Three-dimensional higher-order topological semimetals in crystalline systems exhibit higher-order Fermi arcs on one-dimensional hinges, challenging the conventional bulk-boundary correspondence. However, the existence of higher-order Fermi arc states in aperiodic quasicrystalline systems remains uncertain. In this work, we present the emergence of three-dimensional quasicrystalline second-order topological semimetal phases by vertically stacking two-dimensional quasicrystalline second-order topological insulators. These quasicrystalline topological semimetal phases are protected by rotational symmetries forbidden in crystals, and are characterized by topological hinge Fermi arcs connecting fourfold degenerate Dirac-like points in the spectrum. Our findings reveal an intriguing class of higher-order topological phases in quasicrystalline systems, shedding light on their unique properties.
@article{arxiv.2307.04334,
title = {Quasicrystalline second-order topological semimetals},
author = {Rui Chen and Bin Zhou and Dong-Hui Xu},
journal= {arXiv preprint arXiv:2307.04334},
year = {2024}
}