Landau levels in the case of two degenerate coupled bands: Kagomé lattice tight-binding spectrum

Xiao, Ying; Pelletier, Vincent; Chaikin, P. M.; Huse, David A.

doi:10.1103/physrevb.67.104505

Cited by 32 publications

(42 citation statements)

References 21 publications

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“…A similar Hamiltonian was obtained by Ref. [16] in the triangular version of the kagomé lattice. However their Hamiltonian -see Eq.…”

Section: Lower Dirac Pointssupporting

confidence: 59%

“…(2.6) in Ref. [16] with d 3 = 0 -breaks time-reversal symmetry which is not possible at the Γ point. This is due to taking the Pauli matrices σ x , σ y instead of σ z , σ x in the Hamiltonian H ++ , see Eq.…”

Section: Lower Dirac Pointsmentioning

confidence: 96%

“…1a). On the other hand, the kagomé model [15,16], chosen here with a square symmetry, (see Fig. 2b) features a quadratic band contact point [17][18][19] between its lower bands: a dispersive band and a flat band resulting from destructive interferences [14] (see Fig.…”

Section: Introductionmentioning

confidence: 99%

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Dirac points emerging from flat bands in Lieb-kagome lattices

et al. 2020

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The energy spectra for the tight-binding models on the Lieb and kagomé lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphene-like Dirac cones in the kagomé limit, the low energy pair evolves until it merges producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low energy pair of Dirac points is particularly interesting in this respect: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudo-spin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

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“…A similar Hamiltonian was obtained by Ref. [16] in the triangular version of the kagomé lattice. However their Hamiltonian -see Eq.…”

Section: Lower Dirac Pointssupporting

confidence: 59%

Section: Lower Dirac Pointsmentioning

confidence: 96%

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Dirac points emerging from flat bands in Lieb-kagome lattices

et al. 2020

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“…A paradigmatic Chern insulator system is the Haldane model [3]. Motivated by this model, some other lattice systems [11][12][13][14][15][16][17][18][19][20][21][22][23] are also predicted to contain topological non-trivial phases. Of these, large-Chern-number phases with QAHE have attracted widespread attention.…”

Section: Introductionmentioning

confidence: 99%

Predicting large-Chern-number phases in a shaken optical dice lattice

Cheng

Yin

et al. 2020

Phys. Rev. A

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With respect to the quantum anomalous Hall effect (QAHE), the detection of topological nontrivial large-Chern-number phases is an intriguing subject. Motivated by recent research on Floquet topological phases, this study proposes a periodic driving protocol to engineer large-Chern-number phases using QAHE. Herein, spinless ultracold fermionic atoms are studied in a two-dimensional optical dice lattice with nearest-neighbor hopping and a Λ/V-type sublattice potential subjected to a circular driving force. Results suggest that large-Chern-number phases exist with Chern numbers equal to C = −2, which is consistent with the edge-state energy spectra.

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“…2 Because of its beautiful structure, the Hofstadter spectrum has attracted many researchers' attention, and the spectra for different 2D lattice symmetries have been reported. Besides the square lattice, there are also triangular lattice, 3 honeycomb lattice, 4 Kagome lattice, 5 and a bipartite periodic structure with hexagonal symmetry. 6 These are all studied within the framework of Bloch electrons in a uniform magnetic field, usually assuming nearest-neighbor ͑NN͒ couplings t 1 only.…”

Section: Introductionmentioning

confidence: 99%

Energy spectrum of Bloch electrons under checkerboard field modulations

Chang

Yang

2004

Phys. Rev. B

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Two-dimensional Bloch electrons in a uniform magnetic field exhibit a complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these symmetries. We have also found an electricmodulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.

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Landau levels in the case of two degenerate coupled bands: Kagomé lattice tight-binding spectrum

Cited by 32 publications

References 21 publications

Dirac points emerging from flat bands in Lieb-kagome lattices

Dirac points emerging from flat bands in Lieb-kagome lattices

Predicting large-Chern-number phases in a shaken optical dice lattice

Energy spectrum of Bloch electrons under checkerboard field modulations

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