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arXiv:2112.13797 · SciPost Physics

Emulating twisted double bilayer graphene with a multiorbital optical lattice

Junhyun Lee, J. H. Pixley

Published Aug 25, 2022• 11 citations
arXivHTMLPDF

Abstract

This work theoretically explores how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching of Bernal stacked bilayer graphene is emulated using a square optical lattice with p_x p x , p_y p y , and d_{x^2-y^2} d x 2 − y 2 orbitals on each site, while the effects of a twist are captured through the application of an incommensurate potential. The quadratic band touching is stable until the system undergoes an Anderson like delocalization transition in momentum space, which occurs concomitantly with a strongly renormalized single particle spectrum inducing flat bands, which is a generalization of the magic-angle condition realized in Dirac semimetals. The band structure is described perturbatively in the quasiperiodic potential strength, which captures miniband formation and the existence of magic-angles that qualitatively agrees with the exact numerical results in the appropriate regime. We identify several magic-angle conditions that can either have part or all of the quadratic band touching point become flat. In each case, these are accompanied by a diverging density of states and the delocalization of plane wave eigenstates. It is discussed how these transitions and phases can be observed in ultracold atom experiments.

DOI
10.21468/scipostphys.13.2.033

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This work theoretically explores how to emulate twisted double bilayer graphene with ultracold atoms in multiorbital optical lattices. In particular, the quadratic band touching of Bernal stacked bilayer graphene is emulated using a square optical lattice with p_x p x , p_y p y , and d_{x^2-y^2} d x 2 − y 2 orbitals on each site, while the effects of a twist are captured through the application of an incommensurate potential. The quadratic band touching is stable until the system undergoes an Anderson like delocalization transition in momentum space, which occurs concomitantly with a strongly renormalized single particle spectrum inducing flat bands, which is a generalization of the magic-angle condition realized in Dirac semimetals. The band structure is described perturbatively in the quasiperiodic potential strength, which captures miniband formation and the existence of magic-angles that qualitatively agrees with the exact numerical results in the appropriate regime. We identify several magic-angle conditions that can either have part or all of the quadratic band touching point become flat. In each case, these are accompanied by a diverging density of states and the delocalization of plane wave eigenstates. It is discussed how these transitions and phases can be observed in ultracold atom experiments.
Rotational misalignment or twisting of two monolayers of graphene strongly influences its electronic properties. Structurally, twisting leads to large periodic supercell structures, which in turn can support intriguing strongly correlated behavior. Here, we propose a highly tunable scheme to synthetically emulate twisted bilayer systems with ultracold atoms trapped in an optical lattice. In our scheme, neither a physical bilayer nor twist is directly realized. Instead, two synthetic layers are produced exploiting coherently coupled internal atomic states, and a supercell structure is generated via a spatially dependent Raman coupling. To illustrate this concept, we focus on a synthetic square bilayer lattice and show that it leads to tunable quasiflatbands and Dirac cone spectra under certain magic supercell periodicities. The appearance of these features are explained using a perturbative analysis. Our proposal can be implemented using available state-of-the-art experimental techniques, and opens the route toward the controlled study of strongly correlated flatband accompanied by hybridization physics akin to magic angle bilayer graphene in cold atom quantum simulators.
In recent years, flat electronic bands in twisted bilayer graphene (TBG) have attracted significant attention due to their intriguing topological properties, extremely slow electron velocities, and enhanced density of states. Extending twisted bilayer systems to new configurations is highly desirable, as it offers promising opportunities to explore flat bands beyond TBG. Here, we study both topological and trivial flat bands in a twisted bilayer honeycomb lattice for ultracold atoms and present the evolution of the flat bands with different interlayer coupling strength (ICS). Our results demonstrate that an isolated topological flat band can emerge at the Dirac-point energy for a specific value of weak ICS, referred to as the ``critical coupling.'' This occurs over a wide range of twist angles, surpassing the limits of the magic angle in TBG systems. When the ICS is slightly increased beyond the critical coupling value, the topological flat band exhibits degenerate band crossings with both the upper and lower adjacent bands at the high-symmetry ${\mathrm{\ensuremath{\Gamma}}}_{s}$ point. As the ICS is further increased into the strong coupling regime, trivial flat bands arise around Dirac-point energy. Meanwhile, more trivial flat bands appear, extending from the lowest to higher energy bands, and remain flat as the ICS increases. The topological properties of the flat bands are studied through the winding pattern of the Wilson loop spectrum. Our research provides deeper insights into the formation of flat bands in ultracold atoms with highly controllable twisted bilayer optical lattices, and may contribute to the discovery of new strongly correlated states of matter.
Moiré superlattices in twisted bilayer graphene and transition-metal dichalcogenides have emerged as a powerful tool for engineering novel band structures and quantum phases of two-dimensional quantum materials. Here we investigate Moiré physics emerging from twisting two independent hexagonal optical lattices of atomic (pseudo-)spin states (instead of bilayers) that exhibit remarkably different physics from twisted bilayer graphene. We employ a momentum-space tight-binding calculation that includes all range real-space tunnelings and show that all twist angles θ≲6° can become magic and support gapped flat bands. Because of the greatly enhanced density of states near the flat bands, the system can be driven to superfluidity by weak attractive interaction. Strikingly, the superfluid phase corresponds to a Larkin-Ovchinnikov state with finite momentum pairing that results from the interplay between flat bands and interspin interactions in the unique single-layer spin-twisted lattice. Our work may pave the way for exploring novel quantum phases and twistronics in cold atomic systems.
Twisted bilayer materials provide a versatile platform for realizing correlated topological states. Motivated by the recent experimental realization of atomic Bose-Einstein condensates in twisted bilayer optical lattices, we investigate the emergence of fractional topological phases in such systems. For experimentally realistic parameters, the single-particle spectrum hosts a pair of quasi-degenerate nearly flat moiré bands. We show using self-consistent Hartree-Fock calculations that atomic interactions spontaneously break time-reversal symmetry, lift the quasi-degeneracy, and generate an isolated nearly flat band with a nonzero Chern number. At fractional filling, exact diagonalization of the Hamiltonian projected to this band reveals a threefold degenerate ground-state manifold and a characteristic particle entanglement spectrum, providing strong evidence for a fractional Chern insulator. The resulting many-body gap is of order 10−3ER10^{-3}E_R10−3ER​, corresponding to a nanokelvin energy scale accessible to state-of-the-art cold-atom experiments. Our scheme requires neither spin-orbit coupling, as in transition metal dichalcogenides, nor a finite magnetic field, as in existing twisted-bilayer-graphene experiments, providing a highly tunable route to strongly correlated topological phases in twisted bilayer optical lattices.
Abstract Observation of strong correlations and superconductivity in twisted-bilayer-graphene have stimulated tremendous interest in fundamental and applied physics. In this system, the superposition of two twisted honeycomb lattices, generating a Moire pattern, is the key to the observed flat electronic bands, slow electron velocity and large density of states. Despite these observations, a full understanding of the emerging superconductivity from the coupled layers and the appearance of a small magic angle remain a hot topic of research. Here, we demonstrate a quantum simulation platform to study superfluids in twisted bilayer lattices based on Bose-Einstein condensates loaded into spin-dependent optical lattices. The lattices are made of two sets of laser beams that independently address atoms in different spin states, which form the synthetic dimension accommodating the two layers. The twisted angle of the two lattices is controlled by the relative angle of the laser beams. We show that atoms in each spin state only feel one set of the lattice and the interlayer coupling can be controlled by microwave coupling between the spin states. Our system allows for flexible control of both the inter- and intralayer couplings. Furthermore we directly observe the spatial Moire pattern and the momentum diffraction, which confirm the presence of atomic superfluid in the bilayer lattices. Our system constitutes a powerful platform to investigate the physics underlying the superconductivity in twisted-bilayer-graphene and to explore other novel quantum phenomena difficult to realize in materials.
We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.