Dimensional Effects on the Density of States in Systems with Quasi-Relativistic Dispersion Relations and Potential Wells

Motivated by the recent discoveries of materials with quasi-relativistic dispersion relations, we determine densities of states in materials with low dimensional substructures and relativistic dispersion relations. We find that these dimensionally hybrid systems yield quasi-relativistic densities of states that are a superposition of the corresponding two- and three-dimensional densities of states.