Fermionic quantum matter in atomic gases and solid state systems

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This project aims at investigating the influence of fermionic degrees of freedom on the macroscopic properties of many-body systems. Although the expected effects typically occur at very low temperatures, it is of central importance for technological applications to understand the underlying mechanisms. Fermionic quantum matter is realized in a variety of physical systems. In this project we explore models for ultracold Fermi gases, high-temperature superconductors, and graphene by means of quantum field theoretical methods like the Renormalization Group. For one, properties of the so-called Sarma phase shall be identified together with parameter regimes for its realization in ultracold Fermi gases and solid state systems. The most remarkable fact about this state of matter is that it shares properties of both metallic and superconducting character. Furthermore, the competition of distinct ordering principles in fermionic systems shall be studied. This has implications on the phase diagrams of cuprate superconductors and graphene.