Theory for the Interdependence of High-T$_c$ Superconductivity and Dynamical Spin Fluctuations

TL;DR

This paper develops a theoretical framework linking high-temperature superconductivity in cuprates to dynamical spin fluctuations, revealing how these interactions influence the superconducting gap and experimental observations.

Contribution

It introduces an Eliashberg-type theory for the 2D Hubbard model that connects d-wave superconductivity with spin fluctuations and predicts new spectral features.

Findings

Maximum T_c at 13% doping

Identification of shadow states below T_c

Strong interplay between d-wave pairing and spin dynamics

Abstract

The doping dependence of the superconducting state for the 2D one-band Hubbard Hamiltonian is determined. By using an Eliashberg-type theory, we find that the gap function $\Delta_{\bf k}$ has a $d_{x^2-y^2}$ symmetry in momentum space and T$_c$ becomes maximal for $13 \; \%$ doping. Since we determine the dynamical excitations directly from real frequency axis calculations, we obtain new structures in the angular resolved density of states related to the occurrence of {\it shadow states} below T$_c$. Explaining the anomalous behavior of photoemission and tunneling experiments in the cuprates, we find a strong interplay between $d$-wave superconductivity and dynamical spin fluctuations.