Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem

Abstract

Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D\ge 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.

arXiv comment13 pages, 10 figures

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• General construction of flat bands with and without band crossings based on wave function singularity
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Molecular-orbital representation with random U(1) variables
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Designing single and degenerate flat bands in the kagome lattice with long-range hopping
• Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
• Interorbital Antisymmetric Hopping Generated Flat Bands on Kagome and Pyrochlore Lattices
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry