High-degeneracy points protected by site-permutation symmetries

TL;DR

This paper demonstrates how to design higher degeneracy points in crystalline systems by exploiting site permutation symmetries, leading to novel pseudospin Dirac fermions across various quasiparticle models.

Contribution

It introduces a general design principle for creating high-degeneracy points protected by site permutation symmetries in spinless systems.

Findings

Proposed new lattice structures with three, four, and five degeneracy points.

Validated the design principles using a tight-binding electronic model.

Showed the applicability to multiple quasiparticle systems.

Abstract

Space group symmetries dictate the energy degeneracy of quasiparticles (e.g., electronic, photonic) in crystalline structures. For spinless systems, there can only be double or triple degeneracies protected by these symmetries, while other degeneracies are usually taken as \textit{accidental}. In this Letter we show that it is possible to design higher degeneracies exploring site permutation symmetries. These design principles are shown to be satisfied in previously studied lattices, and new structures are proposed with three, four and five degeneracy points for spinless systems. The results are general and apply to different quasiparticle models. Here, we focus on a tight-binding approach for the electronic case as a proof of principle. The resulting high-degeneracy points are protected by the site-permutation symmetries, yielding pseudospin-1 and -2 Dirac fermions. The strategy proposed here can be used to design lattices with high-degeneracy points in electronic (e.g. metal-organic frameworks), photonic, phononic, magnonic and cold-atom systems.