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Related Experiment Videos

Hofstadter butterfly and integer quantum hall effect in three dimensions.

M Koshino1, H Aoki, K Kuroki

  • 1Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan.

Physical Review Letters
|February 15, 2001
PubMed
Summary

We discovered a 3D Hofstadter butterfly in anisotropic lattices under magnetic fields. This phenomenon, arising from third-direction hopping, occurs in smaller fields and exhibits quantized Hall conductivity.

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Area of Science:

  • Condensed matter physics
  • Solid-state physics
  • Quantum mechanics

Background:

  • Landau quantization in magnetic fields typically smears in 3D lattices.
  • Anisotropic systems exhibit unique electronic properties.

Purpose of the Study:

  • Investigate the emergence of Hofstadter's butterfly in 3D lattices.
  • Explore the role of third-direction hopping and magnetic field angle.
  • Analyze Hall conductivity quantization.

Main Methods:

  • Theoretical modeling of 3D lattices in magnetic fields.
  • Analysis of hopping parameters and system anisotropy.
  • Calculation of Hall conductivity using topological invariants (Kohmoto-Halperin-Wu formula).

Main Results:

Related Experiment Videos

  • A 3D Hofstadter butterfly is observed in anisotropic systems when a specific criterion is met.
  • The angle of the magnetic field mimics field intensity in 2D, enabling butterfly formation in weaker fields.
  • Quantized Hall conductivity (sigma(xy) and sigma(zx)) is demonstrated.

Conclusions:

  • Third-direction hopping can induce 3D Hofstadter butterfly in anisotropic lattices.
  • Magnetic field angle is a critical parameter for observing this 3D phenomenon.
  • Topological invariants confirm quantized Hall conductivity, offering insights into topological phases.