Flat bands and Dirac cones in breathing lattices

Essafi, Karim; Jaubert, Ludovic D. C.; Udagawa, Masafumi

doi:10.1088/1361-648x/aa782f

Cited by 36 publications

(30 citation statements)

References 38 publications

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“…Our treatment extends previous observations on the flat band in kagome, such as the observed stability of the flat band and band-touching points to breathing anisotropy 41 , and opens up new perspectives: We show how to selectively gap out the flat band, or the Dirac cones, or all bands. Thus, our results reinforces the role of the kagome lattice as a platform for the study of topological physics and flat band physics in general, in particular the physics of perturbations and disorder in flat bands.…”

Section: Introductionsupporting

confidence: 79%

Disordered flat bands on the kagome lattice

Bilitewski

Moessner

2018

Phys. Rev. B

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We study two models of correlated bond-and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered flat band ferromagnetism. arXiv:1809.10726v2 [cond-mat.str-el]

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Section: Introductionsupporting

confidence: 79%

Disordered flat bands on the kagome lattice

Bilitewski

Moessner

2018

Phys. Rev. B

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“…As is discussed in Ref. 53, this type of the band structure does not contradict the Nielsen-Ninomiya theorem on the fermion doubling in lattice models [54], and is indeed seen in various lattice models such as a Lieb lattice [55], a superhoneycomb lattice [56], and a breathing kagome lattice with the upward triangles having opposite-sign hoppings to those on the downward ones [57]. A: Schematic picture of the reduction of three sites connected by t -bonds to a single site, and the resulting kagome lattice.…”

Section: A Polymerized Triptycene Containing Phenylsupporting

confidence: 60%

Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices

Mizoguchi

Maruyama

Okada

et al. 2019

Phys. Rev. Materials

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In a class of carbon-based materials called polymerized triptycene, which consist of triptycene molecules and phenyls, exotic electronic structures such as Dirac cones and flat bands arise from the kagome-type network. In this paper, we theoretically investigate the tight-bind models for polymerized triptycene, focusing on the origin of flat bands and the topological properties. The mechanism of the existence of the flat bands is elucidated by using the "molecular-orbital" representation, which we have developed in the prior works. Further, we propose that the present material is a promising candidate to realize the two-dimensional second-order topological insulator, which is characterized by the boundary states localized at the corners of the sample. To be concrete, we propose two methods to realize the second-order topological insulator, and elucidate the topological properties of the corresponding models by calculating the corner states as well as the bulk topological invariant, namely the Z3 Berry phase.

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“…Another interesting deformation is one leading to alternately sized equilateral triangles, dubbed the trimerized or breathing kagome lattice [34], in analogy to the breathing pyrochlores [35]. Correspondingly, the kagome lattice features an alternation of interactions, with the triangles pointing up (having a superexchange coupling J ) and those pointing down (with J ) [36]; see Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

et al. 2018

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The nature of the ground state of the spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e., with different superexchange couplings J and J within elementary up-and downpointing triangles) is investigated within the framework of Gutzwiller projected fermionic wave functions and Monte Carlo methods. We analyze the stability of the U(1) Dirac spin liquid with respect to the presence of fermionic pairing that leads to a gapped Z2 spin liquid. For several values of the ratio J /J , the size scaling of the energy gain due to the pairing fields and the variational parameters are reported. Our results show that the energy gain of the gapped spin liquid with respect to the gapless state either vanishes for large enough system size or scales to zero in the thermodynamic limit. Similarly, the optimized pairing amplitudes (responsible for opening the spin gap) are shown to vanish in the thermodynamic limit. Our outcome is corroborated by the application of one and two Lanczos steps to the gapless and gapped wave functions, for which no energy gain of the gapped state is detected when improving the quality of the variational states. Finally, we discuss the competition with the "simplex" Z2 resonating-valence-bond spin liquid, valence-bond crystal, and nematic states in the strongly anisotropic regime, i.e., J J .arXiv:1712.04579v2 [cond-mat.str-el] 15 Mar 2018 J /J = 1 J /J = 0.9 J /J = 0.7 J /J = 0.5 J /J = 0.3 J /J = 0.1 Z of J ) in the strong anisotropy limit:FIG. 7. For different values of the breathing anisotropy J /J , the finite-size scaling of the energy gain (in units of J ) of the sixsite unit-cell VBC with respect to the U(1) Dirac spin liquid, i.e., [E(VBC)−E(U(1))]/J . The clusters considered are L = 8, 12, 16, and 20.

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Flat bands and Dirac cones in breathing lattices

Cited by 36 publications

References 38 publications

Disordered flat bands on the kagome lattice

Disordered flat bands on the kagome lattice

Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices

Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet

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