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arXiv:1912.12736 · Physical Review Letters

Simulating Twistronics without a Twist

Tymoteusz Salamon, Alessio Celi, Ravindra W. Chhajlany, Irénée Frérot, Maciej Lewenstein, Leticia Tarruell, Debraj Rakshit

Published Jul 14, 2020• 72 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.125.030504

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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.
Creating crystal bilayers twisted with respect to each other would lead to large periodic supercell structures, which can support a wide range of novel electron correlated phenomena, where the full understanding is still under debate. Here, we propose a scheme to realize an interaction-induced twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the intrinsic atomic interaction to couple different layers and dynamically induce a supercell structure, distinct from the conventional wisdom to achieve the static twisted-bilayer lattices. To illustrate that, we study the dynamics of a two-component BEC and show that the intrinsic interaction effect arising from interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moir\'e structures. One of the interesting moir\'e-physics effects, i.e., the flat-band physics, is shown through investigating the dynamics of a wave packet of the BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and leads to an alternative way to study twistronics in cold atom quantum simulators.
Stacking two layers of graphene with a relative twist angle gives rise to Moir\'e patterns, which can strongly modify electronic behavior and may lead to unconventional superconductivity. A synthetic version of twisted bilayers can be engineered with cold atoms in optical lattices. Here, the bilayer structure is mimicked through coupling between atomic sublevels, and the twist is achieved by a spatial modulation of this coupling. In the present paper, we investigate the superconducting behavior of fermionic atoms in such a synthetic twisted bilayer lattice. Attractive interactions between the atoms are treated on the mean-field level, and the superconducting behavior is analyzed via the self-consistently determined pairing gap. A strong enhancement of the pairing gap is found when a quasi-flat band structure occurs at the Fermi surface, reflecting the prominent role played by the twist on the superconductivity. The tunability of interactions allows for the switching of superconducting correlations from intra (synthetic) layer to inter (synthetic) layer. This includes also the intermediate scenario, in which the competition between inter- and intra-layer coupling completely destroys the superconducting behavior, resulting in re-entrant superconductivity upon tuning of the interactions.
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.
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.
Creating crystal bilayers twisted with respect to each other would lead to large periodic supercell structures, which can support a wide range of novel electron correlated phenomena, where the full understanding is still under debate. Here, we propose a new scheme to realize a nonlinearity-induced dynamical self-organized twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the nonlinear effect from the intrinsic atomic interactions to couple different layers and induce a dynamical self-organized supercell structure, dramatically distinct from the conventional wisdom to achieve the static twisted-bilayer lattices. To illustrate that, we study the dynamics of a two-component BEC and show that the nonlinear interaction effect naturally emerged in the Gross-Pitaevskii equation of interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moiré structures. One of the interesting moiré phenomena, i.e., the flat-band physics, is shown through investigating the dynamics of the wave packet of BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and reveal a profound connection between the nonlinearity and twistronics in cold atom quantum simulators.
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.