Flat-band engineering in tight-binding models: Beyond the nearest-neighbor hopping

Abstract

In typical flat-band models, defined as nearest-neighbor tight-binding models, flat bands are usually pinned to the special energies, such as top or bottom of dispersive bands, or band crossing points. In this paper, we propose a simple method to tune the energy of flat bands without losing the exact flatness of the bands. The main idea is to add farther-neighbor hoppings to the original nearest-neighbor models, in such a way that the transfer integrals depend only on the Manhattan distance. We apply this method to several lattice models including the two-dimensional kagome lattice and the three dimensional pyrochlore lattice, as well as their breathing lattices and nonline graphs. The proposed method will be useful for engineering flat bands to generate desirable properties, such as enhancement of Tc of superconductors and nontrivial topological orders. arXiv:1810.10830v2 [cond-mat.str-el]

Compact localized states and localization dynamics in the dice lattice

“…7(c), initial-state | (0) with sites 8, 9, 12, and 13 equally excited is an equal amplitude superposition of four single-site excitations shown in Eqs. (33), (27), (29), and (23). The superposition coefficients are 1/2.…”

“…In the condensed-matter physics, optics, and quantum physics, the flatbands exist in various lattices of onedimension (1D) and two-dimension (2D) geometries. These lattices include the rhombic [3][4][5][6][7][8][9][10][11][12], sawtooth [13,14], crossstitch [15][16][17], dice [18][19][20][21], honeycomb [22,23], kagome [24][25][26], and pyrochlore lattices [27][28][29]. The formation of flatbands, the CLSs, the localization, the effects of disorder, as well as the interaction and nonlinearity are studied.…”

Mode conversion and resonant absorption in inhomogeneous materials with flat bands

“…Many models having one or more flat bands have been studied theoretically. Two-dimensional (2D) lattices such as the Lieb, dice, and kagome lattices and onedimensional (1D) lattices such as the stub, sawtooth, and diamond lattices are among the examples [18][19][20][21]. The low-energy physics of the aforementioned 2D lattices can be described by two Dirac cones intersected by a flat band and modeled by the pseudospin-1 Dirac equation in 2D [22][23][24][25][26].…”

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

“…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.…”