Designing flat-band tight-binding models with tunable multifold band touching points

Abstract

Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this work presents a straightforward method to build flatband tight-binding models with short-range hoppings on any periodic lattice. The method consists in starting from a CLS and engineering families of Bloch Hamiltonians as quadratic (or linear) functions of the associated Bloch state. The resulting tight-binding models not only exhibit a flat band, but also multifold quadratic (or linear) band touching points (BTPs) whose number, location, and degeneracy can be controlled to a large extent. Quadratic flat-band models are ubiquitous: they can be built from any arbitrary CLS, on any lattice, in any dimension and with any number N ≥ 2 of bands. Linear flat-band models are rarer: they require N ≥ 3 and can only be built from CLSs that fulfill certain compatibility relations with the underlying lattice. Most flat-band models from the literature can be classified according to this scheme: Mielke's and Tasaki's models belong to the quadratic class, while the Lieb, dice and breathing Kagome models belong to the linear class. Many novel flat-band models are introduced, among which an N = 4 bilayer honeycomb model with fourfold quadratic BTPs, an N = 5 dice model with fivefold linear BTPs, and an N = 3 Kagome model with BTPs that can be smoothly tuned from linear to quadratic.

Ferromagnetism in armchair graphene nanoribbon heterostructures

“…Indeed, in the last one year alone, there has been new flatband research in many different areas, like their experimental observation in atomically precise one-dimensional (1D) chains [7], as well as the study of flat-bands in strongly correlated systems [8][9][10][11][12][13][14][15][16], search for flat-bands in kagome-type lattices [17,18], study of symmetry aspects of flat-band systems [19][20][21], holographic construction of flat-bands [22], flat-bands in pyrochlore lattices [23,24], analysis of randomness in flat-band Hamiltonians [25], topological aspects of flat-band systems [26][27][28][29][30][31], construction of flat-band tightbinding models starting from compact localized states [32], and study of flat-bands in graphene and graphene-like lattices [33][34][35][36][37].…”