Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts

Abstract

Quasicrystals allow for symmetries that are impossible in crystalline materials, such as eight-fold rotational symmetry, enabling the existence of novel higher-order topological insulators in two dimensions without crystalline counterparts. However, it remains an open question whether three-dimensional higher-order topological insulators and Weyl-like semimetals without crystalline counterparts can exist. Here, we demonstrate the existence of a second-order topological insulator by constructing and exploring a three-dimensional model Hamiltonian in a stack of Ammann-Beenker tiling quasicrystalline lattices. The topological phase has eight chiral hinge modes that lead to quantized longitudinal conductances of $4e^2/h$. We show that the topological phase is characterized by the winding number of the quadrupole moment. We further establish the existence of a second-order topological insulator with time-reversal symmetry, characterized by a ${\mathbb{Z}}_2$ topological invariant. Finally, we propose a model that exhibits a higher-order Weyl-like semimetal phase, demonstrating both hinge and surface Fermi arcs. Our findings highlight that quasicrystals in three dimensions can give rise to higher-order topological insulators and semimetal phases that are unattainable in crystals.

7 pages, 6 figures

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Cited by in corpus (6)

• Structural disorder-induced topological phase transitions in quasicrystals
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Higher-order topology in twisted multilayer systems: a review
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals