The SSH model is the simplest possible topological insulator: a 1D chain of sites
with two atoms per unit cell (A and B), linked by alternating hopping
amplitudes — a strong/weak bond inside each cell (v) and a strong/weak
bond between neighbouring cells (w). Even though every atom looks
identical, the pattern of bond strengths alone decides whether the chain is an
ordinary (trivial) insulator or a topological one.
v > w, the chain is trivial: it dimerizes into isolated strong-bonded pairs and the ends are unremarkable.v < w, the chain is topological: a mid-gap, zero-energy state appears at each end of an open chain, exponentially localized and protected by the chain's chiral symmetry — cutting the chain shorter or adding modest disorder cannot remove it, only strong disorder that closes the gap can.The SSH model was originally written down in 1979 to describe soliton defects in polyacetylene, a conducting polymer — decades before "topological insulator" became a term of art. It remains the textbook minimal model for topological band theory.
A 3D Su-Schrieffer-Heeger chain of coupled sites where alternating hopping strengths between neighbours decide whether the chain is an ordinary insulator or a topological one with protected edge states.
When the inter-cell hopping exceeds the intra-cell hopping, a mid-gap state appears at each end of the open chain, exponentially localized and protected by the winding number of the bulk — the essence of bulk-boundary correspondence.
Drag the intra-cell and inter-cell hopping sliders to cross the phase transition and watch the atoms at each end glow as edge states switch on. Compare open and periodic geometry, or let the phase sweep animate automatically.
The SSH model was first written down in 1979 to explain solitons in polyacetylene — decades before "topological insulator" existed as a term — yet it remains the field's minimal textbook example.