# Triple point fermions in a minimal symmorphic model

## TL;DR

This paper introduces a minimal three-band model that hosts triple point fermions protected by specific crystal symmetries, enabling easier study of their properties and behaviors in topological materials.

## Contribution

The authors present a simple, minimal model for triple point fermions that are protected by a combination of C4 rotation and mirror symmetry, differing from previous non-symmorphic models.

## Key findings

- Model hosts anisotropic triple point fermions.
- TPFs can be created or annihilated in pairs.
- Provides a computationally accessible platform for studying TPFs.

## Abstract

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 non-symmorphic crystals, where they are pinned to high symmetry points of the Brillouin zone. In this work, we introduce a minimal, three-band model which hosts TPFs protected only by the combination of a C4 rotation and an anti-commuting mirror symmetry. Unlike current non-symmorphic 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.