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arXiv:2102.11288 · Physical review. B./Physical review. B

Two-dimensional Bose-Hubbard model for helium on graphene

Jiangyong Yu, Ethan Lauricella, Mohamed M. Elsayed, Kenneth Shepherd, Nathan Nichols, Todd Lombardi, Sang Wook Kim, Carlos Wexler, Juan M. Vanegas, Taras I. Lakoba, Valeri N. Kotov, Adrian Del Maestro

Published Jun 9, 2021• 14 citations
arXivHTMLPDF

Abstract

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 $(U\ensuremath{\approx}\ensuremath{\infty})$, repulsive nearest-neighbor $(V>0)$ and small attractive $({V}^{\ensuremath{'}}<0)$ 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 $^{4}\mathrm{He}$ 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.

DOI
10.1103/physrevb.103.235414

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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\ensuremath≈\ensuremath∞)(U\ensuremath{\approx}\ensuremath{\infty})(U\ensuremath≈\ensuremath∞), repulsive nearest-neighbor (V>0)(V>0)(V>0) and small attractive (V\ensuremath′<0)({V}^{\ensuremath{'}}<0)(V\ensuremath′<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^{4}\mathrm{He}4He adsorbed on graphene deep in the commensurate solid phase with 1/31/31/3 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.
Atoms deposited on atomically thin substrates are a playground for exotic quantum many-body physics due to the highly tunable, atomic-scale nature of the interaction potentials. The ability to engineer strong interparticle interactions can lead to the emergence of collective states of matter, not possible in the context of dilute atomic gases confined in optical lattices. While it is known that the first layer of adsorbed helium on graphene is permanently locked into a solid phase, we motivate, with a physically intuitive mean-field calculation, and confirm, with quantum Monte Carlo simulations, that simple isotropic graphene lattice expansion unlocks a large variety of two-dimensional ordered commensurate, incommensurate, cluster atomic solid, and superfluid states for adsorbed atoms. It is especially significant that an atomically thin superfluid phase of matter emerges under experimentally feasible strain values, with potentially supersolid phases in close proximity on the phase diagram.
Abstract Atoms deposited on 2D electronic materials, such as graphene, can exhibit unconventional many‐body correlations, not accessible in other settings. All of these are driven by van der Waals forces: between the atoms themselves and atom‐material interactions. For example 4He atoms on 2D materials can potentially form a variety of exotic quantum states of matter, such as 2D supersolids and superfluids, in addition to solid phases. For the “most quantum” case of a single helium layer we discuss, from a theoretical perspective, how the effective low‐energy (Bose–Hubbard) description can take advantage of the extreme sensitivity of this unique system to the interplay between the atomic (helium) and solid‐state (graphene) components. Due to the extraordinary variety and tunability of 2D electronic materials, it is envisaged that a wide range of correlated atomic phases can be realized under favorable conditions. Exciting possibilities in the opposite extreme of many atomic layers forming a liquid on top of graphene are also outlined —in this case a so‐called “spinodal dewetting” pattern can form at the liquid–vapor interface which reflects the presence and electronic properties of graphene underneath. Such patterns could be manipulated by choosing different atoms and materials, with potential technological applications.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
The Hubbard model underlies our understanding of strongly correlated materials. Whereas its standard form only comprises interactions between particles at the same lattice site, extending it to encompass long-range interactions is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interactions, a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of exotic many-body quantum phases.
We study the extended Bose-Hubbard model on a two-dimensional honeycomb lattice by using large-scale quantum Monte Carlo simulations. We present the ground-state phase diagrams for both the hard-core and the soft-core bosons. For the hard-core case, the transition between the $\ensuremath{\rho}=1∕2$ solid and the superfluid is first order, and the supersolid state is unstable toward phase separation. For the soft-core case, due to the presence of multiple occupation, a stable particle-induced supersolid (SS-p) phase emerges when $1∕2<\ensuremath{\rho}<1$. The transition from the solid at $\ensuremath{\rho}=1∕2$ to the SS-p phase is second order with the superfluid density scaling as ${\ensuremath{\rho}}_{s}\ensuremath{\sim}\ensuremath{\rho}\ensuremath{-}1∕2$. The SS-p phase has the same diagonal order as the solid at $\ensuremath{\rho}=1∕2$. As the chemical potential increases further, the SS-p phase turns into a solid where two bosons occupy each site of one sublattice through a first-order transition. We also calculate the critical exponents of the transition between the $\ensuremath{\rho}=1∕2$ solid and superfluid at the Heisenberg point for the hard-core case. We find the dynamical critical exponent z=0.15z=0.15z=0.15, which is smaller than results obtained on smaller lattices. This indicates that zzz approaches zero in the thermodynamic limit, and thus the transition is also first order even at the Heisenberg point.
To address the issue of electron correlation driven superconductivity in graphene, we perform a systematic quantum Monte Carlo study of the pairing correlation in the $t\ensuremath{-}U\ensuremath{-}V$ Hubbard model on a honeycomb lattice. For V=0V=0V=0 and close to half filling, we find that pairing with d+idd+idd+id (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}^{\ensuremath{'}}$ in its specific form) symmetry dominates pairing with extended-sss symmetry. However, as the system size or the on-site Coulomb interaction increases, the long-range part of the d+idd+idd+id pairing correlation decreases and tends to vanish in the thermodynamic limit. An inclusion of nearest-neighbor interaction VVV, either repulsive or attractive, has a small effect on the extended-sss pairing correlation, but strongly suppresses the d+idd+idd+id pairing correlation.