Phonon softening in Peierls transition in an anisotropic triangular lattice

The 2D Peierls transition in an anisotropic triangular lattice is studied from the view point of phonon softening. The model is obtained by introducing a coupling in one of the diagonal directions to the isotropic square lattice, for which the multimode Peierls phase, involving not only the nesting vector component but also other Fourier components of distortion with wave vectors parallel to the nesting vector, is predicted. The results indicate that the multimode type Peierls transition can be expected as far as the diagonal coupling is weak compared to the nearest neighbor coupling in the square lattice.