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\nstructures that we call ``partial line graphs''.In tight-binding models on\npartial line graphs, energy bands with flat energy dispersions emerge.This\nmethod can be applied to two- and three-dimensional systems. We show examples\nof partial line graphs of square and cubic lattices. The method is useful in\nproviding a guideline for synthesizing materials with flat energy bands, since\nthe tight-binding models on the partial line graphs provide us a large room for\nmodification, maintaining the flat energy dispersions.\n