Scaling of the Hamiltonian and momentum in semiconductors

We compute self-consistently the matrix elements of the Hamiltonian H and the momentum →p in a localized basis for covalent semiconductors. This basis is connected with the Wannier functions of the system obtained by means of a variational method. The calculation has been performed for different lattice constants in order to look for a d^-α dependence law for H and →p. The results are more satisfactory in Si, where H roughly scales as d^-2. The scaling of the Cartesian components of →p is rather more complicated, but a simple behavior is obtained for the modulus |→p|.