An accurate tight binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation

Abstract

A major hurdle in understanding the phase diagram of twisted bilayer graphene (TBLG) are the roles of lattice relaxation and electronic structure on isolated band flattening near magic twist angles. In this work, the authors develop an accurate local environment tight binding model (LETB) fit to tight binding parameters computed from ab initio density functional theory (DFT) calculations across many atomic configurations. With the accurate parameterization, it is found that the magic angle shifts to slightly lower angles than often quoted, from around 1.05 • to around 0.99 • , and that isolated flat bands appear for rigidly rotated graphene layers, with enhancement of the flat bands when the layers are allowed to distort. Study of the orbital localization supports the emergence of fragile topology in the isolated flat bands without the need for lattice relaxation.

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].…”