Eur. Phys. J. Plus (2022) 137: 796
https://doi.org/10.1140/epjp/s13360-022-02975-2

Regular Article

Higher-order topological matter and fractional chiral states

¹ LPHE, Modeling and Simulations, Faculty of Science, Mohammed V University in Rabat, Rabat, Morocco
² Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich & JARA, Jülich, Germany
³ CPM, Centre of Physics and Mathematics, Faculty of Science, Mohammed V University in Rabat, Rabat, Morocco
⁴ College of Physical and Chemical Sciences, Hassan II Academy of Sciences and Technology, Km 4, Avenue Mohammed VI, Rabat, Morocco

^a lalla-btissam.drissi@fsr.um5.ac.ma, l.drissi@fz-juelich.de

Received: 24 December 2020
Accepted: 18 June 2022
Published online: 9 July 2022

Abstract

We develop a chiral anomalous fermion hamiltonian proposal to study the higher-order topological (HOT) phase with chiral symmetry $\mathcal{C}$ fractionalized like ${\mathcal{C}}_x{\mathcal{C}}_y{\mathcal{C}}_z$. First, we solve the $\mathcal{C}$-chiral symmetry constraint for eight band models and describe those induced by the partial ${\mathcal{C}}_i$’s. Then, we determine the explicit expression of fractional states characterising HOT matter and comment on the relationships amongst them and with the standard Altland–Zirnbauer gapless modes. We also give characteristic properties of the gapless fractional states and compute their contribution to the topological index of the chiral model. The findings of this work are shown to be crucial for investigating and handling high order topological phase.