Hourglass Fermions and Cohomological Insulators

We present a new fermion, the Hourglass fermions, which extends the currently known Dirac, Weyl and Majorana classification. We further present a set of materials which host this particle as a surface state. The materials already exist in nature and have a large gap. The topological index involves group cohomology, and, in our particular material example, a group-extension of an already non-symmorphic group.