Correlation functions and characteristic lengthscales in flat band superconductors

TL;DR

This paper investigates the coherence length in flat band superconductors, calculating correlation functions and challenging existing assumptions about its relation to quantum geometry, revealing complexities in defining coherence length.

Contribution

It systematically computes correlation functions in flat band systems and questions the proposed link between coherence length and quantum metric, highlighting the need for a clearer definition.

Findings

Coherence length is of the order of the lattice spacing.

Coherence length is weakly sensitive to interaction strength.

The proposed relation between coherence length and quantum metric does not hold.

Abstract

The possibility of an unconventional form of high temperature superconductivity in flat band (FB) material does not cease to challenge our understanding of the physics in correlated systems. Here, we calculate the normal and anomalous one-particle correlation functions in various one and two dimensional FB systems and systematically extract the characteristic lengthscales. When the Fermi energy is located in the FB, it is found that the coherence length ($\xi$) is of the order of the lattice spacing and weakly sensitive to the strength of the electron-electron interaction. Recently, it has been argued that in FB compounds $\xi$ could be decomposed into a conventional part of BCS type ($\xi_{BCS}$) and a geometric contribution which characterises the FB eigenstates, the quantum metric ($\langle g \rangle$). However, by calculating the coherence length in two possible ways, our calculations show that $\xi \neq \sqrt{\langle g \rangle.}$ This may suggest that the link between QM and coherence length is more complex, and leaves us with the open question: what is the appropriate definition of the coherence length in flat-band systems?