Peierls Instability & Dimerization

A 1D metal with a half-filled band is unstable toward lattice dimerization (Peierls 1955). Alternating bond lengths open a gap at k = ±π/2a, lowering electronic energy at the cost of elastic energy — a spontaneous symmetry-breaking phase transition.

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1.00
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Gap 2Δ
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Electronic E gain
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Net ΔE
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E(k) = ±√(t₀²cos²(ka) + δ²t₀²sin²(ka)) — SSH-like dimerized chain