Two-dimensional Bose-Hubbard model for helium on graphene

• Published in: Physical review. B 2021-06, Vol.103 (23), p.1, Article 235414
• Main Authors: Yu, Jiangyong, Lauricella, Ethan, Elsayed, Mohamed, Shepherd, Kenneth, Nichols, Nathan S., Lombardi, Todd, Kim, Sang Wook, Wexler, Carlos, Vanegas, Juan M., Lakoba, Taras, Kotov, Valeri N., Del Maestro, Adrian
• Format: Article
• Language: English
• Subjects: Bosons; Correlation; Graphene; Helium; Parameter sensitivity; Phase transitions; Solid phases; Two dimensional models
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.103.235414

An exciting development in the field of correlated systems is the possibility of realizing two-dimensional (2D) phases of quantum matter. For a system of bosons, an example of strong correlations manifesting themselves in a 2D environment is provided by helium adsorbed on graphene. We construct the effective Bose-Hubbard model for this system which involves hard-core bosons ( U ≈ ∞ ) , repulsive nearest-neighbor ( V > 0 ) and small attractive ( V ′ < 0 ) next-nearest-neighbor interactions. The mapping onto the Bose-Hubbard model is accomplished by a variety of many-body techniques which take into account the strong He-He correlations on the scale of the graphene lattice spacing. Unlike the case of dilute ultracold atoms where interactions are effectively pointlike, the detailed microscopic form of the short-range electrostatic and long-range dispersion interactions in the helium-graphene system is crucial for the emergent Bose-Hubbard description. The result places the ground state of the first layer of 4He adsorbed on graphene deep in the commensurate solid phase with 1 / 3 of the sites on the dual triangular lattice occupied. Because the parameters of the effective Bose-Hubbard model are very sensitive to the exact lattice structure, this opens up an avenue to tune quantum phase transitions in this solid-state system.