The spectrum and eigstate of the 2D lattice. (IMAGE)
Caption
(a-c) and (d-f) show the energy spectra. Insets depict the dispersion relations and representative topological eigen boundary states. The full 2D lattice spans 53 × 53 with the square domain boundary spanning 7 × 7 sites, and diamond domain boundary reaching 13 sites along both diagonal axes. Used in pairs, the first and second symbols respectively denote the parameters of the inner and outer regions(θin, θout), which are separated by either a square domain wall (a-c) or a diamond domain wall (d-f), where θin is fixed in the blue circle phase region (characterized by the topological triplet invariant (−,−,−)). For θout in the red square phase region (-, +, -) or purple downward-triangle phase region (+, +, -), the system exhibits chiral or non-chiral edge states (corresponding to strong or weak topological phases) regardless of the domain wall geometry. In contrast, for θout in the magenta upward-triangle phase region (-, -, +), the system supports second-order corner states for square domain walls but non-chiral edge states for diamond domain walls.
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