investigation of properties of excitations. The network analogue is applied to the calculation of the dynamical conductivity in the nearest-neighbour hopping regime for all Hubbard-interaction strength.

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.

LATTICE DYNAMICS OF AN F-TYPE ICOSAHEDRAL QUASICRYSTAL

By using a matrix-continued fraction approach we calculate the density of vibrational states (DOS) of a tiling model based on the 6D face centered lattice. Parameters of the Lennard-Jones pair interaction are obtained from relaxation calculations. With a ternary decoration the tiling was found to be stable. The DOS was approximated by weighting the local DOS (LDOS) of the allowed vertex configurations by their relative frequencies in the infinite tiling. These frequencies were obtained by using extended deflation rules. Results of this approach are compared to exact finite cluster calculations and an embedded cluster approach. We find the DOS to consist of a single band (in our resolution) and a rich structure at higher frequencies.

On the structure of the energy distribution function in the hopping regime

The impact of the dispersion of the transport coefficients on the structure of the energy distribution function for charge carriers far from equilibrium has been investigated in the effective medium approximation for a model density of states. The investigations show that two regimes can be observed in energy relaxation processes. Below a characteristic temperature the structure of the energy distribution function is determined by the dispersion of the transport coefficients. Thermal energy diffusion is irrelevant in this regime. Above the characteristic temperature the structure of the energy distribution function is determined by energy diffusion. The characteristic temperature depends on the degree of disorder and increases with increasing disorder. Explicit expressions for the energy distribution function in both regimes are derived for a constant and an exponential density of states.