Condensation energy in the spin-fermion model for cuprates

TL;DR

This paper calculates the condensation energy in the spin-fermion model for cuprates using the Scalapino-White relation, showing that at strong coupling, the energy is mainly due to high-energy spectral weight, aligning with experimental data.

Contribution

It demonstrates that the condensation energy in cuprates at strong coupling arises from high-energy spectral weight, providing a theoretical explanation consistent with experimental observations.

Findings

Condensation energy is linked to high-energy spectral weight at strong coupling.

Resonance peak spectral weight is compensated at energies much larger than the gap.

The model's results align with experimental data for cuprates.

Abstract

We use the Scalapino-White relation between the condensation energy and the difference between the dynamical structure factor in the normal and the superconducting states to compute the condensation energy in the spin-fermion model. We show that at strong coupling, the extra low-frequency spectral weight associated with the resonance peak in the dynamical structure factor in a superconductor is compensated only at energies $\sim J$ which are much larger than the superconducting gap $\Delta$. We argue that in this situation, the condensation energy is large and well accounts for the data for cuprates.