Research

In many quantum materials, strong correlations of different type coexist and can compete or reinforce each other. As a result we observe complex phase diagrams with different phases in close proximity.
A fascinating example for such a situation are unconventional superconductors, which also represent materials with some of the highest transition temperatures at ambient pressure - cuprates and iron-based superconductors. Further exciting systems for the study of potentially unconventional superconductivity and more generally competing orders are graphene-based heterostructures and other moiré materials like twisted transition metal dichalcogenides. 
In the phase diagrams of unconventional superconductors, the superconducting phase often appears next to a magnetic or charge-ordered phase, whose fluctuations are crucial for mediating the attraction between electrons that is necessary for the formation of a superconducting condensate. 
We study the complex interplay of phases in these materials and characterize properties of the resulting states. In doing so we account for the effect of different symmetries and degrees of freedom such as spin, orbital or valley, which can give rise to collective phenomena with novel functionalities.

The state of a system and its characteristic excitations change qualitatively when undergoing a phase transition. At a second order phase transition, these excitations are subject to strong fluctuations and if the transition happens at zero temperature, the quantum as opposed to the thermal origin of fluctuations can be revealed.
In particular, order-parameter and electronic fluctuations are strongly coupled near a quantum phase transition in a metal and must be treated on equal footing. As a result, the critical behavior in the vicinity of the quantum transition differs from its classical counterpart. The characterization of the corresponding new universality classes is an issue of fundamental interest.
Furthermore, the coupling between order-parameter and electronic fluctuations gives rise to a complex interplay of incoherence and non-Fermi-liquid behavior on the one side, and mediation of attraction and pairing tendencies on the other side, which is believed to be responsible for the rich phase diagram of several strongly correlated electron systems.
We study these different aspects of quantum phase transitions motivated by Dirac materials, high-temperature superconductors or heavy-fermion materials. We investigate how the critical behavior manifests itself in thermodynamic or transport observables and who wins the competition between non-Fermi liquid and pairing. 
 

In order to analyse interacting many-body systems, our group utilizes and develops a variety of field-theoretical techniques ranging from microscopic numerical descriptions to analytical methods for effective field theories. 
For example, we make use of unbiased parquet or functional renormalization group methods, which can account for the crucial interplay of ordering tendencies on equal footing. For the study of phase transitions, we employ both perturbative and non-perturbative renormalization group schemes, which can describe the strongly correlated regime around the transition. We combine our analyses with the self-consistent calculation of correlation functions, effective mean-field theories or Landau-Ginzburg descriptions.