Energetic balance of the superconducting transition across the BCS-Bose E instein crossover in the attractive Hubbard model

TL;DR

This study uses Dynamical Mean-Field Theory to analyze the energetic and scale evolution during the BCS-Bose-Einstein crossover in the attractive Hubbard model, revealing insights into superconductivity mechanisms and their relation to cuprate behaviors.

Contribution

It provides a detailed analysis of the energy scales and their hierarchy across the BCS-BE crossover, highlighting the kinetic and potential energy roles in different coupling regimes.

Findings

Superconducting transition involves a shift from potential to kinetic energy stabilization.

The hierarchy of energy scales changes with interaction strength, affecting $T_c$.

The model qualitatively explains optical spectral weight changes in cuprates.

Abstract

We investigate by means of Dynamical Mean-Field Theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs in the attractive Hubbard model. We follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap $\Delta_0$ and the superfluid stiffness $D_S$, which controls the phase coherence. The BCS-BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two controlling the critical temperature. In the whole intermediate-to-strong coupling region $T_c$ scales with $D_S$, while $T_C$ is proportional to $\Delta_0$ only in the BCS regime. This evolution as a function of the interaction qualitatively resembles what happens in the cuprates when the doping is decreased towards the Mott insulator. This continuous change reflects also in the energetic balance at the superconducting transition. While superconductivity is stabilized by a potential energy gain in the BCS regime, the strong-coupling superconductivity is made stable by a reduction of kinetic energy. Interestingly the intermediate-coupling region, where the maximum $T_c$ is achieved, behaves similarly to the strong-coupling regime. The above finding implies that the attractive Hubbard model can account qualitatively for the anomalous behavior of optical spectra around $T_c$, where an increase of spectral weight is observed in under and optimally doped cuprates, while the overdoped samples have a more standard behavior. This qualitative agreement is lost in the normal phase, specifically at strong-coupling, calling for the inclusion of strong correlation effects in the theoretical description.