Flat-band superconductivity in systems such as magic-angle twisted bilayer graphene has recently attracted significant interest. In the flat-band limit, the vanishing Fermi velocity implies a zero coherence length in conventional BCS theory, which contradicts experimental observations. While the quantum metric is known to resolve this by governing macroscopic length scales, previous mean-field studies have failed to capture the crucial superconducting fluctuations inherent to the strong-coupling (BEC) regime of flat bands.

This study elucidates how the quantum metric affects the pseudogap and drives the BCS-BEC crossover. Employing the multi-orbital T-matrix approximation, which incorporates infinite-order superconducting fluctuations, we examine the normal-phase electronic states just above the transition temperature.

First, using a two-dimensional model where the quantum metric is tuned while preserving band flatness, we calculate the single-particle spectrum and find a pseudogap with an extremely sharp spectral structure. We demonstrate that increasing the quantum metric enhances the effective coherence length and significantly suppresses the pseudogap originating from local preformed pairs. Furthermore, by introducing dispersion into the model, we confirm that tuning the quantum metric alters the self-energy near the chemical potential from a fluctuation-dominated state to Fermi-liquid-like behavior.

We conclude that the quantum geometric effect suppresses preformed pairs by driving a crossover from the BEC to the BCS regime.