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This study analyzes topological insulators with disorder, revealing boundary correlations match a relativistic model. Edge conductance is quantized, while susceptibility is non-universal, offering insights into disordered quantum systems.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Disordered Systems

Background:

  • Topological insulators exhibit unique edge states protected by topology.
  • Quasi-periodic disorder can significantly alter the behavior of quantum systems.
  • The Haldane model provides a foundational example of a topological insulator.

Purpose of the Study:

  • To investigate the impact of weak quasi-periodic disorder on two-dimensional topological insulators.
  • To analyze the boundary correlations and edge transport properties of these systems.
  • To establish a theoretical framework for understanding disordered topological materials.

Main Methods:

  • Multiscale analysis applied to disordered systems.
  • Rigorous renormalization group (RG) methods adapted for quasi-periodic potentials.
  • Kubo formula used for calculating transport coefficients.
  • Lattice Ward identities employed for theoretical proofs.

Main Results:

  • Boundary correlations were shown to agree with a renormalized, translation-invariant, massless relativistic model in 1+1 dimensions.
  • Explicit expressions for edge conductance and susceptibility were derived.
  • Quantization of edge conductance was proven.
  • Non-universality of edge susceptibility was demonstrated.

Conclusions:

  • The presence of weak quasi-periodic disorder leads to boundary correlations described by a relativistic model.
  • Edge transport properties are fundamentally linked to the renormalized Fermi velocity of edge modes.
  • The study confirms quantized edge conductance and non-universal susceptibility in these disordered topological insulators.