My current research interests revolve around hyperbolic lattices and the application of (quantum) information theoretic tools to condensed matter systems.
Hyperbolic lattices are lattices in negatively curved space and as such they are the analogue of periodic structures in that space. In contrast to positively curved spaces, such as the surface of a sphere, the negative counterpart cannot be completely embedded in three-dimensional space. However, recent experiments with metamaterials have shown that hyperbolic lattices enable us to emulate the negatively curved hyperbolic space. In our work, we have implemented a particular hyperbolic lattice in electric circuits and demonstrated that signatures of the negative curvature can indeed be experimentally observed. On the theory side, we have on the one hand studied several fundamental models of topological band insulators on hyperbolic lattices (see here) and on the other hand made progress in developing the generalization of band theory to hyperbolic lattices. I am also interested in the interplay of interactions and the negative curvature and am currently studying that aspect.
More recently, I have become interested in applying quantum information theoretic tools such as entanglement entropy and mutual information to study condensed matter systems. In the future, I would like to connect back to my earlier work on information theory and statistical physics and use the tools of quantum information theory to develop algorithms useful for studying condensed matter systems.
Previously, I have worked on topological band theory in the context of real materials (in contrast to metamaterials). I have studied various spects of multiband topology, such as momentum space degeneracies (band nodes), topological invariants and their relation to symmetries. In particular, I am interested in a multiband perspective on the above topics. This has culminated in a large project about triple (nodal) points, which are degeneracies of three bands in momentum space. We have completed the missing classification of those band nodes in the absence of spin (which applies to systems where spin-orbit interactions are negligible but also to many other systems such as photons, phonons, magnons including may metamaterials) and have found a universal higher-order bulk-boundary correspondence as well as relationships to multiband topology. For more information, check out the project description.
Besides these main parts of my research I am also interested in other topics, on some of which I have previously worked while others might lead to future projects: