Peierls instability — periodic electron density modulation and gap opening
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Physics
Charge density waves arise from the Peierls instability (1955): a 1D metal is always unstable to a periodic lattice distortion at wavevector q = 2k_F, which opens a gap at the Fermi level. The electron density becomes ρ(x) = ρ₀ + δρ·cos(2k_F·x + φ). The CDW transition temperature: k_BT_P = 1.13·ℏω_D·exp(-1/λ). Below T_P, the CDW is pinned by impurities; above a threshold electric field (depinning), it slides coherently and contributes to conductivity. The Kohn anomaly: phonon softening at q=2k_F precedes the transition.