Obstructed insulators and flat bands in topological phase-change materials

Phase-change materials are ubiquitous in technology because of their ability to transition between amorphous and crystalline phases fast and reversibly, upon shining light or passing a current. Here we argue that to fully understand their electronic properties, it is necessary to define a novel electronic phase: the amorphous obstructed insulator. It differs from an obstructed insulator crystal in that it presents localized edge or surface states irrespective of the sample termination. Consequently, we show that obstructed amorphous insulators in three dimensions host a surface two-dimensional flat band, detectable using angle-resolved photoemission spectroscopy. Our work establishes basic models for materials where topological and obstructed properties can be switched on and off externally, including two-dimensional surface flat bands.