Density wave mechanism with a variable wave vector from a Dirac-fermion-Landau-level perspective

A density wave is an ordered phase formed by electrons in materials under certain conditions. In the conventional Peierls' mechanism or Fermi surface nesting theory, when the temperature is below Tc, the renormalized phonon frequency touches zero at a specific wave vector, which corresponds to a periodic distortion of the lattice and a new distribution of charge or spins in real space. However, these theories have some obvious drawbacks such as the high dependence on the shape of the Fermi surface. We propose a new density wave mechanism based on the low-energy effective theory of the Landau level at the Dirac point, which does not depend on the shape of the Fermi surface, and the wave vector can change continuously according to the variation of the coupling strength. At the same time, we give a class of models applicable to this theory and perform numerical calculations and analysis for a particular model.