Condensed Matter Journal Club: On Moiré phonons in Small-angle Twisted Bilayer Graphene

Abstract: Twisted bilayer graphene (TBG) continues to be a system of interest in condensed matter physics. Theory and experiment have shown that structural behavior in TBG significantly impacts its electronic properties, primarily due to its large-scale periodic triangular Moiré pattern created by a small interlayer twist angle. To investigate the structural properties of this system, we present a study of the low-energy in-plane shear phonon modes of small-angle TBG, also termed the Moiré phonons. Typically the low-energy phonon spectrum is thought to be understood in terms of a simple continuum elastic model. We check this idea using atomistic calculations based on quantum Monte Carlo data and find surprising differences even in regimes in which continuum models should be accurate. In particular, we find that for small twist angles, the continuum model largely overestimates the band splitting within the Moiré phonon band spectrum, while underestimating corrugation and commensuration effects.