Effective Model for Fractional Topological Corner Modes in Quasicrystals,Physical Review Letters

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Effective Model for Fractional Topological Corner Modes in Quasicrystals
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-07-29 , DOI: 10.1103/physrevlett.129.056403
Citian Wang ₁ , Feng Liu ₂ , Huaqing Huang _{1,

3,

4}

Affiliation

High-order topological insulators (HOTIs), as generalized from topological crystalline insulators, are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special

k

points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. Here, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective

k \cdot p

Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone. We show that an in-plane Zeeman field can induce mass kinks at the intersection of adjacent edges of a 2D quasicrystal topological insulators and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an

s

-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics.

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