Localized basis for effective lattice Hamiltonians: Lattice Wannier functions.

A systematic method is presented for constructing effective Hamiltonians for general phonon-related structural transitions. The key feature is the application of group theoretical methods to identify the subspace in which the effective Hamiltonian acts and construct for it localized basis vectors, which are the analogue of electronic Wannier functions. The results of the symmetry analysis for the perovskite, rocksalt, fluorite and A15 structures and the forms of effective Hamiltonians for the ferroelectric transition in PbT iO3 and BaTiO3, the oxygen-octahedron rotation transition in SrT iO3, the JahnTeller instability in La1−x(Ca, Sr,Ba)xMnO3 and the antiferroelectric transition in PbZrO3 are discussed. For the oxygen-octahedron rotation transition in SrT iO3, this method provides an alternative to the rotational variable approach which is well behaved throughout the Brillouin zone. The parameters appearing in the Wannier basis vectors and in the effective Hamiltonian, given by the corresponding invariant energy expansion, can be obtained for individual materials using first-principles density-functional-theory total energy and linear response techniques, or any technique that can reliably calculate force constants and distortion energies. A practical approach to the determination of these parameters is presented and the application to ferroelectric PbT iO3