Quantum mechanics

Phase (matter)

Phase transition

Acoustics

Statistical physics

Lattice (music)

Fractal

Physics

Mathematics

Condensed matter physics

Mathematical analysis

Quantum

Quasiperiodic function

Quantum phase transition

Critical phenomena

Physical review. B./Physical review. B

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 novel quasiperiodic spin-orbit coupled lattice model with experimental feasibility to realize a fundamentally new 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 the new quantum phase. Accordingly, this phase exhibits new 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 new localization and critical phenomena with novel transport and thermoelectric effects.

Quantum phase with coexisting localized, extended, and critical zones