The Flexoelectric Twist: Persistence of Heavy Fermion Picture in Small-Angle Twisted Bilayer Graphene

Abstract

Twisted bilayer graphene (TBG) near the first magic angle ($θ\approx1.05^{\circ}$) hosts topological flat bands that provide a fertile ground for exploring strongly correlated phases. At smaller twist angles ($θ<1^{\circ}$), lattice relaxation profoundly alters the moiré landscape. The extent to which moiré lattice reconstruction at different length scales affects the electronic structure through electro-mechanical coupling remains unresolved. Using scanning tunneling microscopy on small-angle TBG devices with different twist angles $θ\approx0.3-0.7^{\circ}$, we observe a pronounced $dI/dV$ peak at the AA site of the moiré lattice on top of a spectrum that is asymmetric about the charge neutrality point; we visualize lattice reconstruction at moiré lattice length scales (20-45\,nm); and we detect a dilation of the atomic lattice at the AA sites at Angstrom length scale. We demonstrate that the inclusion of moiré lattice reconstruction supports compact localized heavy fermion $f-$states at AA sites whereas the inclusion of atomic lattice dilation generates a strong flexo-electric response that breaks particle-hole symmetry, pushing the $f$-states down in energy. Consequently, these heavy fermion states energetically coexist with itinerant $c$-electrons at the AB/BA sites. Our spatially resolved spectroscopic measurements visualize this coexistence, confirming the persistence of the heavy fermion model in the small-angle regime $θ<1^{\circ}$. Our findings show that flexo-electric responses can realize qualitatively distinct electronic landscapes in moiré materials beyond the single-particle picture. Looking ahead, small-angle TBG could prove an ideal platform to explore the interacting large-$N$ Kondo lattice problem with high tunability of the $f-$occupation and $c-$density through twist-angle and electrostatic back gates, respectively.