Eur. Phys. J. Plus (2021) 136: 68
https://doi.org/10.1140/epjp/s13360-020-01037-9

Regular Article

Domain walls in topological tri-hinge matter

¹ LPHE, Modeling and Simulations, Faculty of Science, Mohammed V University in Rabat, MB 1014 RP, Rabat, Morocco
² CPM, Centre of Physics and Mathematics, Faculty of Science, Mohammed V University in Rabat, Rabat, Morocco
³ Hassan II Academy of Science and Technology, Rabat, Morocco

^a lalla-btissam.drissi@um5.ac.ma, b.drissi@academiesciences.ma

Received: 25 July 2020
Accepted: 22 December 2020
Published online: 11 January 2021

Abstract

Using a link between graph theory and the geometry hosting higher-order topological matter, we fill part of the missing results in the engineering of domain walls supporting gapless states for systems with three vertical hinges. The skeleton matrices which house the particle states responsible for the physical properties are classified by the Euler characteristic into three sets with topological index $\chi =0,1,2.$ A tri-hinge Hamiltonian model invariant under the composite ${\mathit{M}}_1\mathit{T}$, ${\mathit{M}}_2\mathit{T}$, ${\mathit{M}}_3\mathit{T}$ is built. In this framework, $\mathit{T}$ is the time-reversing symmetry obeying ${\mathit{T}}^2=-I$ and the ${\mathit{M}}_i$’s are the generators of the three reflections of the dihedral ${\mathbb{D}}_3$ symmetry of triangle. To capture the tri-hinge states, candidate materials are suggested, thus opening up a variety of possibilities for investigating and designing robust materials against disorder and deformation.