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Quantum Hall Network Models as Floquet Topological Insulators.

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Network models describe integer quantum Hall (IQH) transitions using scattering matrices. We show how energy-dependent parameters recover the Chern number, unifying IQH and Floquet systems.

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Area of Science:

  • Condensed matter physics
  • Quantum Hall effect
  • Topological phases of matter

Background:

  • Network models are used to describe equilibrium integer quantum Hall (IQH) transitions.
  • These models utilize unitary scattering matrices, which also represent nonequilibrium Floquet systems.
  • Floquet bands in these models typically exhibit zero Chern number, being characterized by a chiral Floquet winding number.

Purpose of the Study:

  • To resolve the apparent contradiction between network models lacking a Chern number and their application to IQH systems.
  • To demonstrate how a nonzero Chern number can be recovered within the network model framework.
  • To investigate the relationship between IQH and chiral Floquet topology-changing transitions.

Main Methods:

  • Employing network models with unitary scattering matrices.
  • Analyzing the properties of resulting Floquet bands, including their winding number.
  • Investigating the energy dependence of network model scattering parameters.

Main Results:

  • The study demonstrates that a nonzero Chern number is recovered from the network model.
  • This recovery is achieved through the energy dependence of the scattering parameters.
  • A direct relationship is established between the network model and the Chern number.

Conclusions:

  • The energy dependence of scattering parameters reconciles network models with the Chern number in IQH systems.
  • Despite different topological origins, IQH and chiral Floquet topology-changing transitions share universal scaling properties.
  • This work unifies the description of equilibrium and nonequilibrium topological phenomena in quantum systems.