SSH Chain: Topological Insulator (2D)

Hopping Strengths

Intra-cell hop v 0.50

Inter-cell hop w 1.00

Unit cells N 12

Geometry

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Phase

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Winding ν

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Band gap Δ

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Decay length ξ

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How it works

Two atoms per unit cell (A, B) linked by an alternating strong/weak bond pattern: intra-cell hop v, inter-cell hop w. When v < w on an open chain, a mid-gap zero-energy state appears at each end, exponentially localized and protected by chiral symmetry.

Winding number ν — 0 (trivial) or 1 (topological); an integer bulk invariant that can't change without closing the gap.
Band gap Δ = 2|v − w|, closing exactly at v = w — the phase transition.
Decay length ξ = 1/ln(w/v) sets how far the edge state leaks into the bulk.

Bulk band structure E(k)