Chapter 12 Relativistic solid state calculations

Abstract

Abstract This chapter provides insight into the application of relativistic electronic structure theory to solids, focusing on the determination of the electronic ground state. Density functional theory (DFT) establishes the general frame for this task. At first, the fundamentals of relativistic DFT are sketched. This includes introductory considerations on the ground state energy, a brief review of four-current DFT, and the outline of approximations needed to arrive at digestible Kohn-Sham-Dirac equations. The second part is devoted to the numerical solution of these equations. One particular method, the relativistic version of the full-potential local-orbital minimum-basis (FPLO) scheme is explained in detail. Though this method is by far not the only possible one, it is distinguished by the combination of three advantages: accuracy, efficiency, and straightforward interpretation of its outcomes in chemical terms. In the final section, the importance of relativistic effects in solid state physics is illustrated with the help of some examples, both from literature and from application of the described relativistic FPLO method. This collection includes specific effects on electronic structure and structural properties, on magnetic ground state properties (orbital moments, magneto-crystalline anisotropy) and on excitations (magneto-optics).