Moire Insulators viewed as the Surface of three dimensional Symmetry Protected Topological Phases

TL;DR

This paper proposes that Moire insulators at certain fillings can be understood as the surfaces of three-dimensional symmetry protected topological phases, revealing their topological nature through symmetry and electron filling considerations.

Contribution

It introduces a theoretical framework linking Moire insulators to 3D SPT phases based on symmetry and filling, providing new insights into their topological properties.

Findings

Moire insulators at 1/2 and 1/4 fillings are boundary states of 3D bosonic SPT phases.

These insulators exhibit 't Hooft anomalies due to spatial symmetries.

The effective models have higher symmetries than typical spin systems.

Abstract

Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality. Before we learn more experimental details and the accurate microscopic models describing the insulators, some general conclusions can already be made about these systems, simply based on their symmetries and electron fillings. The insulator in the Moire superlattice is described by an effective spin-orbital model with approximate higher symmetries than ordinary spin systems. We demonstrate that both the insulators observed at the 1/2 and 1/4 fillings away from the charge neutrality can be viewed as the boundary of a three-dimensional bosonic symmetry protected topological phase, and hence have the 't Hooft anomaly once the spatial symmetries are viewed as internal symmetries.