Xin-Chi Zhou

Abstract Anderson localization describes the suppression of wave transport in disordered media. In quantum systems, it gives rise to extended, localized and critical eigenstates, with the latter showing properties between the other two. Characterizing critical states is challenging because it requires analysis in the thermodynamic limit or a universal mechanism that identifies them.

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization.

Abstract Higher-order topological phase transitions (HOTPTs) are associated with closing either the bulk energy gap (type-I) or boundary energy gap (type-II) without changing symmetry, and conventionally, both transitions are captured in real space and characterized separately. Here, we propose a momentum-space topological characterization of HOTPTs which unifies both types of topological transitions and enables a precise detection by quench dynamics.