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Researchers discovered a new type of topological insulator, the intrinsic statistical topological insulator (STI), which exists in disordered systems and has no counterpart in clean systems. This axion STI is protected by average C4T symmetry.

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Area of Science:

  • Condensed Matter Physics
  • Topological Matter
  • Quantum Materials

Background:

  • Symmetry-protected topological states (SPTS) in pure states are well-understood.
  • Ensembles with average symmetries exhibit richer topological phenomena, leading to average symmetry-protected topological states (ASPTs).
  • The free-fermion counterpart of ASPTs in disordered systems is the statistical topological insulator (STI).

Purpose of the Study:

  • To demonstrate the existence of an intrinsic statistical topological insulator (STI) that lacks a clean system counterpart.
  • To characterize an axion STI protected by average C4T symmetry.
  • To provide a lattice realization and explore the phase diagram of this intrinsic STI.

Main Methods:

  • Real-space construction using a topological crystal.
  • Theoretical proof demonstrating the impossibility of the θ=π state in the clean limit for (C4T)4=1.
  • Lattice model construction and numerical phase diagram exploration.

Main Results:

  • Discovery of an intrinsic axion STI characterized by an average axion angle θ̄=π, protected by average C4T symmetry with (C4T)4=1.
  • Proof that the θ=π state is unattainable in the clean limit, confirming the intrinsic nature of the STI.
  • Identification of an axion STI phase in the lattice model, separated from band and Anderson insulators by a metallic phase.
  • Demonstration of robustness against electron-electron interactions.

Conclusions:

  • The study presents the first intrinsic crystalline ASPT and its lattice realization.
  • The axion STI lacks band insulator correspondence, highlighting its unique topological nature.
  • The findings open new avenues for exploring topological matter in disordered systems.