Quantum dynamical manifolds: Pair states in high‐temperature superconductivity

Abstract

AbstractThe formation of Dirac pair states is shown to be crucial to the formation of the superconductive state. The properties of these Dirac bipolaron states is studied using a quantum dynamical extension of Cartan's moving frame approach to differential geometry. The overall geometric method, called quantum dynamical manifold theory (QDMT), is used to obtain the Dirac quasiparticle pair states (cooperons and potential cooperons or Dirac polaron pairs) in a polarizable medium appropriate for high‐temperature superconductors (HTSCs). The matrix solutions of the equations describing the quantum dynamical manifold have a (flavor) symmetry also occurring in other closed‐shell systems. By independently coupling each Dirac electron to a polarizable background in a semiclassic approximation, and solving the resulting quantum dynamical manifold equations (QDMEs), there are found new, nonperturbative, analytic solutions to the polaron pair (bipolaron) problem. This enables us to show that these cooperon states are closed shells with su(2) Lie algebraic symmetry. These are used to describe the cooperon system above and below the superconduction critical temperature. It is shown how these Dirac polaron pairs can be correlated for electron–electron interactions via virtual exciton exchange and screened Coulomb repulsion and then used in a homogeneous Bethe–Salpeter equation approach to study the onset of superconductivity of polaronic superconductors involving pairs of Dirac polarons. The relation of these states to the formation of a Bose–Einstein condensation (BEC) is discussed. To numerically investigate the question of the existence of high‐temperature superconductivity mediated by the screened Coulomb and boson exchange of virtual excitons, a wave vector‐ and frequency‐dependent effective interaction, Veff(k, ω), between electron or hole polaron pairs in the electronic polaron model is used in lieu of a full pairing interaction, thereby simplifying the analysis of interacting pair states. We include the temperature dependence of the dielectric function, ε−1(k, ω, T), for many‐body systems of these quasiparticles. An effective mass method is employed to further simplify the computations. Analysis of the results shows that the attractive part of Veff for the electronic polaron model persists to high temperature. Further, polarons not participating in the superconductive state produce a measurable Fermi surface even in the presence of the bipolaron BEC. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004