Elektronische Struktur kondensierter Materie: Forschungsschwerpunkte
Electronic Structure of Condensed Matter: Research Topics
Prof. Rohlfing has moved
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(WilhelmKlemmStr. 10, 48149 Münster, Room 708; EMail: rohlfin@unimuenster.de; phone: +49 251 8336340)
Allgemeiner Überblick Im Mittelpunkt unserer Arbeiten stehen angeregte elektronische Zustände in kondensierter Materie. Diese Zustände und ihre Spektren spielen eine zentrale Rolle beim Verständnis optischer Eigenschaften, bei der strukturellen Charakterisierung von Materialien, und vielem mehr. Besonders interessieren uns Systeme, die durch quantenmechanische Zustände auf der Längenskala der atomaren Bindung gekennzeichnet sind. Die Eigenschaften derartiger nanoskopisch geprägter Materialien gehen qualitativ weit über den ausgedehnten Festkörper hinaus und lassen sich nicht durch dessen Kenngrößen beschreiben. Sie erfordern vielmehr eine mikroskopische Theorie, die als kleinste Einheit am einzelnen Atom und seinen Orbitalen ansetzt und als abinitio Theorie, also ohne Vorgabe von Parametern, formuliert wird. Darüber hinaus werden elektronische Zustände und ihre Spektren erheblich von VielteilchenEffekten beeinflusst (insbesondere von elektronischer Korrelation), deren sorgfäaltige Behdnalung mittels VielteilchenStörungstheorie einen Hauptaspekt dieses Forschungsgebiets darstellt. Ein essentieller Bestandteil unserer Methoden ist die Symbiose grundlegender physikalischer Konzepte mit numerischen Verfahren, also die Umsetzung der ElektronenstrukturTheorie in effiziente ComputerAlgorithmen. Mittels solcher Software untersuchen wir interessante Aspekte verschiedenster Materialklassen. Die Verfahren lassen sich daher in den Grenzbereich zwischen Vielteilchenphysik, numerischer Computerphysik, und Materialwissenschaft einordnen.   General overview The focus of our work is on excited electronic states in condensed matter. Such states and their spectra play a key role in understanding optical properties, in characterizing materials, for optoelectronic mechanisms, and more. Of particular interest are systems that are characterized by quantummechanical stateson the length scale of the atomic bond. The properties of such nanostructured materials go far beyond those of the extended solid. They require a microscopic theory which takes the single atom and its orbitals as the smallest unit, and which is formulated as an abinitio theory, without adjustable parameters. In addition, electronic states and their spectra are significantly affected by manybody effects (in particular, electronic correlation effects) whose careful treatment by manybody perturbation theory constitutes one of the main aspects of this field. An important part of our work is given by the symbiosis between fundamental physical concepts and numerical methods, i.e. by the realization of electronicstructure theory in efficient computer algorithms. Employing this software we investigate interesting topics of various material classes. The approach can thus be classified as belonging to the boundary between fundamental manybody physics, computational physics, and materials science.  
Key issues:
 Chemical bonding and geometric structure
Already in the electronic ground state, there is a delicate balance between the nuclei, electrons, electrostatics, and quantum mechanics. For many systems, densityfunctional theory (DFT) allows to treat the quantum mechanics of the manyelectron system, to energyoptimize the geometry, and to understand details of chemical bonding. 
 
 Excited states: electrons and holes
There are lots of spectroscopic techniques that add or substract electrons to the system in question: ionization, photoemission, inverse photoemission, tunneling spectroscopy, ballistic conductance. The careful determination of the corresponding quantummechanical states, their energies, and wave functions, is of great importance for the interpretation of the experimental data. To this end, manybody perturbation theory is used to take care of electronic correlation effects that. 
 
 Excited states: optical spectra
Optical spectra (continous spectra, excitons, chargetransfer states, and localized states like selftrapped excitons) are heavily influenced by electronic correlation, as well, in particular by electronhole interaction effects. Such issues are important both for the characterization of systems, as well as for applications like optielectronics or photovoltaics. 



 Interrelation between electrons and the atomic geometry
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. 
 
 Femtosecond dynamics
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 electronelectron interaction.
 Picosecond dynamics
Closely related to the electrongeometry interrelation, the motion of the geometry can also be investigated in real time, employing moleculardynamics techniques that are common for geometry optimization, nonlinear vibrations, and chemical reactions. For the determination of excitedstate dynamics, however, the excitedstate potentialenergy surface and the corresponding forces must be evaluated first, which is more demanding than the groundstate forces for groundstate dynamics.  STM simulation
In experiment, very detailed information about geometric and electronic structures can be obtained from scanningtunneling microscopy (STM). The simulation ofSTM images is thus an important tool at the interface between theory and experiment.
Theoretical concept: The spectral properties of a manyelectron 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., holelike and electronlike excitations, whose energies define the band structure), as well as excited states without changing thenumber of electrons (in particular, electronhole 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 densityfunctional theory (DFT).
This step is necessary for groundstate geometry optimiztation and to provide the basis for the following considerations.  Determination of the singleparticle spectrum by manybody perturbation theory (MBPT).
By solving the equation of motion of the singleparticle 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 socalled 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 19651970; 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 electronhole correlation isincluded in the excitation process. This leads to the problem of solving an equation of motion of a twoparticle Green function (given by the BetheSalpeter equation); this is a consequent extension of MBPT. The ''perturbation'' is again dominated by the electron selfenergy 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 timedepending Schroedinger equation.
By evaluating the time propagation for excited electronic states (either for single quasiparticles or for coupled electronhole 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 excitedstate 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 moleculardynamics techniques.