Quantum phase with coexisting localized, extended, and critical zones

Conventionally a mobility edge (ME) marks a critical energy that separates two different transport zones where all states are extended and localized, respectively. Here we propose a quasiperiodic spin-orbit coupled lattice model with experimental feasibility to realize a quantum phase with three coexisting energy-dependent zones, i.e., the extended, critical, and localized zones, and uncover the underlying generic mechanism for the occurrence of this quantum phase. Accordingly, this phase exhibits types of MEs which separate the extended states from critical ones and the localized states from critical ones, respectively. We introduce the diagnostic quantities to characterize and distinguish the different zones and show that the predicted phase can be detected by measuring the fractal dimension or conductivities. The experimental realization is also proposed and studied. This work extends the concept of ME and enriches the quantum phases in disordered systems, which sheds light on searching for localization and critical phenomena with transport and thermoelectric effects.