Theory of the generalised pseudoatom in crystals

The change in charge density due to a phonon and its connection with the electron-phonon interaction and the change in potential is discussed. It is shown that these are analytic functions of q in metals and where Z eff is zero. The charge density and the potential can be uniquely split into a part that rigidly follows an ion and a part that deforms as the ions move; the composite is called 'the generalised pseudo-atom' and is shown to be neutral. The behaviour of the potential near q=0 in metals is discussed. Using a relation between the ionic potential, the dielectric function matrix and the electron-phonon interaction, a useful expression for the dynamical matrix is easily derived. The discussion is generalised from the Fourier representation to other representations. It is shown that finite-range rigid-atom potentials give incorrect results near q=0 and that in cubic metals with one ion per unit cell or with rocksalt structure, deformation occurs, but only in Fourier components outside the first Brillouin zone. The occurrence and possible results of deformation are discussed.