Vertex Corrections to the Conductivity

The strong interaction between electrons leads, in many solids, to strong correlations among them them. This correlation gives rise to some of the most fascinating physical phenomena such as high- temperature superconductivity and quantum criticality. On the other hand, correlated electron systems are particularly challenging to calculate. A successful method to this end is the dynamical mean field theory (DMFT)-both for model and actual material calculations. However DMFT only includes local electronic correlations. In recent years we have seen stunning progress to account also for non-local correlations beyond DMFT. This progress has been brought about through novel methods that are based on a combination of numerical and quantum field theoretical concepts. This development started with the dynamical vertex approximation (DGA) and allowed, among others, the calculation of critical exponents and pseudogaps in the spectrum. In the present project we enter uncharted territory by studying how the dynamical vertex effects the conductivity. This aspect is a blank spot for strongly correlated electron systems. For weakly correlated electron systems, we know from perturbation theory that such vertex corrections give rise to fascinating physical phenomena such as excitons in semiconductors and weak localization corrections to the conductivity in disordered systems. Thanks to the recently developed diagrammatic extensions of DMFT, we are now able to study the same kind of phenomena also for strongly correlated systems. As particularly important applications we will study: (1) Vertex corrections to the optical conductivity of the Hubbard model which has possible implications for recent experiments indicating unexpected electron scattering in high-temperature superconductors. (2) Oxide heterostructures, where the conductivity is the key for prospective oxide electronics and vertex corrections are considered important because of the thinness of the conducting interface. (3) The interplay of weak localization and excitons for the Falicov-Kimball model. (4) Vertex corrections to the conductance through a nanoscopic systems which are important to understand e.g. in the context of molecular electronics. As this is a journey into the unknown we may expect the discovery of completely new phenomena.

A new quasiparticle, the pi-ton, has been discovered in the FWF project VeCoCo Originally, Karsten Held and coworkers have been looking for something completely different in the FWF project VeCoCo. Calculating the optical conductivity, i.e., the DC conductivity at frequencies in the optical range, they were looking for excitons. These are quasiparticles, generated by light and found in semiconductors. Here, the light excites an electron from a low energy to a higher energy. The missing electron can also be considered as a hole. That is, an electron-hole pair is created. Since the electron is negatively charged and the hole is positively charged, there is an attractive interaction. The bound electron and hole form an exciton. However, the research team was studying semiconductors but so-called strongly correlated electron systems. These often show strong charge or antiferromagnetic fluctuations that alternate from site-to-site. Such an alternation can be described by an angle of 180 degrees or pi in radian. With the newly developed methodology, the computational study was not biased toward any particle kind of physics such as excitons. This paved the way for the discovery of a new particle, coined pi-ton by the researchers. It consists of two electron-hole pairs (instead of one for the exciton) that are coupled to the incoming and outgoing light. The two distinct electron-hole pairs are glued together by the charge and antiferromagnetic fluctuations of the system. These pi-tons have been identified in many models for strongly correlated electrons so that it only appears to be a matter of time before it is also found in experiment.