# Cavity Moir\'e Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction

## TL;DR

This paper theoretically demonstrates that strong quantum light-matter interactions in cavity QED can be used to control magnetic frustration in moiré materials, potentially enabling the realization of exotic quantum phases.

## Contribution

It introduces a novel theoretical framework combining cavity QED with moiré materials to control magnetic properties via quantum light-matter interactions.

## Key findings

- Quantum geometry leads to electromagnetic vacuum dressing of electrons.
- Cavity confinement can control magnetic frustration in moiré materials.
- Predicted phase diagram shows potential for exotic phases like quantum spin liquids.

## Abstract

Cavity quantum electrodynamics (QED) studies the interaction between light and matter at the single quantum level and has played a central role in quantum science and technology. Combining the idea of cavity QED with moir\'e materials, we theoretically show that strong quantum light-matter interaction provides a way to control frustrated magnetism. Specifically, we develop a theory of moir\'e materials confined in a cavity consisting of thin polar van der Waals crystals. We show that nontrivial quantum geometry of moir\'e flat bands leads to electromagnetic vacuum dressing of electrons, which produces appreciable changes in single-electron energies and manifests itself as long-range electron hoppings. We apply our general formulation to a twisted transition metal dichalcogenide heterobilayer encapsulated by ultrathin hexagonal boron nitride layers and predict its phase diagram at different twist angles and light-matter coupling strengths. Our results indicate that the cavity confinement enables one to control magnetic frustration of moir\'e materials and might allow for realizing various exotic phases such as a quantum spin liquid.