The project has received dedicated input and been rather successful. The themes, being the search of novel symmetry-protected topological phases in excitation spectra and out-of-equilibrium context have delivered many results that have been disseminated in 19 publications and, even though covid-19 severely restricted travelling during this period, in 5 on-line theory seminars, a research visit, via the hosting of colleagues/collaborators and an invited talk at the Material Research Society meeting in 2021. On top of delivering on the proposed objectives we have also extended our research programme into new areas such as topological characterizations of quasi-crystalline order.
Turning to the out-of-equilibrium results, we highlight that via two publications in Physical Review Letters our efforts indeed resulted in the discovery of novel effects and phases. In the first we found that when two-fold rotations and time-reversal symmetry are present out-of-equilibrium phases can exhibit new quench signatures that can be measured via standard techniques. In the second, we found that Floquet engineering using bicircular light is a versatile way to control magnetic symmetries and topology in materials and showed that in Weyl materials, such as Cd3As2 in particular, this leads to novel topological phases that can be observed in the laboratory using current techniques. Finally, in an Editor’s suggested Physical Review Research publication, we introduced a new class of two-dimensional topological materials known as optical N-insulators that possess obstructions to constructing localized molecular polarizabilities. That is, we found a manner to characterize electromagnetic linear response theory in terms of topological winding numbers.
Turning to the second theme, we have also found substantial results. Firstly, we found in a series of two Physical Review B papers, one of which was chosen as an Editor’s suggestion, that there exists a general class of electronic configurations within a set of anti-ferromagnetic-compatible space groups that must be topological, thereby leading to novel effect such as specific boundary states. In addition, we worked with experimentalist to characterize and observe new topological states in specifically designed acoustic metamaterals, being a striking example of an excitation spectrum. This study was published in Nature Physics. In addition, we contributed, using our expertise on the interplay of topology and magnetism, to a rather prominent discovery published in Nature that experimentally observed a novel splitting effect in magnetic topological materials. Finally, we also addressed new typed of topological charges in phonic spectra, using new topological insights.
