Charge Density Wave & Fermi Surface Nesting

When a nesting vector Q connects parallel Fermi surface sheets, divergent susceptibility drives the Peierls instability: a CDW gap opens and charge modulates at wavevector 2k_F

System Parameters

χ(Q) = —

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Peierls instability: In 1D (or quasi-1D), perfect nesting means χ(2k_F) diverges logarithmically as T→0: χ(Q) ≈ N(E_F) ln(E_F/T). Any finite electron-phonon coupling λ triggers spontaneous lattice distortion and CDW gap Δ ≈ 2E_F exp(−1/λN(E_F)). In 2D/3D, nesting is imperfect and the susceptibility peak broadens, suppressing the instability. The CDW creates a real-space charge modulation ρ(x) = ρ₀ + δρ cos(Qx + φ) with Q = 2k_F.