Drude weight of an interacting flat-band metal

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.

7+23 pages, 3+2 figures. Updated to the peer-reviewed version

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• Quantum Metric in Step Response
• Quantum Geometry and the Hidden Scales in Materials
• Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Functional approach to superfluid stiffness: Role of quantum geometry in unconventional superconductivity
• Quantum geometric tensors from sub-bundle geometry
• Superfluid stiffness of superconductors with delicate topology
• Generalized Peierls substitution for Wannier obstructions: response to disorder and interactions
• Magneto-conductivity and CME in Dirac semimetals from Keldysh technique in Landau levels basis
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity