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2020

Quantum Geometry and Stability of Moir\'e Flatband Ferromagnetism

Wu, Fengcheng, Sarma, S. Das

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Several moir\'e systems created by various twisted bilayers have manifested magnetism under flatband conditions leading to enhanced interaction effects.

We theoretically study stability of moir\'e flatband ferromagnetism against collective excitations, with a focus on the effects of Bloch band quantum geometry.
The spin magnon spectrum is calculated using different approaches, including Bethe-Salpeter equation, single mode approximation, and an analytical theory.
One of our main results is an analytical expression for the spin stiffness in terms of the Coulomb interaction potential, the Berry curvatures, and the quantum metric tensor, where the last two quantities characterize the quantum geometry of moir\'e bands.

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