Graphene Electronic Structure in Charge Density Waves

We introduce the idea that the electronic band structure of a charge density wave system may mimic the electronic structure of graphene. In that case a class of materials quite different from graphene might be opened up to exploit graphene's remarkable electronic properties. The theory of such materials, along with superconductivity, is based on the material's dynamical, rather than its static, properties. The charge density wave system turns out to have a number of requirements: (1) a specific wave geometry simply related to graphene; (2) a self-consistency among the electrons that requires the net Coulomb and phonon-mediated parts of the electron-electron interactions to be attractive. We develop a model that leads to an analytical expression for the total energy in terms of the effective electron mass $\mu$, the electron density $\rho_0$, and the strength $\tilde{\nu}_{K}$ of the net electron-electron interaction. For constant $\mu>0$ and $\rho_0$, we examine the limitations set upon $\tilde{\nu}_{K}$ by self-consistency, stability, and the approximation in the electronic state calculation, and find them to be mutually compatible. This demonstrates the viability of our model.