Nontrivial quantum geometry of degenerate flat bands

Quasi-localization and Wannier obstruction in partially flat bands

“…Flat bands have received significant attention because they are considered an ideal playground to study many-body physics and geometric properties of the Bloch wave function beyond topological aspects [24][25][26][27][28][29][30][31][32][33] . While it has long been believed that the flat band can only be realized in artificial systems [34][35][36][37][38][39][40] , including the Aharonov-Bohm cage with the twoband Creutz ladder and the three-band rhombic lattice [41][42][43][44][45] , there has recently been a surge of research on synthesizing flat band materials [46][47][48][49][50][51] after discovering the unconventional superconductivity originating from the flat band in the twisted bilayer graphene 52 .…”