Localized states in bipartite fcc lattices

Abstract

The Hubbard model in a bipartite face-centered cubic (fcc) lattice is studied in the tight-binding limit and using the mean-field approximation. This bipartite lattice can be obtained from the traditional fcc lattice by considering a larger four-atom cubic unit cell and allowing electron hopping to occur only between atoms on the vertexes and atoms on the faces of each unit cell. We find that two of the tight-binding energy bands of this type of lattice are flat, as expected, and the other two bands are energetically symmetrical about the zero-energy level. This result contrasts with the single, energetically asymmetrical energy band that is found on the traditional fcc lattice. The transition from the traditional (asymmetrical) case to the new (symmetrical) one is studied in two ways: via comparison of the density of states, and through mean-field calculations.In what concerns the density of states, we begin by considering all hoppings between nearest neighbors, which is the traditional assumption for the fcc lattice. The density of states in this case is known to be asymmetrical. We then gradually decrease the hopping parameter for jumps between atoms on different faces of the cubic unit cell, and find that, as this parameter approaches zero (and the fcc lattice becomes bipartite), localized states appear and the density of states becomes symmetrical.Our mean-field analysis consists of calculating the magnetization of the Hubbard model on both the traditional and the bipartite fcc lattices. One consequence of the asymmetry of the bands in the traditional fcc lattice is the absence of the particle-hole symmetry that occurs in the bipartite fcc lattice. The mean-field results are in agreement with both Lieb’s theorem and the uniform density theorem, and suggest an extension of the former in the limit of high Hubbard U.