Triple point fermions in a minimal symmorphic model

Gapless topological phases of matter may host emergent quasiparticle excitations which have no analog in quantum field theory. This is the case of so called triple point fermions (TPF), quasiparticle excitations protected by crystal symmetries, which show fermionic statistics but have an integer (pseudo) spin degree of freedom. TPFs have been predicted in certain three-dimensional nonsymmorphic crystals, where they are pinned to high symmetry points of the Brillouin zone. In this Rapid Communication, we introduce a minimal, three-band model which hosts TPFs protected only by the combination of a C-4 rotation and an anticommuting mirror symmetry. Unlike current nonsymmorphic realizations, our model allows for TPFs which are anisotropic and can be created or annihilated pairwise. It provides a simple, numerically affordable platform for their study.