Engineering 2D square lattice Hubbard models in 90$^\circ$ twisted Ge/SnX (X=S, Se) moir\'e supperlattices

Abstract

Due to the large-period superlattices emerging in moire two-dimensional (2D) materials, electronic states in such systems exhibit low energy flat bands that can be used to simulate strongly correlated physics in a highly tunable setup. While many investigations have thus far focused on moire flat bands and emergent correlated electron physics in triangular, honeycomb and quasi-one-dimensional lattices, tunable moire realizations of square lattices subject to strong correlations remain elusive. Here we propose a feasible scheme to construct moire square lattice systems by twisting two or more layers of 2D materials in a rectangular lattice by 90 degrees. We demonstrate the concept with twisted GeX/SnX (X=S, Se) moire superlattices and calculate their electronic structures from first principles. We show that the lowest conduction flat band in these systems can be described by a square lattice Hubbard model with parameters which can be controlled by varying the choice of host materials, number of layers, and external electric fields. In particular, twisted double bilayer GeSe realizes a square lattice Hubbard model with strong frustration due to the next nearest neighbour hopping that could host unconventional superconductivity{, in close analogy to the Hubbard model for copper-oxygen planes of cuprate high-temperature superconductors}. The presented scheme uses 90-degree twisted 2D materials with rectangular unit cells as a promising platform for realizing the physical phenomena of square lattice Hubbard models, establishing a new route for studying its rich phase diagram of magnetism, charge order, and unconventional superconductivity in a highly tunable setting.