Drude weight of an interacting flat-band metal

TL;DR

This paper investigates the transport properties of interacting flat-band systems using the Drude weight, revealing new geometric contributions and the role of Berry curvature in low-frequency spectral weight.

Contribution

It introduces a quantum geometric approach to analyze interacting flat bands and uncovers unexplored four-point geometric contributions affecting conductivity.

Findings

Spectral weight relates to variance of Berry curvature for long-range interactions.

Uncovered four-point geometric contributions unrelated to quantum metric.

Demonstrated the potential of geometric methods at intermediate temperatures.

Abstract

Flatband systems form a new class of materials that challenge the conventional wisdom of transport. The intrinsically strong electronic correlations combined with the vanishing kinetic energy scale suggest a sensitive dependence of transport properties on the flat band states and make interacting flat bands promising candidates for exotic quantum transport. Utilizing the Drude weight, we investigate the low-frequency spectral properties of the electrical conductivity within a controlled analytic treatment of the many-body response at temperatures above the bandwidth and the interaction strength and below the bandgap. Focusing on this new transport regime, we demonstrate the potential of a quantum geometric approach for interacting systems and intermediate temperatures. The derived spectral weight yields unexplored four-point geometric contributions unrelated to the quantum metric, which questions the previously proposed projection methods. For long-ranged interactions, we show that the low-frequency spectral weight reduces to the variance of the Berry curvature.