Designing flat-band tight-binding models with tunable multifold band touching points
| Autor: | Graf, Ansgar, Piéchon, Frédéric |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 104, 195128 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.104.195128 |
| Popis: | 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 flat-band tight-binding models with short-range hoppings \emph{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 $N\geq2$ of bands. Linear flat-band models are rarer: they require $N\geq3$ 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. Comment: Published version |
| Databáze: | arXiv |
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