The anomalous low temperature properties of glasses are commonly believed to originate from localized quantum-mechanical two-level tunneling systems, which couple to phonons and other elementary excitations, as well as to external fields. Although a broad range of experimental observations can be explained in terms of this idea, the microscopic nature of these two-level systems is generally unknown. Therefore, another class of substances is often considered, namely mixed crystals. Here, the microscopic nature of the tunneling units is clear. A substitutional defect (e.g. a Li defect in a KCl host crystal) is located in one of several off-center positions, and the defect can move from one potential well to the other by quantum tunneling. Mixed crystals thus allow an immediate investigation of the physics of tunneling units.
The research activities of our group deal with different aspects of tunneling systems, in particular their microscopic characterisation, their interactions, and their coupling to heat baths or external fields.
There exists a strong cooperation with the experimental group of S. Hunklinger and C. Enss , one of the leading experimental teams in this field.
We propose a microscopic translationally invariant glass model which exhibits two level tunneling systems, and shows the salient low-temperature anomalies of glassy systems. Results so far obtained are in good accord with experiment. Qualitative universality is due to the collective origin of the glassy potential energy landscape. However, we obtain a simple explanation also for the mysterious so-called quantitative universality that manifests itself e.g. in the in the unusually weak dependence of values for the internal friction plateau on substance or system parameters.
We investigate effects of interactions between substitutional defects on the properties of defect crystals at low temperatures, where defect motion is governed by quantum effects. Both, thermal and dynamical properties are considered. The influence of interactions on defect motion is described via a collective effect. Our treatment is semiclassical in the sense that we analyze collective effects in a classical setting, and analyze the influence on quantized defect motion only thereafter. Our theory describes a crossover to glassy behavior at sufficiently high defect concentration. Our approach is meant to be general. For the sake of definiteness, we evaluate most of our results with parameters appropriate for Li-doped KCl crystals.
We report on a refined version of our spin-glass type approach to the low-temperature physics of structural glasses. Its key idea is based on a Born von Karman expansion of the interaction potential about a set of reference positions in which glassy aspects are modeled by taking the harmonic contribution within this expansion to be random. Within the present refined version the expansion at the harmonic level is reorganized so as to respect the principle of global translational invariance. By implementing this principle, we have for the first time a mechanism that fixes the distribution of the parameters characterizing the local potential energy configurations responsible for glassy low-temperature anomalies solely in terms of assumptions about interactions at a microscopic level.
We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments.
We discuss a spin-glass type approach to the physics of structural glasses, which leads to a class of models that exhibit both glassy low-temperature phases and double- and single-well configurations in their potential energy landscape. The low-temperature anomalies characteristic of amorphous systems are reproduced, and within our model the universality issue can be illuminated. We consider the interaction between localized excitations and phonons, and we present a general expression for the dynamic susceptibility, from which dynamic properties such as the internal friction can be calculated.
We review a model-based rather than phenomenological approach to low-temperature anomalies in glasses. Specifically, we present a solvable model inspired by spin-glass theory that exhibits both, a glassy low-temperature phase, and a collection of double- and single-well configurations in its potential energy landscape. The distribution of parameters characterizing the local potential energy configurations can be computed , and is found to differ from those assumed in the standard tunneling model and its variants. Still, low temperature anomalies characteristic of amorphous materials are reproduced. More importantly perhaps, we obtain a clue to the universality issue. That is, we are able to distinguish between properties which can be expected to be universal and those which cannot. Our theory also predicts the existence, under suitable circumstances of amorphous phases without low-energy tunneling excitations.
Substitutional defects in a cubic symmetry (such as a lithium defect in a KCl host crystal) can be modeled appropriately by an eight-state-system. Usually this tunneling degree of freedom is approximated by a two-level-system. We investigate the observable differences between the two models in three contexts. First we show that the two models predict different relations between the temperature dependence of specific heat and static susceptibility. Second we demonstrate that in the presence of external forces (pressure and electric field) the eight-state-system shows features that cannot be understood within the framework of the two-level-approximation. In this context we propose an experiment for measuring the parameter for tunneling along the face diagonal. Finally we discuss the differences between the models appearing for strongly coupled pairs. Geometric selection rules and particular forms of asymmetry lead to clear differences between the two models.
A random matrix approach to glassy physics is introduced. It leads to a class of models which exhibit both, glassy low-temperature phases, and double- and single-well configurations in their potential energy. The distribution of parameters characterizing the local potential energy configurations can be computed, and differ from those assumed in the standard tunneling model and its variants. Still, the low-temperature anomalies characteristic of amorphous systems are reproduced, and we are able to distinguish properties which can be expected to be universal from those which cannot.
An analytically tractable model is introduced which exhibits both, a glass-like freezing transition, and a collection of double-well configurations in its zero-temperature potential energy landscape. The latter are generally believed to be responsible for the anomalous low-temperature properties of glass-like and amorphous systems via a tunneling mechanism that allows particles to move back and forth between adjacent potential energy minima. Using mean-field and replica methods, we are able to compute the distribution of asymmetries and barrier-heights of the double-well configurations analytically, and thereby check various assumptions of the standard tunneling model. We find, in particular, strong correlations between asymmetries and barrier-heights as well as a collection of single-well configurations in the potential energy landscape of the glass-forming system - in contrast to the assumptions of the standard model. Nevertheless, the specific heat scales linearly with temperature over a wide range of low temperatures.
The book is a review of ten years of progress in our understanding of interacting tunneling systems. The dielectric and elastic response of [111} off-center impurities in alkali halides is investigated in detail and the coherent motion of an impurity pair is discussed in view of recently observed rotary echos. The low temperature properties of defect crystals with an impurity concentration higher than 100ppm are reviewed and the dipolar interaction is shown to drive the cross-over to relaxational dynamics. This comprehensive presentation of the theory is illustrated by experimental data for lithium, cyanide and hydroxyl impurities in various host crystals.
Paraelectric impurities contribute significantly to the low-temperature properties of alkali halide crystals. Even at very low density the dipolar interaction of adjacent defect ions may lead to deviations from the behaviour expected for isolated impurities; in a certain range of concentration it is sufficient to consider pairs of coupled defects. Applying a projection operator method, previous work on this pair model is extended to the case of finite asymmetry and weak coupling to acoustic phonons. After performing the ensemble average the specific heat and the zero-frequency susceptibility are calculated and compared with experimental data on KCl:Li and KCl:CN. The isotope effect on Rabi frequency and relaxation rate is discussed.
Relaxation due to incoherent tunnelling is shown to be responsible for the anomalous temperature dependence of the homogeneous linewidth of optical transitions in glasses. The distribution function of the tunnelling model for the parameters of the tunnelling systems (TS) is used , and dipole-dipole coupling between the chromophore and the TS is assumed. Within this, a bending from a linear to a quadratic temperature dependence of the homogeneous linewidth at $T\approx 5K$ is derived. Measurements on SiO$_2$, GeO$_2$ and BeF$_2$ doped with Eu$^{3+}$ and $Pr$$^{3+}$ are quantitatively accounted for by our theory. This interpretation is supported by acoustic measurements on oxide glasses.
An exact solution for the dynamics of a coupled pair of symmetric two-level-systems is given by calculating the resolvent of the Liouvillian and the statistical operator of the problem. At low temperatures interference effects between the two systems turn out to be of major importance. Depending on the value and the sign of the interaction parameter the susceptibility of the pair increases or decreases compared to the situation of isolated systems. For high temperatures the interference contributions disappear.
A mode-coupling theory (MCT) is presented for the spin-boson model with a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual decoupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and analytically by means of a frequency dependent ansatz for the memory functions. There is a transition to incoherent motion at a temperature $T^*$ where a bare two-level energy is equal to the damping rate, in contradiction to results obtained previously from a path integral formulation. The discrepancy arises since in the MCT the relevant self-energy function does not exhibit a $1/z$-pole at $z=0$. For tunnelling systems in dielectrics this yields a new relaxation mechanism due to incoherent tunnelling: the present results might require to modify some of the basic assumptions of the standard tunnelling model for dielectric glasses.
A new relaxation mechanism is shown to arise from 1< overdamped two-level systems above a critical temperature $T^*\approx 5K$, thus yielding an explanation for experimental observations in dielectric glasses in the temperature range below the relaxation peak. Using the distribution function of the tunnelling model for the parameters of the two-level systems, both the linear decrease of the sound velocity and the linear increase of the absorption up to the relaxation maximum, are quantitatively accounted for by our theory.
A Mori approach to the dynamics of coupled tunneling systems in defect crystals is presented. Transverse and longitudinal correlation functions of two-level systems are given as continued fractions; the memory kernels are evaluated in a usual decoupling approximation. Due to the random configuration of the defects on the host lattice both two-level splitting and relaxation rates show a broad distribution; the corresponding distribution function is derived for the case of a dipolar interaction of the defects. The theory covers both weak and strong coupling; the average interaction energy turns out to be the essential parameter. Dependence on frequency, temperature and concentration of the dynamical susceptibility is discussed. When passing from weak to strong coupling, the zero-temperature susceptibility shows a crossover from a constant value to a decrease with the third power of inverse defect concentration; there is quite a strong relaxational peak in the susceptibility. The theory accounts for several features observed in a recent low frequency experiment on KCL:LI.