Studying the properties of matter requires solving the Schrödinger equation. Exact solutions are only possible for very small numbers of electrons (of order 1) where the symmetry is very high. Because condensed matter contains of order 1023 electrons, drastic simplifying approximations are necessary. The most important is to require translation symmetry in order to reduce the problem to one of considering the electrons in a single unit cell. This translational invariance forms the starting point for "Solid State Physics", the study of the physics of solids.
Finding exact solutions of the Schrödinger equations is still not possible for the tens of electrons found in typical unit cells of interest and resort must be made to additional physical approximations and to numerical methods. This whole field of endeavour is called "Electronic Structure Theory"
Ideally one would like to make predictions about the properties of matter without using any experimental input other than the fundamental physical constants
c - the speed of light
h - Planck's constant
e - the charge of an electron
me the mass of the electron
The formalism called "Density Functional Theory" has been particularly successfull in making this possible. Great progress has been made over the last thirty years in constructing clever algorithms to solve the appropriate coupled Schrödinger equations of Density Functional Theory for condensed matter systems. The two methods we use mostly in our work are the so-called
- Linear Muffin Tin Orbital (LMTO) method
- Car - Parrinello method
When combined with the powerful workstations which are now commonly available, this branch of theoretical solid state physics called "Computational Materials Science" (CMS) forms the basis of our understanding of the physical properties of real materials and is becoming increasingly useful in the search for new materials and for materials optimization. Topics of current interest in the department are:
Our current work in Electronic Structure Theory focuses on:
- developing methods to study transport in layered magnetic materials. We use a Green's function technique to calculate the electronic structure for systems without translational invariance and calculate the electrical transport properties using the Landauer-Büttiker formalism. This work is carried out together with the theory group in Delft within the framework of two projects financed by the European Union.
- calculating the optical properties using a method going beyond the independent particle approximation. This work is carried out in collaboration with the theory group in Eindhoven.
Edymar Gonzalez A