Our work in theoretical condensed matter physicist is concerned with the emergent collective phenomena that arise in many-body systems as a consequence of competing interactions, disorder, coupling to the environment, and quantum geometry/topology. Besides fundamental research questions, it is motivated by quantum technological applications of the plethora of phases that can be hosted in these systems.
Using a variety of different many-body techniques, we analyze unconventional, topological, non-reciprocal, non-equilibrium, and two-dimensional superconductivity, competing and associated vestigial phases, the impact of reduced symmetries, disorder, and spin-orbit coupling in novel materials. Furthermore, our research aims at elucidating the consequences of interactions in topological systems, deepening our understanding of quantum magnets, spin liquids, and altermagnets. Apart from studying “regular” crystalline quantum matter, we explore the potential of engineered quantum materials (interfaces, heterostructures, superlattices, etc.) to design and probe exotic phases, see figure below. Also concerning methodology, the research has interdisciplinary character by combining analytical (e.g., field theory, exactly solvable limits), numerical many-body techniques, and machine learning. We also have close collaborations with a variety of experimental groups.
A summary of our key scientific achievements thus far can be found here.
Generally speaking, we are interested in the following sets of problems and questions:
Superconductivity beyond BCS
This includes unconventional, strongly coupled, multi-band, interband, spin-orbit coupled, vestigial, charge-4e, and non-reciprocal superconductors, as well as pairing states emerging from low-symmetry normal states. Key questions are: How can we determine the microscopic form of the superconducting order parameter, in particular, its symmetry and topological properties? What is the pairing mechanism? What are the key degrees of freedom hosting superconductivity that need to be included in a minimal model for it? What is the impact of different types of impurities on superconductivity? Is spin-orbit coupling relevant? What are competing phases? How can we design and control material realizations of exotic superconducting phases with desired properties?
Frustrated magnets, spin liquids, and fractionalization
We are interested in studying how frustrated magnetic interactions can induce complex magnetic textures and in the extreme limit lead to spin liquids, which are characterized by topological order. How can these, so far, elusive states of matter be identified experimentally? Motivated by their potential relevance to the cuprate high-temperature superconductors and twisted van der Waals systems, we work on models where spin liquids can coexist with metallic phases and the underlying topological order is intertwined with broken symmetries. What are the characteristic spectral and transport features? We are interested in the detailed comparison between predictions of candidate effective field theories and both numerical studies of the Hubbard model and experiment. We further study fractionalized Chern insulators in moiré systems, and the unique possibilities that emerge from unconventional magnets for the electronic properties and how to probe them.
Interaction effects in & stability of topological phases
How can topological phases arise spontaneously as a consequence of interactions? Can disorder stabilize non-trivial topological states? What is the interplay of topological obstructions and strong interactions? Are topological terms, such as Wess-Zumino-Witten terms, relevant to the phase diagram of twisted-bilayer graphene? What is the impact of phase competition on a topological phase and on its signatures? How fragile are topological qubits against time-dependent or non-Hermitian perturbations?
Machine learning for many-body physics
as a useful complementary tool to solve difficult physics problems. We are interested in both unsupervised algorithms that can learn directly from the data and do not require human supervision, and supervised approaches. We apply machine learning techniques both to numerically generated and experimental data. We further combine powerful variational neural quantum states with human-comprehensible effective theories, to get the best of both worlds. This line of research is also motivated by the hope of mutual benefits in the sense that concepts and formalisms of theoretical physics might prove useful to understand how machine-learning techniques work and vice versa.
Funding
Our research is funded by an ERC Starting grant of the European Union on "Understanding, Engineering, and Probing correlated many-body physics in superlattices of graphene and beyond" and the DFG (Deutsche Forschungsgemeinschaft).