This project has led to a variety of results ranging from the advancement of our fundamental understanding of topology in band structures to the prediction of material realization of new topologies in many different settings. In particular, this project has made impactful contributions to the study of new nodal topological phases associated to non-Abelian homotopy charges of nodal (Weyl) points and new topological insulating phases associated to the Euler class invariant of real Bloch Hamiltonians. A central point here is the intrinsic relation between the conversion of the non-Abelian charges of nodal points through braiding and the phase transitions between distinct gapped Euler phases. Furthermore, these theoretical considerations were systematically extended to the prediction of real systems holding the new topological phases and this for different settings. More precisely, we predicted the manifestation of the non-Abelian and Euler topologies in (1) the electronic band structures of Weyl semimetals with spin-orbit coupling, either using strain or temperature-induced structural phase transitions, (2) the phonon band structures of materials such as layered silicates and Al2O3, where the braiding of nodal points is controlled by strain and gating, (3) the vibration spectrum of spring-mass systems. Moreover, (4) these topological phases were realized experimentally in acoustic meta-materials. We also unveiled the manifestation of Euler topology and non-Abelian braiding in systems out-of-equilibrium, such as quenched cold atoms and time-periodically driven Floquet phases.
These results were presented in high-impact journals (Nature Physics, Nature Communications, Physical Review Letters, Science Bulletin) and in other more specialized high-standard journals (Physical Review B, Physical Review Research, Carbon, New Journal of Physics, etc.). They were also communicated to the scientific community in large scientific conferences, e.g. the March Meeting of the American Physical Society, workshops and invited seminars in different leading groups in the world. I participated actively in co-supervising master students and PhD students, and finalizing several collaborations with principal investigators and post-docs in Cambridge University. I have further disseminated the new knowledge accumulated during the project through invited lectureships and frequent discussions with the students in Cambridge.
