Magnetism and Quantum Melting in Moir\'e-Material Wigner Crystals

TL;DR

This paper investigates how electron localization and magnetic properties in moiré materials evolve from classical Wigner crystals to metallic states using momentum-space exact diagonalization, revealing insights into quantum melting and magnetism.

Contribution

It introduces a momentum-space exact diagonalization approach to study the transition from Wigner crystals to metallic states in moiré materials at fractional fillings.

Findings

Identification of magnetic ground states at fillings 1/3 and 2/3.

Observation of quantum melting of Wigner crystals with increasing hopping.

Insights into the interplay between electron localization and magnetism.

Abstract

Recent experiments have established that semiconductor-based moir\'e materials can host incompressible states at a series of fractional moir\'e-miniband fillings. These states have been identified as generalized Wigner crystals in which electrons localize on a subset of the available triangular-lattice moir\'e superlattice sites. In this article, we use momentum-space exact diagonalization to investigate the many-body ground state evolution at rational fillings from the weak-hopping classical lattice gas limit, in which only spin degrees-of-freedom are active at low energies, to the strong-hopping metallic regime where the Wigner crystals melt. We specifically address the nature of the magnetic ground states of the generalized Wigner crystals at fillings $\nu$ = 1/3 and $\nu$ = 2/3.