Peierls Instability & Charge Density Wave

Peierls Instability (1955): A 1D metal at half-filling is always unstable to a lattice distortion that doubles the unit cell. The instability is driven by the logarithmic divergence of the electronic susceptibility χ(2k_F) at the nesting wavevector q=2k_F.

Mechanism: Dimerization opens a gap Δ ∝ exp(−1/λ) at the Fermi level, lowering electronic energy by ~Δ² ln(1/Δ) while costing elastic energy ~δ². The net energy gain is always positive for any λ>0.

CDW: The resulting charge density wave has period π/k_F. In 1D conductors (NbSe₃, TaS₃), CDWs cause metal-insulator transitions and slide under applied fields.