Berry phases and pairing symmetry in Holstein-Hubbard polaron systems

Abstract

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferromagnet. Our treatment is based on a path integral formulation of the adiabatic (Born-Oppenheimer) approximation, combined with manybody tight-binding, instanton, constrained lattice dynamics, and many-body exact diagonalization techniques. The applicability and limitations of the adiabatic approximation in polaron tunneling problems are discussed in detail and adiabatic results are compared to exact numerical results for a two-site polaron problem. Our results are mainly based on the Holstein-tJ and, for comparison, on the Holstein-Hubbard model. We also study the effects of 2nd neighbor hopping and long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics is mapped onto an effective low-energy Hamiltonian which takes the form of a fermion tight-binding model with occupancy dependent, predominantly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupancy, and an effective intersite charge interactions. Antiferromagnetic spin correlations in the original many-electron Hamiltonian are reflected by an attractive contribution to the 1st neighbor charge interaction and by Berry phase factors which determine the signs of effective polaron tunneling matrix elements. In the two-polaron case, these phase factors lead to polaron pair wave functions of either d x 2 −y 2 -wave symmetry or p-wave symmetry with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconducting polaron pair condensate are discussed and compared to observed properties of the cuprate high-Tc materials. 71.38.+i, 75.10.Lp, 71.27.+a

Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study

“…The problem has in fact been studied in various approaches. 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26 This is by no means a theoretical curiosity, since there are various classes of materials in which both the electron-electron and electron-phonon interactions are simultaneously strong. A typical example is the solid fullerene doped with alkali-metal atoms, (A 3 C 60 , A = K, Rb, ...), 27,28,29 where the C 60 fullerene molecules are aligned in a face-centered cubic (fcc) lattice, for which the alkali atoms supply electrons making the conduction band half-filled.…”