Implementation of the bilayer Hubbard model in a moir\'e heterostructure

TL;DR

This paper reports the experimental realization of a bilayer Hubbard model in a moiré heterostructure, enabling studies of correlated electron physics and magnetic phases in a controllable two-layer system.

Contribution

It demonstrates the creation of a staggered bilayer triangular lattice in MoSe₂/WS₂ heterostructures, providing a new platform for exploring bilayer Hubbard model physics.

Findings

Charge filling proceeds layer-by-layer in the heterostructure.

Experimental evidence of spin correlations on the bilayer lattice.

Electrostatic tunability of magnetic interactions such as RKKY.

Abstract

Moir\'e materials provide a unique platform for studies of correlated many-body physics of the Fermi-Hubbard model on triangular spin-charge lattices. Bilayer Hubbard models are of particular significance with regard to the physics of Mott insulating states and their relation to unconventional superconductivity, yet their experimental implementation in moir\'e systems has so far remained elusive. Here, we demonstrate the realization of a staggered bilayer triangular lattice of electrons in an antiparallel MoSe$_{2}$/WS$_{2}$ heterostructure. The bilayer lattice emerges due to strong electron confinement in the moir\'e potential minima and the near-resonant alignment of conduction band edges in MoSe$_{2}$ and WS$_{2}$. As a result, charge filling proceeds layer-by-layer, with the first and second electron per moir\'e cell consecutively occupying first the MoSe$_{2}$ and then the WS$_{2}$ layer. We describe the observed charging sequence by an electrostatic model and provide experimental evidence of spin correlations on the vertically offset and laterally staggered bilayer lattice, yielding absolute exciton Land\'e factors as high as $600$ at lowest temperatures. The bilayer character of the implemented spin-charge lattice allows for electrostatic tunability of Ruderman-Kittel-Kasuya-Yosida magnetism, and establishes antiparallel MoSe$_{2}$/WS$_{2}$ heterostructures as a viable platform for studies of bilayer Hubbard model physics with exotic magnetic phases on frustrated lattices.