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Researchers show how to create a Hopf insulator, a special topological insulator, using interacting spins. This work paves the way for new quantum materials with protected conducting edge states.

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Area of Science:

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

Background:

  • Hopf insulators are a class of weak topological insulators in 3D.
  • They feature insulating bulk and conducting edge states protected by a topological invariant.
  • These states are typically found in two-band models.

Purpose of the Study:

  • To demonstrate a physical realization of the Hopf insulator in a lattice of dipolar-interacting spins.
  • To explore the role of spin exchange and dipole-dipole interactions in realizing topological properties.
  • To investigate the robustness of edge states in different lattice geometries.

Main Methods:

  • Theoretical modeling of a spin lattice with long-range, anisotropic dipole-dipole interactions.
  • Analysis of the momentum-space structure and complex hopping phases.
  • Investigation of edge states at both smooth and sharp edges with crystalline symmetry.

Main Results:

  • The Hopf insulator can be naturally realized in lattices of dipolar-interacting spins.
  • Spin exchange mimics particle hopping, while dipole interactions provide necessary momentum-space structure.
  • Robust gapless edge states are found at smooth and certain sharp edges.
  • The two-band picture breaks down at sharp edges, yet edge states persist.

Conclusions:

  • Dipolar-interacting spin lattices offer a viable platform for realizing Hopf insulators.
  • This approach provides a route to engineer topological phases with protected edge states.
  • The findings have implications for the design of novel quantum materials and devices.