Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations

Abstract

We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an entirely different system -- 3D metals applied with weak external periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic potentials interferes with Landau's quantization due to an applied magnetic field $\Vec{B}$, resulting generally in fractal energy gaps as a function of the tilting angle of $\Vec{B}$, for which the accompanying quantized Hall tensors are computed. The phenomenon arises from the fact that, while the present system has a different physical origin for the butterfly from the 3D tight-binding systems, the mathematical forms are remarkably equivalent.

4 pages, 2 figures

References in corpus (3)

• Hofstadter butterfly and integer quantum Hall effect in three dimensions
• Phase Diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions
• Wrapping Current versus Bulk Integer Quantum Hall Effect in Three Dimensions

Cited by in corpus (4)

• Chern numbers and chiral anomalies in Weyl butterflies
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system