Simulating Twistronics without a Twist

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

doi:10.1103/physrevlett.125.030504

Cited by 53 publications

(36 citation statements)

References 52 publications

(55 reference statements)

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“…Note Added: While this manuscript was under consideration following its announcement in arXiv:1809.04604, independent proposals to simulate twistronics in cold atoms appeared and were published in refs. 64,65 .…”

Section: Discussionmentioning

confidence: 99%

Magic-angle semimetals

König

Wilson

et al. 2020

npj Quantum Mater.

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Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

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Section: Discussionmentioning

confidence: 99%

Magic-angle semimetals

König

Wilson

et al. 2020

npj Quantum Mater.

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“…We note that there has been recent interest in simulating spatially-varying lattice Hamiltonians [60] motivated by the electronic properties of twisted bilayer graphene. We note that this model does not offer spatial variation of the Hamiltonian in two lattice dimensions or variation which is incommensurate with the lattice spacing, which prevents Moiré supercell structure.…”

Section: Discussionmentioning

confidence: 99%

Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices

Hughes,

Jaksch

2021

Preprint

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Recent experimental progress in magnetic atoms and polar molecules has created the prospect of simulating dipolar Hubbard models with off-site interactions. When applied to real-space cylindrical optical lattices, these anisotropic dipole-dipole interactions acquire a tunable spatially-dependent component while they remain translationally-invariant in the axial direction, creating a sublattice structure in the azimuthal direction. We numerically study how the coexistence of these classes of interactions affects the ground state of hardcore dipolar bosons at half-filling in a finite-size cylindrical optical lattice with octagonal rings. When these two interaction classes cooperate, we find a solid state where the density order is determined by the azimuthal sublattice structure and builds smoothly as the interaction strength increases. For dipole polarisations where the axial interactions are sufficiently repulsive, the repulsion competes with the sublattice structure, significantly increasing entanglement and creating two distinct ordered density patterns. The spatially-varying interactions cause the emergence of these ordered states as a function of interaction strength to be staggered according to the azimuthal sublattices.

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“…On the other hand, recent developments in the ability to accurately twist van der Waals heterostructures [7][8][9][10][11] have opened the door for a new level of control over two-dimensional solid-state materials. Recent theoretical work has proposed realizations of this phenomena in ultracold atomic systems by either twisting the optical lattice [12] or its spin state [13], as well as emulating the effects of a twist using incommensurate, quasiperiodic potentials [14][15][16][17][18]. Recently, experiments have successfully twisted optical lattices holding a Bose-Einstein condensate opening the door for experimental realizations of twistronics of ultracold atoms [19].…”

Section: Introductionmentioning

confidence: 99%

Emulating twisted double bilayer graphene with a multiorbital optical lattice

Lee¹,

Pixley²

2021

Preprint

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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 px, py, and 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.

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Simulating Twistronics without a Twist

Cited by 53 publications

References 52 publications

Magic-angle semimetals

Magic-angle semimetals

Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices

Emulating twisted double bilayer graphene with a multiorbital optical lattice

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