Schematic illustration of one-dimensional periodic metallic lattice and Peierls distorted insulating lattice. (a) Without electron–phonon interaction, the lattice with a period of a exhibits a constant charge density and filled electron states up to Fermi level. (b) Considering the electron–phonon interaction, the Peierls distortion results in the periodically modulated charge density and an energy gap at the Fermi level. Reproduced from Ref. [6] with permission. Copyright 1988, American Physical Society.