. Georgia Institute of Technology / Westfälische Wilhelms-Universität
Electronic Transport in Aperiodic Solids
The concept of transport and transport coefficient will be introduced with an emphasis upon dissipation mechanisms. The Kubo formula will be derived both for perfect metals (Drude formula) and for aperiodic media. Emil Prodan designed a code based upon the non commutative approach to describing electrons in aperiodic solids that makes the Kubo formula computable in a numerically stable way. A series of numerical results related to the Quantum Hall Effect will be presented. They show that several accurate predictions can be made, unseen before.
Coherent transport, transport of charges occurring without dissipation, and can be observed experimentally at very low temperature, will be introduced as well as the scaling exponents which characterize it. The competition between coherent transport and dissipation has consequences on the low temperature behavior of the electric conductivity. It leads to an anomalous Drude formula representing well the strange behavior of aperiodic solids, like quasicrystals or doped semiconductors, at low temperature. An emphasis upon the case of quasicrystals will be provided, with two different regimes, based on an argument by Thouless, which may be an explanation for various observations made so far by experimentalists.