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arXiv:2211.07672 · Physical review. B./Physical review. B

Atomically thin superfluid and solid phases for atoms on strained graphene

Sang Wook Kim, Mohamed M. Elsayed, Nathan Nichols, Taras I. Lakoba, Juan M. Vanegas, Carlos Wexler, Valeri N. Kotov, Adrian Del Maestro

Published Feb 20, 2024• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.109.064512

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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.
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)(V>0)(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 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.
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.
A controlled twist between separate potentials can drastically influence localization properties of quantum particles between ordered and (quasi)disordered limits. Transport properties of single-particle and correlated fermionic materials have been extensively studied in connection with twisted bilayer graphene, but their bosonic counterpart remains largely unexplored. Here, we study bosonic matter in twisted potentials. We use continuous-space quantum Monte Carlo simulations to determine the unique phase diagrams of strongly correlated ultracold bosons in twisted optical lattices. For commensurate twisting angles, spectral gaps govern the formation of insulators, separated by thin superfluid domains. These domains form weak superfluids; with low superfluid fraction at zero temperature and high sensitivity to thermal fluctuations, but may be stabilized under appropriate parameter control. In contrast, slightly changing the twisting angle to an incommensurate value destroys most spectral gaps, leaving behind a prominent Bose glass phase. Our results are directly applicable to current generation experiments that quantum simulate moiré physics. Published by the American Physical Society 2024
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin, which have Feshbach-induced spin-dependent interactions, to produce a quantum dimer model. I propose an experiment to detect the ground state in this system. In a final project, I develop tools to simulate the dynamics of fermionic superfluids in which fermions interact via a short-range interaction.
Abstract Cold atoms in an optical lattice with brick-wall geometry have been used to mimic graphene, a two-dimensional material with characteristic Dirac excitations. Here we propose to bring such artificial graphene into the proximity of a second atomic layer with a square lattice geometry. For non-interacting fermions, we find that such bilayer system undergoes a phase transition from a graphene-like semi-metal phase, characterized by a band structure with Dirac points, to a gapped band insulator phase. In the presence of attractive interactions between fermions with pseudospin-1/2 degree of freedom, a competition between semi-metal and superfluid behavior is found at the mean-field level. Using the quantum Monte Carlo method, we also investigate the case of strong repulsive interactions. In the Mott phase, each layer exhibits a different amount of long-range magnetic order. Upon coupling both layers, a valence-bond crystal is formed at a critical coupling strength. Finally, we discuss how these bilayer systems could be realized in existing cold atom experiments.
Novel two-dimensional, atomically thin materials, notably graphene and transition-metal dichalcogenides, exhibit exotic Dirac quasiparticle spectra and can serve as experimental and theoretical laboratories for understanding fundamental physical phenomena, such as the nature of the van der Waals force between atoms and material surfaces. van der Waals forces are the most common manifestations of electromagnetism in Nature and govern the interactions between neutral objects on mesoscopic scales. Yet they are very hard to “engineer” and manipulate effectively, and here the newly-discovered graphene-type materials can lead to fundamental progress. I will discuss recent progress and my results in the following main directions: (1) I will describe how van der Waals interactions between cold atoms and graphene arise and the way physicists calculate them. The atoms have to be fairly “cold” so that thermal motion and other dissipation effects do not interfere with the main phenomenon. (2) I will present recent results on how we can effectively change the strength of these interactions. In particular I will discuss how changing the number of electrons in the graphene sheet (via application of voltage) can lead to changes in the van der Waals force. Other ways of manipulating, or “quantum engineering” such forces will also be mentioned, namely effects of strain and using other atomically thin materials instead of graphene.