## Research

### Graphene

Graphene is a simple honeycomb lattice of carbon that displays a number of remarkable physical properties.
The essential reason for all the fascinating properties of graphene is
that the low energy excitations behave as if governed not be the Schrödinger equation, but instead by
an effective Dirac-Weyl equation. This latter equation describes particles of *zero rest mass* which (therefore)
travel at the speed of light.

Much of the strange physics of this equation transfers to the physics of graphene, producing several novel properties (Klien tunneling, absence of back scattering). On the other hand, the more humble origin of this this effective equation can itself still be seen at several places in the physics of graphene which, therefore, consists of an mixture of exotic Dirac-Weyl physics with standard solid state physics.

Note that by an effective equation we simply mean that while the electrons are, of course,
governed by the Schrödinger equation they are conspiring in some way
to produce low energy behavior that *appears* as if they were governed by a quite different
equation. Since we are dealing with an *effective equation*
the Dirac-Weyl equation that describes low energy graphene excitations
contains not the speed of light *c*, but
an effective constant (which turns out to be just the Fermi velocity).

The following link provides a derivation of the origin of the Dirac-Weyl in graphene physics,
and allows one to see how various properties of the quasi-particles such as their *chirality* emerge.

Continuum approximation description of graphene

Possible projects that can be done within the group are briefly described here:

Projects

### Reduced density-matrix functional theory

An abstract for possible diploma projects can be found here

.### DFT - Developments

- Time Dependent DFT: fundamentals
- excited states and dynamical exchange-correlation effects
- relation to many-body theory
- diagrammatic representation for dynamic exchange-correlation kernel

- Time Dependent DFT: applications
- real-time description of electronic and chemical processes

### DFT - Applications

- electronic structure of SiC polytypes
- polytype-polytype heterostructures
- impurities, native defects and defect complexes in semiconductors
- first-principles calculation of EPR parameters for defects in SiC
- diffusion in Semiconductors
- electronic structure of silicides and silicide thin films and surfaces
- metallic silicides (Co, Fe,...)Si
- insulator - metal transition in Fe-silicide films
- Pt- and Ir-silicides

- Two-dimensional interacting electrons in disordered systems