Electronic Structure and Physical Properties

Abstract

In solid state theory two different approaches exist. Starting from a model Hamiltonian (e.g. Hubbard model, Ising model, Heisenberg model, Anderson model, …) one can elucidate a large number of electronic and magnetic properties qualitatively. On the other hand, during the last decades first principle methods have been developed which are able to describe both the qualitative and quantitative behaviour of the considered systems and to predict its properties. In first principle calculations the only input parameters are (besides some fundamental physical constants) the atomic numbers and masses of the constituent atoms. These parameters are inserted into equations derived from the Schrödinger equation, the fundamental equation of quantum theory. Using the techniques of band structure theory, the one-electron Schrödinger like Kohn-Sham equation is solved to calculate the electronic structure and other properties of the system, like total energy, cohesive energies, bulk modulii and atomic volumes. Although it is possible to calculate the equilibrium crystal structure from first principles this process is mostly shortened by taking the lattice spacings as input values from experiment. Most of the considerations are limited to translationally invariant systems (pure metals, intermetallic compounds). In crystalline materials the Bloch theorem holds due to the periodicity of the corresponding lattice and the electronic states can be described in terms of Bloch waves, band structure and Fermi surface. But in real systems different kinds of disorder exist. At T > 0 the ideal crystal is perturbed by phonons. At T = 0 imperfections of an otherwise perfect crystalline host, as impurities and interstitials have a great influence on its physical properties.