Peierls Instability & CDW
1D metal dimerization — charge density wave gap opening
Parameters
Dimerization δ:
0.30
Filling n (electrons/site):
0.50
Temperature T/T_P:
0.00
Electron-phonon g:
0.50
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