A hybrid method for the efficient calculation of the band structure of 3-D metallic crystals

In this paper, we propose a new hybrid method to characterize the band structure of three-dimensional metallic crystals. We formulate an auxiliary problem that has the same spectrum as the metallic crystal. We prove that the spectrum of the auxiliary problem can be efficiently computed using the plane-wave method and the method of moments. Thus, the band structure of the metallic crystal can also be efficiently calculated. Our approach is much more effective than root-searching methods, because all of the eigenvalues are obtained at once and degenerate cases pose no difficulty. This is a generalization of a previously proposed method for two-dimensional structures.