Chapter 9 Dynamic Polarization Theory of Superconductivity F. A. Matsen Departments of Chemistry and Physics, The University of Texas, Austin, TX 78712 The dynamic-polarization theory employs a negative-U, Hubbard Hamiltonian to compute the spectrum of a one-dimensional array of sites (S). The lowest pair of states are split by a small gap and are predominantly superpositions of a pair of oppositely-polarized, ionic states |S-S+...S-S+>and |S S-.....S S->. An electric field polarizes the ground state into one or the other of the ionic states producing electron-pair transport with no scattering by the lattice. Excited states are formed by breaking an anion pair and forming a covalent bond with a nearest-neighbor cationic site; e. g., |S-S...S-S+>. Standard electrodynamics yields the London equation for the current density and the penetration depth, and the Pippard equation for the coherence length. The two-dimensional, system is discussed briefly and a condensation mechanism suggested. +
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In this paper we present a non-BCS theory based on a negative U Hubbard Hamiltonian (NUHH) which may serve as an effective Hamiltonian for the several excitonic, pairing mechanisms which have recently been proposed. The Negative-U. Hubbard Hamiltonian (NUHH) and its States The dynamic polarization theory subdivides the perovskite crystal into rectangular parallelpipeds called sites (S) each of which contains at its center a metal atom (copper or bismuth) surrounded by an environment of oxygen and counterions. Except for its electroneutrality the electron structure and electron density is unspecified. To the array of sites we apply a Hubbard Hamiltonian with U and IB> = IS S"...S S"> with nearest neighbor anionic (or cationic) sites excluded. Note that IA> and IB> are oppositely polarized; i . e., = - D g where D A and D g are the dipole moments of IA> and IB>, respectively. For point charges and an intersite separation of a, D ^ = - Mea/2. The ionic states are highly-correlated, singlet, reference states from which singlet, excited states are constructed by means of the generators. A single excitation breaks one anion electron-pair and forms one covalent bond with its nearest neighbor. The states are classified by the degree of excitation, u, which equals the number of covalent bonds. The u*h excited states is written for ν odd as follows: +
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lvv\...uA> = E
v + l j V
E
U + 1 > U
IA>W2U
and lvv\...uB> = E
V f V +
i
E
U j U +
ilB>/V2U
The number of u-excited states { IUJX>, X = A or Β} is given by the binomial coefficient, W(M/2,u) = (M/2)!/u!(M/2 - u)! From the IUJX> we form the symmetric state luX> = IjlujX>/VW(M/2,u) The remaining W(M/2,u) - l u states are made orthogonal to luA>. The perturbation matrix elements between these states and all other vectors vanish so these states play no dynamic role. The nonzero, perturbation matrix elements are given generally by
