Quasicrystalline second-order topological semimetals

TL;DR

This paper introduces a new class of three-dimensional quasicrystalline second-order topological semimetals characterized by hinge Fermi arcs, expanding the understanding of topological phases beyond crystalline systems.

Contribution

It demonstrates the emergence of higher-order topological semimetals in quasicrystals by stacking 2D quasicrystalline insulators, protected by forbidden rotational symmetries.

Findings

Existence of topological hinge Fermi arcs in quasicrystals

Protection by rotational symmetries forbidden in crystals

Connection of Fermi arcs to Dirac-like points

Abstract

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.