Higher-order topological phases in crystalline and non-crystalline systems: a review

Abstract

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in nonperiodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

52 pages, 27 figures. An invited topical review to Journal of Physics: Condensed Matter. Comments are welcome

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Cited by in corpus (24)

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• Structural disorder-induced topological phase transitions in quasicrystals
• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Non-Hermitian Quantum Fractals
• Gapless higher-order topology and corner states in Floquet systems
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• Unveiling Higher-Order Topology via Polarized Topological Charges
• Topological Insulators with Hybrid-order Boundary States
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