Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2003-12-04
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
4 pages, 2 figures
Scientific paper
10.1103/PhysRevB.69.081303
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.
Aoki Hideo
Koshino Mikito
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