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Kibble-Zurek Behavior in Disordered Chern Insulators.

Lara Ulčakar1, Jernej Mravlje2, Tomaž Rejec3

  • 1Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia and Faculty for Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.

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Summary

Topological quantum phase transitions in Chern insulators show critical behavior in the local Chern marker, similar to a local order parameter. Disorder and slow system changes reveal Kibble-Zurek scaling in inhomogeneities.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Topological Phases of Matter

Background:

  • Topological quantum phase transitions (TQPTs) lack local order parameters, unlike conventional Landau theory.
  • Berry curvature in clean Chern insulators shows critical behavior near quantum critical points.
  • Disorder in Chern insulators introduces spatial inhomogeneities.

Purpose of the Study:

  • Investigate critical properties of the local Chern marker in weakly disordered Chern insulators.
  • Analyze the scaling behavior of spatial inhomogeneities near a quantum critical point.
  • Examine the applicability of Kibble-Zurek scaling to TQPTs in driven systems.

Main Methods:

  • Numerical investigation of local Chern marker critical properties.
  • Analysis of spatial inhomogeneity scaling under weak disorder.
  • Driving the system through a quantum phase transition under non-equilibrium conditions.

Main Results:

  • Local Chern marker inhomogeneities exhibit power-law scaling with critical exponents matching clean systems.
  • The characteristic size of post-quench inhomogeneities follows Kibble-Zurek scaling.
  • Kibble-Zurek scaling is observed for inhomogeneities in excitations and orbital polarization.

Conclusions:

  • The local Chern marker acts analogously to a local order parameter in disordered Chern insulators undergoing TQPTs.
  • Kibble-Zurek scaling provides a framework for understanding defect formation in driven topological phase transitions.
  • Disorder and non-equilibrium dynamics are crucial for observing order-parameter-like behavior in TQPTs.