Abstract
In an -dimensional crystal, an energy band is usually made of several branches which are connected with each other. Accordingly, the Bloch states of wave vector K which are eigenfunctions of a one-electron Hamiltonian and which belong to a given band , define a subspace of finite dimensionality. For a large class of potentials, two properties concerning the subspaces which are associated with a fixed band have been proved for -dimensional crystals. (1) The projection operator on can be defined for complex values of K, and its matrix elements are analytic in a strip of the complex K space; this strip is centered on the real K space and is independent of r and r'. (2) The projection operator (integration on the Brillouin zone) has matrix elements which decrease exponentially when the length|r-| goes to infinity.
- Received 16 March 1964
DOI:https://doi.org/10.1103/PhysRev.135.A685
©1964 American Physical Society