## Research interests - Prof. Dr. Michael Rohlfing

At the center of our work are excited electronic states in condensed matter. These states and their spectra play a central role in the understanding of optical properties, in the structural characterization of materials, and much more. We are particularly interested in systems characterized by quantum mechanical states on the atomic bond length scale. The properties of such nanoscopic materials are qualitatively far beyond the extended solid and can not be described by its characteristics. On the contrary, they require a microscopic theory which, as the smallest unit, attaches itself to the individual atom and its orbitals and is formulated as an ab initio theory, that is to say without specification of parameters. In addition, electronic states and their spectra are significantly influenced by many-particle effects (in particular electronic correlation), the careful handling of which by means of many-particle perturbation theory is a major aspect of this field of research.

An essential part of our methods is the symbiosis of fundamental physical concepts with numerical methods, i.e. the conversion of electronic structure theory into efficient computer algorithms. By means of such software we examine interesting aspects of different material classes. The methods can therefore be classified in the boundary between many-particle physics, numerical computer physics, and materials science.

Already in the electronic ground state, there is a delicate balance between the nuclei, electrons, electrostatics, and quantum mechanics. For many systems, density-functional theory (DFT) allows to treat the quantum mechanics of the many-electron system, to energy-optimize the geometry, and to understand details of chemical bonding.

Optical spectra (continous spectra, excitons, charge-transfer states, and localized states like self-trapped excitons) are heavily influenced by electronic correlation, as well, in particular by electron-hole interaction effects. Such issues are important both for the characterization of systems, as well as for applications like optielectronics or photovoltaics.

Since the electronic structure deoends on the atom positions, it is not surprising that the atom positions depend on the electronic structure, as well. In particular, the geometry may change if the electronic structure is excited. A number of consequences arise, like vibrational broadening of electronic transitions, Stokes shifts between light absorption and emission, self trapping of excitons, and fragmentation of the system.

Excitations often happen via states that are not eigenstates of the electronicstructure, thus giving rise to state propagation in time which typically happens on a femtosecond time scale. Two prominent examples are resonant charge transfer processes (e.g., from an adsorbate to the substrate) and decay mechanisms dueto the finite lifetime of electronic states resulting from electron-electron interaction.

Closely related to the electron-geometry interrelation, the motion of the geometry can also be investigated in real time, employing molecular-dynamics techniques that are common for geometry optimization, non-linear vibrations, and chemical reactions. For the determination of excited-state dynamics, however, the excited-state potential-energy surface and the corresponding forces must be evaluated first, which is more demanding than the ground-state forces for ground-state dynamics.

In experiment, very detailed information about geometric and electronic structures can be obtained from scanning-tunneling microscopy (STM). The simulation ofSTM images is thus an important tool at the interface between theory and experiment.

The spectral properties of a many-electron system are determined by transitionsbetween its ground state and the excited states. For the problems we have in mind two classes of excited states are relevant: states with an electron number changing by plus/minus 1 (i.e., hole-like and electron-like excitations, whose energies define the band structure), as well as excited states without changing thenumber of electrons (in particular, electron-hole pairs that are relevant for optical excitations). Correspondingly, the mathematical description and its numerical realization of these concepts on powerful computer platforms is carried outin several consecutive steps.

**Determination of the ground state by density-functional theory (DFT)**

This step is necessary for ground-state geometry optimiztation and to provide the basis for the following considerations.**Determination of the single-particle spectrum by many-body perturbation theory (MBPT)**

By solving the equation of motion of the single-particle Green function, the band structure of electrons and holes is obtained. As the crucial quantity, the electron self energy must be evaluated, describing the exchange and correlation effects among the electrons. This is done within the so-called GW approximation. The key aspect of this approximation is the inclusion of dielectric creening effects, that dominate the Coulomb interaction between charged particles in condensed matter. This concept has first been suggested in the years of 1965-1970; since about 1985 it has become possible to employ it for real systems,as well, including numerically demanding systems like complex surfaces and large molecules.**Investigation of optical excitations within MBPT**

Optical transitions can only be described if electron-hole correlation isincluded in the excitation process. This leads to the problem of solving an equation of motion of a two-particle Green function (given by the Bethe-Salpeter equation); this is a consequent extension of MBPT. The ''perturbation'' is again dominated by the electron self-energy operator. This method allows to investigatethe entire linear optical spectrum, both in the frequency range of bound excitons and in the range of resonant states above the fundamental energy gap.**Solution of the time-depending Schroedinger equation**

By evaluating the time propagation for excited electronic states (either for single quasiparticles or for coupled electron-hole states), the dynamics of charge carriers, resonant charge transfer, etc. is addressed. This step is easilydone within MBPT, just taking the MBPT Hamiltonian as time propagator.**Evaluation of excited-state atom dynamics**

This step requires the calculation of total energies, of the resulting potential surfaces, and the resulting forces these potentials, thus allowing to solve the atoms' equation of motion by conventional molecular-dynamics techniques.