Flat bands by latent symmetry

Morfonios, C. V.; Röntgen, M.; Pyzh, M.; Schmelcher, P.

doi:10.48550/arxiv.2102.12446

Cited by 2 publications

(2 citation statements)

References 53 publications

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“…In particular, many researchers have tried to develop schemes that systematically generate flat-band TB models. Such schemes make use of graph theory [6,7,[21][22][23], Origami rules [24], repeated miniarrays [25], a bipartite lattice structure [26,27], generic existence conditions [28,29], or the extension of known flat-band lattices [29][30][31]. Also, over the last years, the close relation between flat bands and compact localized states (CLSs) [32] was increasingly exploited [33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Designing flat-band tight-binding models with tunable multifold band touching points

Graf,

Piéchon

2021

Preprint

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Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this work presents a straightforward method to build flatband tight-binding models with short-range hoppings on any periodic lattice. The method consists in starting from a CLS and engineering families of Bloch Hamiltonians as quadratic (or linear) functions of the associated Bloch state. The resulting tight-binding models not only exhibit a flat band, but also multifold quadratic (or linear) band touching points (BTPs) whose number, location, and degeneracy can be controlled to a large extent. Quadratic flat-band models are ubiquitous: they can be built from any arbitrary CLS, on any lattice, in any dimension and with any number N ≥ 2 of bands. Linear flat-band models are rarer: they require N ≥ 3 and can only be built from CLSs that fulfill certain compatibility relations with the underlying lattice. Most flat-band models from the literature can be classified according to this scheme: Mielke's and Tasaki's models belong to the quadratic class, while the Lieb, dice and breathing Kagome models belong to the linear class. Many novel flat-band models are introduced, among which an N = 4 bilayer honeycomb model with fourfold quadratic BTPs, an N = 5 dice model with fivefold linear BTPs, and an N = 3 Kagome model with BTPs that can be smoothly tuned from linear to quadratic.

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Section: Introductionmentioning

confidence: 99%

Designing flat-band tight-binding models with tunable multifold band touching points

Graf,

Piéchon

2021

Preprint

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“…In past decades, the studies of flat-band (FB) systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] have been mostly focused on strong correlation physics such as fractional quantum Hall effect [16][17][18][19], ferromagnetism [20][21][22], Wigner crystallization [23], and so on, which originate from the flat energy dispersion. On the other hand, the recent discoveries of FBs in the kagome materials [24][25][26] and twisted bilayer graphene [27][28][29] have demonstrated that the nontrivial topological and geometric properties can also arise in FB systems due to the characteristics of the FB wave functions.…”

Section: Introductionmentioning

confidence: 99%

General construction of flat bands with and without band crossings based on wave function singularity

Hwang,

Rhim,

Yang

2021

Preprint

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In this work, we develop a systematic method of constructing flat-band models with and without band crossings. Our construction scheme utilizes the symmetry and spatial shape of a compact localized state (CLS), and also the singularity of the flat-band wave function obtained by a Fourier transform of the CLS (FT-CLS). In order to construct a flat-band model systematically using these ingredients, we first choose a CLS with a specific symmetry representation in a given lattice. Then, the singularity of FT-CLS indicates whether the resulting flat band exhibits a band crossing point or not. A tight-binding Hamiltonian with the flat band corresponding to the FT-CLS is obtained by introducing a set of basis molecular orbitals, which are orthogonal to the FT-CLS. Our construction scheme can be systematically applied to any lattice so that it provides a powerful theoretical framework to study exotic properties of both gapped and gapless flat-bands arising from their wave function singularities.

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Flat bands by latent symmetry

Cited by 2 publications

References 53 publications

Designing flat-band tight-binding models with tunable multifold band touching points

Designing flat-band tight-binding models with tunable multifold band touching points

General construction of flat bands with and without band crossings based on wave function singularity

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