New topological phases and new materials using Topological Quantum Chemistry

During this talk, I will examine topological metals and insulators stabilized by any of the
230 crystal symmetry groups. By defining the concept of elementary band representations
of the double group augmented by time reversal, we can predict how many bands are
connected in momentum space based on the lattice positions (Wyckoff multiplicities) and
character (s,p,d) of the elements/orbitals existent in the material. This allows for the
prediction of symmetry-enforced semimetals whenever the valence number of electrons
that occupies the orbitals is a fraction of the band connectivity. Our theory also provides a
set of rules of how bands can be connected in momentum space when the centre of charge
is not at a Wyckoff position or when it does not respect local time reversal or spatial
symmetries. In this sense we are able to predict new topological materials and new toplogical phases.

References:
[1] B. Bradlyn et al. Science 353 (6299), aaf5037
[2] B. Bradlyn et al. Nature 547, 298–305 (2017)