Quasicrystalline second-order topological semimetals

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.

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• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Multi higher-order Dirac and nodal line semimetals
• Higher-order topology in twisted multilayer systems: a review
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Five-dimensional Floquet topological semimetals with emergent Yang monopoles and linked Weyl surfaces
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Floquet composite Dirac semimetals
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Superconducting order parameter in aperiodic binary systems