Shadow features and shadow bands in the paramagnetic state of cuprate superconductors

TL;DR

This paper investigates the precursor shadow features in the spectral function of cuprate superconductors' paramagnetic state, identifying conditions for their appearance and their dependence on temperature and doping.

Contribution

It provides a theoretical analysis of three types of shadow effects in cuprates, clarifying their origin, temperature dependence, and doping conditions, especially predicting their absence in optimally doped materials.

Findings

Dispersive shadow peaks exist at finite temperature in the classical regime.

Non-dispersive shadow features are always very small at zero temperature.

Shadow effects are predicted to be absent in optimally doped cuprates.

Abstract

The conditions for the precursors of antiferromagnetic bands in cuprate superconductors are studied using weak-to-intermediate coupling approach. It is shown that there are, in fact, three different precursor effects due to the proximity to antiferromagnetic instability: i) the shadow band which associated with new pole in the Green's function ii) the dispersive shadow feature due to the thermal enhancement of the scattering rate and iii) the non-dispersive shadow feature due to quantum spin fluctuation that exist only in $\vec{k}-$scan of the spectral function $A(\omega _{Fixed},\vec{k})$. I found that dispersive shadow peaks in $A(\omega,\vec{k})$ can exist at finite temperature T in the renormalized classical regime, when $T\gg \omega _{sf}$, $\xi_{AFM} >\xi_{th}=v_F/T$ ($\omega _{sf}$ is the characteristic energy of spin fluctuations, $\xi_{th}$ is the thermal wave length of electron). In contrast at zero temperature, only non-dispersive shadow feature in $% A(\omega_{Fixed},\vec{k})$ has been found. I found, however, that the latter effect is always very small. The theory predict no shadow effects in the optimally doped materials. The conditions for which shadow peaks can be observed in photoemission are discussed.