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Time-reversal-breaking induced quantum spin Hall effect.

Wei Luo1,2, D X Shao1, Ming-Xun Deng1

  • 1National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China.

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The quantum spin Hall (QSH) effect is not observed in a standard square lattice. However, introducing staggered magnetic fluxes can induce the QSH effect, protected by a composite symmetry, even under a Zeeman field.

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Area of Science:

  • Condensed Matter Physics
  • Topological Materials
  • Quantum Phenomena

Background:

  • The quantum spin Hall (QSH) effect is a topological state of matter characterized by insulating bulk and conducting edge states.
  • Standard square lattice models often fail to exhibit the QSH effect due to cancellations in spin-orbit coupling.

Purpose of the Study:

  • To investigate the conditions for inducing the QSH effect in a square lattice model.
  • To explore the role of magnetic fluxes and symmetries in protecting topological edge states.
  • To examine the robustness of the QSH state against magnetic perturbations.

Main Methods:

  • Theoretical modeling of a square lattice with staggered magnetic fluxes.
  • Analysis of spin-orbit coupling and its cancellation.
  • Investigation of composite symmetries (time-reversal and a novel phase transformation).
  • Study of edge state properties and their response to Zeeman fields.

Main Results:

  • The intrinsic QSH effect is absent in the square lattice model due to canceling spin-orbit coupling.
  • Staggered magnetic fluxes can induce the QSH effect when a specific Peierls phase is achieved.
  • A composite symmetry (ΘΡ-) protects gapless edge states at a special phase value.
  • Edge states remain gapless even in the presence of a Zeeman field for a specific phase range.

Conclusions:

  • The QSH effect can be realized in square lattices through engineered magnetic fluxes.
  • Composite symmetry plays a crucial role in protecting the topological edge states.
  • The induced QSH state demonstrates robustness against magnetic perturbations, highlighting potential for spintronic applications.