ROLE OF PHONONS IN METAL-INSULATOR PHASE TRANSITION

The ground state insulating phase of certain transition-metal oxides is associated with a macroscopic crystallographic distortion which doubles the basic unit cell. We show that the microscopic theory (electrons, phonons, and their interactions) leads to a metal-insulator phase transition, and discuss some of the properties of the insulating phase. The new conduction and valence band edges have anomalously high densities of states. This results in low mobility and polaronic effects in the insulating or semi-conducting phase. Pressure and strain effects shift the critical temperature and change the nature of the phase transition. We treat several aspects of a soluble model which exhibits an insulator-metal phase transition, polaron effects, low mobility, and a tendency toward superconductivity. This model has several features of certain nonmagnetic transition-series oxides [ I , 21. Unlike the Hubbard model [3, 41, the present model has no significant magnetic properties, so that it is only applicable to non-magnetic oxides. Based a t it is on the electron-phonon interaction, we believe this model to apply when the effective coupling parameter g 2 / h o exceeds the Coulomb parameter U by a sufficient amount so that qualitativelyit is legitimate to ignore U. Otherwise, the Hubbard model is applicable and one obtains antiferromagnetic ordering in the grouhd state. In the present model, the ground-state insulating phase is associated with finite crystallographic distortion whereby the unit cell is doubled. The bands then split and what might have been mistaken for a metal with a half-filled band becomes an insulator. Moreover, the density of states near the band edges becomes anomalously large, resulting in surprising thermodynamic and transport properties. We shall later show that the details of the metalinsulator phase transition depend sensitively on band structure. We have previously reported on some preliminary aspects of this model [5], the results of several months' close collaboration between Dr. William D. Langer and the present author. In this communication, we repeat part of this material (for which calculated curves will be found in ref. [5]) and introducesomenew developments. At first, we assume a highly symmetric sc or bcc band structure. We start with + h o 1 a: a , + gN-' C (a , + a?,) c,*+,,, ck,, The subscript m refers to the spin of the electron, the momentum subscripts are understood to belong to a (*) Supported by a grant of thc United State Air Force O@ce of Scientific Research No AFOSR 69-1642. set of N vectors in a three-dimensional Brillouin zone. The first term is the energy of Bloch-state electrons [i. e., for tight binding in a simple-cubic structure W &k = 3 (COS k, + cos ky + cos kJ and n,,, is the number operator]. The second term is the repulsive interaction between pairs of electrons on the same site, treated in a previous paper. The phonons (creation and destruction operators a" and a ) are assumed to have an Einstein spectrum. In the fourth term, electrons are scattered from k to k + q by an appropriate phonon. We adjust particle number by means of chemical potential p. With sufficiently weak Coulomb repulsion this Hamiltonian might be expected to have a superconducting ground state and a metallic high-temperature phase. But in some crystal structures (sc or bcc with tightbinding structures) a dominant phonon mode affects the lattice, causing a gap in the electronic density of states, and unusual insulating properties. (Some superconducting features will also be found.) In sc and bcc II lattices, the vector Q = _+ ( 1 , 1, I), where a = lat-