Crystalline Euler phases in topological condensed matter systems

Recently, a new class of topological materials that depend on multi-gap conditions have been discovered. These feature non-Abelian braiding properties in reciprocal space, where band nodes are protected against annihilation by the existence of a topological invariant termed the 'Euler class'. The project will involve a systematic investigation of all possible two- and three-dimensional crystalline symmetry operations for both spinless and spinful cases, with the aim of mapping out all possible crystalline Euler phases.