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Defects play an important role for surface reconstructions and therefore also influence the substrate growth. In this work we present a first principle calculation for the Ge(001) surface without and with tin impurities incorporated into the top surface layer. By mapping the system onto an Ising-type model, with interaction constants taken from density functional theory, the stability of the surface reconstructions under the influence of different concentrations of tin impurities is explored. This approach allows us to simulate the possible phase transitions for the different surface reconstructions including the local structure around the tin impurity atoms. In addition, we compare our theoretical results with experimental STM images on clean and Sn-doped Ge(100) surfaces.
The time-dependent Gutzwiller approximation is rederived on the basis of a variational wave function which is a direct product of a Slater determinant and a coherent state. The latter can be related to the slave-boson formulation by Kotliar and Ruckenstein, and our approach offers a convenient way to generalize the theory towards the implementation of symmetry-broken states and the study of non-equilibrium phenomena. We discuss the concept with regard to applications in the linear response limit and for quenched antiferromagnetic order for which we evaluate the optical conductivity in non-equilibrium situations.