Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures

Abstract

We introduce a systematic method for constructing a class of lattice structures that we call ``partial line graphs''.In tight-binding models on partial line graphs, energy bands with flat energy dispersions emerge.This method can be applied to two- and three-dimensional systems. We show examples of partial line graphs of square and cubic lattices. The method is useful in providing a guideline for synthesizing materials with flat energy bands, since the tight-binding models on the partial line graphs provide us a large room for modification, maintaining the flat energy dispersions.

9 pages, 4 figures

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• Superconductivity from Flat Dispersion Designed in Doped Mott Insulators
• Ferromagnetism in a Hubbard model for an atomic quantum wire: a realization of flat-band magnetism from even-membered rings

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