The effect of quantum phonons on the Peierls transition temperature in a one-dimensional commensurate system is studied. The nonadiabatic effect due to finite phonon frequency ωp>0 are treated through an energy-dependent electron-phonon scattering function δ(k′,k). By using the Green’s-function perturbation theory we have shown that our theory gives a good description of the effect of quantum phonons: (i) There exists a critical electron-phonon coupling gc2. The Peierls transition temperature Tp=0 when the coupling g2<gc2 and Tp increases with increasing g2>gc2. (ii) The ratio 2Δ/Tp could be much larger than the BCS value 3.527.
Physical Review B (Condensed Matter and Materials Physics) 65(1), 014304(8 pages)