Below you can find brief descriptions of various research directions that have been keeping the group busy recently. Our research is mostly linked to topological phases of matter, quantum, and not so quantum. It is strongly driven by experiment and we usually strive to either explain experimental observations or suggest probes for novel phenomena. We do this by considering systems with complex behavior and attempting to distill a simple effective model to describe them and extract observables from such models. We often collaborate with experimental groups to assist in efforts is realizing the effects we predict. The systems we study borrow ideas and inspirations from multiple disciplines, such as models from high-energy physics and elements of material science, which we then integrate in order to obtain a complete picture of the system at hand.
-Non-Hermitian systems: what happens to quantum mechanics when the underlying assumption of the Hermiticity of the Hamiltonian is dropped? This sounds like a purely mathematical question, however, it turns out that the dynamics of some systems can be described by a Schrodinger like equation with a non-Hermitian Hamiltonian. We are interested in studying the topological band theory of periodic systems with non-Hermitian Hamiltonians in order to understand the generalized Berry phase effects occurring in the bandstructure and the subtle implication it has on observables.
-Topological semimetals: these systems are metals in nature, but their elementary excitations behave like relativistic fermions. We are particularly interested in Weyl semimetals where the effective Hamiltonian that captures the behavior of the quasi-particles is the Weyl Hamiltonian. We can then ask interesting questions about how elements from the theory of Weyl fermions can be manifested in a solid-state system, and how it can be detected. Two examples to these that we have been working on are triggering the chiral or gravitational anomaly by lattice deformations, that mimic the effect of external fields or curvature. Recently we wrote a review of pseudo-fields in topological semimetals for Nature Reviews Physics.
-Topological insulator nanowires: When systems reach small dimensions they become quantized. We are interested in the exceptionally tunable behavior of nano-wires made from all sorts of topological insulators, where the interior of the wire is gapped but their surface is conducting. By tuning various parameters such as strain, flux, or magnetization, and taking into consideration the effects of symmetries and Berry curvature, these systems become exceptionally rich in their phenomenology and can show perfect transmission of modes, or topological superconductivity.
Nat Rev Phys 2, 29–41 (2020)
SciPost Phys. 6, 060 (2019)
-Condensed-matter analogs in metamaterials: Metamaterials represent engineering marvels where the geometric arrangement of the components of a system endow it with unusual global properties or responses that cannot be obtained otherwise in nature. Such systems represent a perfect playground to explore phenomena defying common intuition. We are particularly interested in creating analogs of quantum condensed matter phenomena appearing on the micro-scale, in a macro scale of such classical systems. Recently we have been thinking about active metamaterials where feedback control can help bypass Newtonian dynamics.
Nat. Phys. 15, 357–361 (2019)