Berry curvature of interacting bosons in a honeycomb lattice

Li, Yun; Sengupta, Pinaki; Batrouni, G. G.; Miniatura, Christian; Grémaud, Benoît

doi:10.1103/physreva.92.043605

Cited by 13 publications

(7 citation statements)

References 52 publications

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“…Assuming that both U and U are smaller than J, we linearise the above Hamiltonian in Eq. (18) by expanding the cosine term to quadratic order, such that this model becomes analytically solvable. Fourier transforming the phase and number variables, we obtain the effective Hamiltonian of the phase fluctuations as,…”

Section: Microscopic Hamiltonian For the Granular Superconductormentioning

confidence: 99%

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Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

et al. 2016

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We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. We show that the Dirac node is preserved in the presence of an inter-grain interaction, despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sublattice symmetry by choosing different on-site potentials for the two sublattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac materials. Dirac node dispersion of bosonic excitations is thus expanding the discussion of the conventional Dirac cone excitations to the case of bosons. We call this case as a representative of Bosonic Dirac Materials (BDM), similar to the case of Fermionic Dirac materials extensively discussed in the literature.

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Section: Microscopic Hamiltonian For the Granular Superconductormentioning

confidence: 99%

“…Ref. [18] finds non-vanishing Berry curvature in honeycomb lattice of soft-core bosons and also talks about anomalous Hall effect in non-equilibrium. Saxena et al discussed the Dirac cones in photonic crystal [19].…”

Section: Introductionmentioning

confidence: 99%

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

et al. 2016

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“…Usually, the appearance of an edge state is a consequence of the non-trivial topological property of bulk system. Although band structures collapse for bosonic systems, a pseudo-Berry curvature could be defined using the equal-time Green function, which can be obtained from the QMC calculation [35,36]. In Fig.…”

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confidence: 99%

Bosonic edge states in gapped honeycomb lattices

et al. 2016

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Using quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we prove the existence of bosonic edge states. For single-layer honeycomb lattices, bosonic edge states can be created, cross the gap, and merge into bulk states using an on-site potential applied to the outermost sites of the boundary. On the bilayer honeycomb lattice, bosonic edge states traversing the gap at half filling are demonstrated. The topological origin of the bosonic edge states is discussed in terms of the pseudo-Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states using ultracold bosons trapped in honeycomb optical lattices. Introduction.-Many important phenomena in condensed matter physics share the same intriguing feature, namely, the presence of edge states in the gap. Well-known examples include the quantum Hall effect (QHE), topological insulators, and graphene systems [1][2][3][4]. The appearance of an edge state is the consequence of the non-trivial topological properties of the bulk band. Edge states have been created in various systems such as quantum wells and graphene [5][6][7][8]; the existence of edge states constitutes a central motivation for studying these kinds of materials. Edge states are perfectly conducting channels and play an important role in electronic transport [9]. Edge states can be engineered to create onedimensional topological superconductors, which support localized Majorana fermions [10].

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“…In exciton polaritons, Bardyn et al, 2016 andBleu et al, 2016 analyzed the Bogoliubov modes of exciton-polariton condensates and proposed models which have topological edge states at the gaps with nonzero excitation energy. The topological edge states at higher energy gaps of Bogoliubov excitations were also discussed in ultracold atomic gases (Di Liberto et al, 2016a;Engelhardt and Brandes, 2015;Furukawa and Ueda, 2015;Li et al, 2015b). In a lattice of photonic cavities under parametric driving, Peano et al, 2016a proposed a model which has a nonzero gap at zero energy.…”

Section: B Emergent Topology Of Bogoliubov Modesmentioning

confidence: 99%

Topological Photonics

Ozawa,

Price,

Amo

et al. 2018

Preprint

142

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Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect. 4. Nonmagnetic designs 54 C. Toward even higher dimensions 55 1. Synthetic dimensions 55 2. Four-dimensional quantum Hall effect 56 VI. Gain and loss in topological photonics 56 A. Non-Hermitian topological photonics 56 B. Emergent topology of Bogoliubov modes 57 VII. Topological effects for interacting photons 58 A. Weak nonlinearities 59 B. Strong nonlinearities 60 VIII. Conclusion and perspectives 62 A. Optical isolation and robust transport 62 B. Quantum emitters and topological laser 63 1. Topological lasers: Theory 63 2. Topological lasers: Experiments 63 C. Measurement of bulk topological and geometrical properties 64 D. Topological quantum computing 65 Acknowledgments 65 References 66

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Berry curvature of interacting bosons in a honeycomb lattice

Cited by 13 publications

References 52 publications

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

Granular superconductor in a honeycomb lattice as a realization of bosonic Dirac material

Bosonic edge states in gapped honeycomb lattices

Topological Photonics

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