Exotic Two-Dimensional Materials
Two-dimensional materials can be reduced to atomically thin sheets and reassembled in heterostructures to create novel devices of augmented functionality. At the König group, we specifically concentrate on the interplay of two-dimensional quantum magnets with metallic or superconducting two-dimensional materials. Most prominently, heterostructures involving candidate quantum spin liquids (i.e. strongly entangled quantum paramagnets) may allow access to novel experimental probes of ultra-quantum phases of matter, lead to exotic metals and superconductors, and, in the long run, may be a fruitful route to harvest quantum entanglement.
Strong Correlations in Topological Insulators and Superconductors

The role of topology in modern condensed matter is multi-faceted. Free fermions and mean-field superconductors may display topology in the way their Bloch wave functions twist around the Brillouin zone. Beyond these simple Slater-determinant states, much more complex, short-range or even long-range entangled quantum many-body states may display may emerge in systems with important interparticle intractions. At the König group, we study topological phases beyond the mean-field approximation, in particular the interplay of Goldstone modes and fermionic topology, as well as the topology of Mott-insulators and fractionalized phases of matter.
Mesoscopic Quantum Design: Solid-State Quantum Simulation

A prominent present-day application of quantum technology is the controlled quantum design of quantum systems in order to emulate or create novel quantum phases of matter. A particularly rich realm is quantum impurity problems, i.e. quantum dots coupled to fermionic (or bosonic) leads which can harbor tunable quantum critical points and a built-up of impurity entropy indicating the presence of anyonic quantum particles of relevance for topological quantum computation. Another research direction concerns the design of novel circuit elements for circuit quantum electrodynamics, most notably quasiperiodic capacitances allowing emulation of quasicrystals using a small superconducting device.
Quantum Computing of, with, and for Fermions
As anticipated early on by Richard Feynman, a main application of a working quantum computer is the simulation of many-electron problems in quantum materials and quantum chemistry. Approaching this goal within the ongoing NISQ era, at the König group we recently started to investigate quantum circuits emulating quantum many-body problems of correlated electrons and study the complexity of fermionic quantum many-body wave functions.