Revisiting Flat bands and localization

Abstract

Flat bands imply lack of itinerancy due to some constraints that, in principle, results in anomalous behaviors with randomness. By a molecular orbital (MO) representation of the flat band systems, random MO models are introduced where the degeneracy due to the flat bands is preserved even with randomness. The zero modes of the chiral symmetric system with sublattice imbalance belong to the class. After explaining the generic flat band construction by MOs, several examples are discussed with numerical demonstration as sawtooth lattice in one dimension and hyper-Pyrochlore lattice in any $d$-dimensions that extends the Kagome ($d=2$) and Pyrochlore ($d=3$) lattices to general dimensions.

12 pages, 3 figures, to appear in proceedings of Localisation 2020

References in corpus (4)

• Topological modes bound to dislocations in mechanical metamaterials
• Anderson localisation in tight-binding models with flat bands
• Four-dimensional graphene and chiral fermions
• Flat bands in Weaire-Thorpe model and silicene

Cited by in corpus (8)

• Multiple quantum scar states and emergent slow-thermalization in the flat-band system
• Molecular-orbital representation with random U(1) variables
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Flat bands in condensed-matter systems -- perspective for magnetism and superconductivity
• Chirally-protected state manipulation by tuning one-dimensional statistics
• Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials
• Machine Learning Study on the Flat-Band States Constructed by Molecular-Orbital Representation with Randomness