Fig. 1: Bulk-topological-defect correspondence and the zero-mode trilogy.
a Summary of the topological modes at topological defects (marked as red points, lines, and plane), where the Dirac mass (with components mx, my, mz) has an undefined singularity in various dimensions. The blue arrows represent the phase (or sign) of the mass terms in the bulk, on the surface, or on the edge. b Zero-mode trilogy. σi are the Pauli matrices, γij = σi⊗σj are the gamma matrices, and Γijk = σi ⊗ σj ⊗ σk, where ⊗ is the Kronecker product. SSH Su–Schrieffer–Heeger18, HCM Hou–Chamon–Mudry28, DFB distributed feedback56, VCSEL vertical-cavity surface-emitting laser57, TCSEL topological-cavity surface-emitting laser40. The scaling behavior between the mode spacing (FSR) and mode volume (V) is listed.
