paper

Quantum Geometry Driven Finite-Momentum Exciton Fluctuations in Flat-Band Systems

arXiv:2606.23598 · doi:10.1016/j.mtquan.2026.100076

Abstract

Quantum geometry is instrumental in stabilizing exotic phenomena in systems ranging from topological insulators to superconductors. In dispersionless flat bands, where the kinetic energy is quenched, the quantum metric emerges as the fundamental driver of macroscopic collective phenomena. Here, we theoretically demonstrate that lattice-geometry-induced flat bands, such as those in kagome and Lieb lattices, provide a fertile platform for realizing a purely quantum-geometry-driven excitonic insulator (EI) phase. By applying an out-of-plane Zeeman field to lift spin degeneracy without spin-orbit coupling, we establish a Ginzburg-Landau framework in which the electron-hole wavefunction-overlap directly maps the flat-band quantum metric onto the macroscopic free energy. This mapping plays a key role in both the EI and the associated superfluid phases, with the coherence length and phase stiffness emerging directly from the quantum metric. Our analysis reveals that under strong interactions, the quantum metric induces a negative effective kinetic coefficient for the amplitude mode. Rather than destabilizing the uniform condensate, this softens the amplitude fluctuations at a finite momentum, giving rise to a finite-momentum superfluid density fluctuation (FMSDF) state. This state is observable as a periodically modulated magnitude of in-plane magnetization fluctuations. Our findings establish a rigorous link between flat-band quantum geometry and dynamic collective excitonic states, with promising pathways for realization in covalent-organic frameworks (COFs).

arXiv comment13 pages, 3 figures

References in corpus (42)