Microscopic Aspects of Stretched Exponential Relaxation (SER) in Homogeneous Molecular and Network Glasses and Polymers

Because the theory of SER is still a work in progress, the phenomenon itself can be said to be the oldest unsolved problem in science, as it started with Kohlrausch in 1847. Many electrical and optical phenomena exhibit SER with probe relaxation I(t) ~ exp[-(t/{\tau}){\beta}], with 0 < {\beta} < 1. Here {\tau} is a material-sensitive parameter, useful for discussing chemical trends. The "shape" parameter {\beta} is dimensionless and plays the role of a non-equilibrium scaling exponent; its value, especially in glasses, is both practically useful and theoretically significant. The mathematical complexity of SER is such that rigorous derivations of this peculiar function were not achieved until the 1970's. The focus of much of the 1970's pioneering work was spatial relaxation of electronic charge, but SER is a universal phenomenon, and today atomic and molecular relaxation of glasses and deeply supercooled liquids provide the most reliable data. As the data base grew, the need for a quantitative theory increased; this need was finally met by the diffusion-to-traps topological model, which yields a remarkably simple expression for the shape parameter {\beta}, given by d*/(d* + 2). At first sight this expression appears to be identical to d/(d + 2), where d is the actual spatial dimensionality, as originally derived. The original model, however, failed to explain much of the data base. Here the theme of earlier reviews, based on the observation that in the presence of short-range forces only d* = d = 3 is the actual spatial dimensionality, while for mixed short- and long-range forces, d* = fd = d/2, is applied to four new spectacular examples, where it turns out that SER is useful not only for purposes of quality control, but also for defining what is meant by a glass in novel contexts. (Please see full abstract in main text

Electronic Transport Properties of Strained Graphene Nanostructures.

In this thesis we theoretically investigate the influence of mechanical deformations on the electronic transport properties of graphene structures, such as nanoribbons, bilayer graphene, and graphene on hexagonal boron nitrite substrates. We find that homogeneous mechanical deformations can induce the formation of zero-conductance plateaus and conductance resonances in nanoribbons, and outline their robustness in the presence of 'double atom' edge disorders. Furthermore we emphasize that even small percentages of 'single atom' edge defects are strong enough to determine the smearing or even suppression of the observed resonant structure. For the case of inhomogeneous deformations we find that the inhomogeneity developed near the contacts aids the resonant transmission of charge carriers through a mode mixing mechanism or via the sublattice-polarized n = 0 pseudo-magnetic Landau level. We also show that in homogeneously strained bilayer graphene the linear response conductance of an n-p-n junction has a non-monotonic dependence on doping and temperature, which varies in size and form as a function of the crys-tallographic orientation of the principal strain axis. We find that uniaxial strain changes the chirality of the electronic plane-wave states in the vicinity of the Lifshitz transition in the low-energy electron spectrum of this crystal, which results in the observed non-monotonicity of the linear response conductance. Finally, we show that mechanical deformations alter the beating of the lattice mismatch in graphene and hexagonal boron nitride heterostructures, which leads to the formation of strained moire superlattices. We observe that in some cases this determines the opening of minigaps in the second generation mini Dirac cones and finalize our study by identifying an extreme parametric regime where the moire patterns become quasi-1D and the dispersion acquires additional Dirac cones