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Advanced Experimental Methods for Low-temperature Magnetotransport Measurement of Novel Materials
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Quantum spin Hall effect in a three-orbital tight-binding Hamiltonian.

Yan He1, Changtao Hou

  • 1College of Physical Science and Technology, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China.

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|July 1, 2014
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Summary

We explore the quantum spin Hall (QSH) state in a three-orbital model, revealing nontrivial Chern parity and wave-function singularities. This research connects the Berry phase to non-Abelian instantons, advancing topological material understanding.

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Area of Science:

  • Condensed Matter Physics
  • Topological Materials
  • Quantum Phenomena

Background:

  • The quantum spin Hall (QSH) state is a topological phase of matter with potential applications in spintronics.
  • The loop current model has been proposed to explain the pseudogap phase in cuprates.
  • Understanding the topological properties of QSH states is crucial for developing new electronic devices.

Purpose of the Study:

  • To investigate the quantum spin Hall (QSH) state within a three-orbital model.
  • To analyze the role of spin loop current order induced by spin-dependent interactions.
  • To explore the topological invariants and wave-function properties of this QSH state.

Main Methods:

  • Utilizing a three-orbital model with spin-dependent interactions.
  • Directly counting the zeros of the Pfaffian of the time reversal operator to determine Chern parity.
  • Connecting the second Chern number to analyze wave-function singularities and their gauge dependence.
  • Mapping the Berry phase of the QSH state to a non-Abelian instanton.

Main Results:

  • The model exhibits nontrivial Chern parity.
  • Singularities in wave-functions are explicitly shown and their dependence on gauge choices is demonstrated.
  • The Berry phase of the QSH state is successfully mapped to a non-Abelian instanton.

Conclusions:

  • The study reveals key topological properties of the QSH state in the considered three-orbital model.
  • The findings provide insights into the connection between spin loop current order, Chern parity, and Berry phase in topological materials.
  • This work contributes to the theoretical understanding of topological phases and their mathematical descriptions.