Quantum phase with coexisting localized, extended, and critical zones

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