Bionic fractionalization in the trimer model of twisted bilayer graphene

Recent experiments on twisted van der Waals materials, inspired our study of a simplified triangular trimer model, which captures electron behavior at one-third filling in twisted bilayer graphene. Though simple, the model shows rich physics, including fractional excitations and fracton-like particles with restricted motion. Using Monte Carlo simulations and effective field theory, we uncover two notable phases: 1. A polar fluid phase with directional order. 2. A critical trimer liquid phase, where excitations carry fractional charge and display power-law correlations. These fractionalized excitations are bionic—they carry pairs of emergent gauge charges, revealed by algebraic correlations with two distinct exponents. Our field theory supports the numerical findings and critical exponents. The triangular trimer model emerges as a key platform to study fractionalization and fractons, where bionic monomers can evolve into fractons in nearby phases. This motivates experimental work in twisted van der Waals systems and materials with intermediate-range interactions. Twisted bilayer graphene has received significant interest for its unique band structure. Here, the triangular trimer model, as a representative framework for extended Wannier orbitals, is applied to twisted bilayer graphene.