Berry phases and pairing symmetry in Holstein-Hubbard polaron systems

TL;DR

This paper investigates the quantum tunneling and pairing mechanisms of polarons in antiferromagnetic materials, revealing how Berry phases influence pairing symmetry and implications for high-temperature superconductivity.

Contribution

It introduces a comprehensive model combining path integral, many-body, and exact diagonalization techniques to analyze polaron tunneling and pairing in Holstein-Hubbard systems, highlighting Berry phase effects.

Findings

Polaron tunneling mapped to an effective fermion tight-binding model.

Berry phases influence the sign and nature of tunneling matrix elements.

Polaron pairs exhibit d-wave or p-wave symmetry depending on phase factors.

Abstract

We study the tunneling dynamics of dopant-induced hole polarons which are self-localized by electron-phonon coupling in a two-dimensional antiferro- magnet. Our treatment is based on a path integral formulation of the adia- batic approximation, combined with many-body tight-binding, instanton, con- strained lattice dynamics, and many-body exact diagonalization techniques. Our results are mainly based on the Holstein-$tJ$ and, for comparison, on the Holstein-Hubbard model. We also study 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, predominant- ly 2nd and 3rd neighbor tunneling matrix elements, excluded double occupan- cy, 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 ma- trix 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 symme- try with zero and nonzero total pair momentum, respectively. Implications for the doping dependent isotope effect, pseudo-gap and Tc of a superconduc- ting polaron pair condensate are discussed/compared to observed in cuprates.