2D Peierls state in a square lattice – Effect of anisotropy

In recent studies, we have shown that the lowest energy state in a 2D square lattice SSH-type model with a half-filled electronic band is not a simple Peierls state involving only distortions with the nesting wave vector Q but complicated multimode states involving distortions with various wave vectors parallel to Q and that there are many degenerate non-equivalent distortion patterns yielding the same ground state energy. In the present work we discuss the effect of anisotropy on these multimode Peierls states. It is indicated within the pertubational treatment combined with numerical calculations that the multimode states can survive as far as the anisotropy is small. Furthermore it is pointed out that the degeneracy can be lifted by the anisotropy. These studies will shed light on the understanding of the Peierls-like behaviors of 2D materials as layered organic conductors.