The Coulomb gap and low energy statistics for Coulomb glasses
We study the statistics of local energy minima in the configuration space of two-dimensional lattice Coulomb glasses with site disorder and the behavior of the Coulomb gap depending on the strength of random site energies. At intermediate disorder, i.e., when the typical strength of the disorder is of the same order as the nearest-neighbor Coulomb energy, the high energy tail of the distribution of the local minima is exponential. We furthermore analyze the structure of the local minima and show that most sites of the system have the same occupation numbers in all of these states. The density of states (DOS) shows a transition from the crystalline state at zero disorder (with a hard gap) to an intermediate, probably glassy state with a Coulomb gap. We analyze this Coulomb gap in some detail and show that the DOS deviates slightly from the traditional linear behavior in 2D. For finite systems these intermediate Coulomb gap states disappear for large disorder strengths and only a random localized state in which all electrons are in the minima of the random potential exists. Dedication: This paper is dedicated to Thomas Nattermann, our dearest friend, brilliant colleague, and outstanding teacher.
Non-Ohmic Variable Range Hopping in Lightly Doped Semiconductors
In this project we have focused on the low temperature electron transport in hopping insulators. At temperatures close to the absolute zero the transport occurs by thermally activated Variable Range Hopping between Anderson localized states. Systems of this kind have been studied for decades and the first models were originally constructed for the lightly doped, compensated semiconductors. In our case the strong, long range Coulomb interactions between the carriers and the dopants are taken into account. The interactions cause a depletion of the density of states near the Fermi level, also known as the Coulomb gap. This strongly influences the system’s conductivity. We have performed numerical Monte Carlo simulations of single electron jumps, and investigated the transport effects when the system is influenced by an electric field. In the linear, Ohmic regime we investigate the Coulomb gap and compare the conductance behaviour to the one predicted by Efros and Shklovskii. In the non-Ohmic case we compare our results to the experimental studies by Aronzon et al. We also observe that the system can be described by two temperatures, a real and an effective one, as the system is heated by the electric field. The effective temperature is extracted from the site occupancy probability distribution which we find is close to the Fermi-Dirac distribution. The results open up for several theoretical questions regarding the relation between the transport, field strength and the effective temperature. A couple of preliminary ideas on how to answer these are introduced.
Design of reinforced concrete lining in pressure tunnels, considering thermal effects and jointed rockmass
Abstract Jaeger's theory (Jaeger, Rock Mechanics and Rock Engineering , Cambridge University Press, 1972) of the design of the lining for a pressure tunnel applies to a tunnel located in an isotropic, homogeneous and elastic medium. The theory is derived from the elasticity equations for the plane stress condition. In this paper, Jaeger's theory is extended to a plane strain situation. Also included is a discussion of the effects of a uniform increase (or decrease) in the lining temperature, jointed rockmass, cracking of the tunnel lining, and cracking of the rockmass around the opening. Tables are presented for the modulus of subgrade reaction for various rockmass conditions and for rock sharing pressures for various lining conditions. The reduction factor to include the effect of joints in rockmass is derived by the analysis of a numerical model of the lined tunnel by the finite-infinite-interface element method.