Theory for the Doping Dependence of Spin Fluctuation Induced Shadow States in High-T$_{c}$ Superconductors

TL;DR

This paper models how shadow states in high-Tc superconductors vary with doping, revealing their connection to antiferromagnetic correlations, flat bands, and Fermi surface nesting, with implications for understanding pseudogap phenomena.

Contribution

It introduces a numerical approach to analyze doping-dependent shadow states in the 2D Hubbard model, linking them to magnetic correlations and Fermi surface features.

Findings

Shadow states occur at finite energies decreasing with doping.

Increased shadow state intensity correlates with a flattened quasiparticle dispersion.

A pseudogap emerges in the density of states due to these effects.

Abstract

We analyze the doping dependence of the intensity and energetical position of shadow states in high -T$_{c}$ superconductors within the 2D Hubbard model and using our recently developed numerical method for the self consistent summation of bubble and ladder diagrams. It is shown that shadow states resulting from short range antiferromagnetic correlations occur for small but finite excitation energies which decrease for decreasing doping, reflecting a dynamically broken symmetry with increasing lifetime. Simultanously, the intensity of these new states increases, the quasiparticle dispersion is strongly flattened, and a pseudogap in the density of states occurs. Finally, we discuss the importance of flat bands at the Fermi level and nesting of the Fermi surface as general prerequisites for the observability of shadow states.