Fractionalization in Fractional Correlated Insulating States at $n\pm 1/3$ filled twisted bilayer graphene

TL;DR

This paper explores fractionalized insulating states in twisted bilayer graphene at specific fillings, revealing fractional charges, restricted mobility, and emergent symmetries, and introduces new quantum phases driven by quantum fluctuations.

Contribution

It demonstrates the existence of fractional excitations with restricted mobility and emergent symmetries in twisted bilayer graphene, and introduces the quantum lemniscate liquid and solid phases.

Findings

Fractional excitations carry fractional charges.

Emergent $U(1) imes U(1)$ 1-form symmetry unifies excitation motions.

Doped systems exhibit emergent Luttinger liquid behavior.

Abstract

Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at $n \pm 1/3$ filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moir\'e graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of ``lemniscate" structured operators drives the system into ``quantum lemniscate liquid (QLL)" or ``quantum lemniscate solid (QLS)". We find an emergent $U(1)\times U(1)$ 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase while providing a new mechanism for fractional excitations in two-dimension. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general $n \pm 1/3$ filling.