Peierls Instability & CDW

1D metal dimerization — charge density wave gap opening

Parameters

Peierls (1955):
1D metal always unstable!
Nesting vector: 2k_F

Gap: Δ = 8t·δ·sin(k_F·a)

Free energy gain:
ΔF = -½N(0)Δ²ln(t/Δ) + Kδ²

Order parameter Δ(T):
BCS-like mean-field