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The studies of dispersion-less bands revealed in electronic and photonic systems have caught great attention recently. Many exotic quantum phenomena, for example, the high-transition-temperature superconductivity associated with the infinitely large density of states of the flat bands, are proposed. In this talk, I will begin with an introduction to the flat bands using Wannier functions. Then I will introduce three tight-binding models, namely the Lieb, kagome, and checkerboard lattices, by considering only the nearest-neighbor hopping parameters and demonstrate that the recognized flat bands associated with the three lattices can be ideally embedded into new structures, respectively [1]. Finally, I will provide several examples for the appearance of nearly flat bands realized in two-dimensional materials with long-range hopping beyond the simplified tight-binding models based on our first-principles calculations for the systems composed of Ge atoms.

Our study clearly demonstrates that the flat bands given by the well-known lattices, namely the Lieb, kagome, and checkerboard lattices, can be ideally embedded into the new structures that cannot be recognized as the original ones. Therefore, the amount of materials that can give interesting flat-band physics could be much larger.

[1] Chi-Cheng Lee et al., arXiv:1904.07048 (2019).

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