Numerically Exact Study of Flat-Band Superconductivity

TL;DR

This study uses diagrammatic Monte Carlo to precisely analyze flat-band superconductivity, revealing the nonlinear $T_c(U)$ relationship and identifying conditions for high transition temperatures.

Contribution

It provides the first controlled, non-mean-field calculation of the full $T_c(U)$ curve in flat-band systems, especially at the point where three bands touch.

Findings

Pairing response diverges linearly with decreasing temperature over a broad $U$ range.

A sharp crossover to long-range correlations occurs at a characteristic temperature $T_*$.

Maximum $T_*$ occurs when three bands touch at a single momentum point.

Abstract

Current theories of high-temperature superconductivity in flat-band systems predict a linear dependence of the transition temperature on the attractive interaction, $T_c(U) = c|U|$. However, neither the value of $c$ nor the full nonlinear $T_c(U)$ curve -- with a maximum at large $|U|$ -- is known beyond mean-field and quantum geometry estimates. Using a controlled diagrammatic Monte Carlo technique, we trace the onset of superfluid response in the Lieb lattice with attractive Hubbard interaction. Focusing on the half-filled flat-band case, where the ordering mechanism differs fundamentally from both BCS and preformed Cooper pair scenarios, we find that the pairing response diverges linearly with decreasing temperature over a broad range of $U$, leading to a sharp crossover to long-range correlations at a characteristic temperature $T_*$, which provides a controlled upper bound on $T_c$. The highest $T_*$ occurs when all three bands touch at a single momentum point, potentially corresponding to high $T_c$ values.