Fractons in moir\'e materials

As a unique opportunity hosted by the magic angle twisted bilayer graphene (MATBG),  the emergence of a novel fractional correlated insulating (FCI) state dictated by the geometry of the three-peak structure of Wannier orbitals has been proposed [1]. While Ref.[1] established the novel FCI state with extensive ground-state landscape at the filling of $n\pm1/3$ from rigorous considerations in the strong coupling limit, little is known about the nature of excitations. At the same time, novel correlated ground states often host unusual excitations. In this talk, I will discuss the nature of two distinct fractionalized excitations in the FCI phase. : (1) fracton-like vortices and (2) soliton-like domain wall edge states. Although both types of excitations carry fractional electric charges, their topological charges are distinct. Moreover, both defects' movements are restricted to emergent low-dimensional subspace embedded in the two-dimensional (2D) space of MATBG and hence ``fractonic''. Specifically, fractonic vortices are immobile while  the domain wall edge states' motion is restricted along one direction, behaving much like a 2D version of solitons in a Su-Schriffer-Heeger chain. We discuss implications of these fractonic excitations on the band-width tuned and doping tuned phase transition from the fractional correlated insulator phase to the Fermi liquid phase. We also discuss how magnetism can intertwine with dynamics of the fractons. We propose experiments to pursue these fractons in the partially filled (n\pm1/3) magic angle twisted bilayer graphene is tantalizing.  

 

[1]: Zhang, et al, arxiv: 2105.13371