Integer quantum Hall effect and Hofstadter's butterfly spectra in three dimensions in modulated metals
Abstract
While the quantum Hall effect (QHE) is usually specific to twodimensional(2D) systems, a threedimensional(3D) QHE is generally implied[1] when there is a gap in the energy spectrum. We have previously shown[2] that one way to realize a systematic (or 'gbutterfly') appearance of gaps is periodic (tightbinding) 3D systems in magnetic fields, B. While Hofstadter's butterfly has been wellknown for 2D, the interplay of Bragg's reflection and Landau's quantization can unexpectedly occur in 3D as B is tilted. Here we propose a novel realization of such spectra in 3D metals with weak periodic modulations as opposed to the tightbinding limit. Fractal spectrum in fact occurs, with a different origin, but the two limits are connected with a duality. The spectral gaps accompany an integer QHE where the topological integers for the Hall tensor components are obtained. We discuss its feasibility for semimetals with acoustic waves injected for realistic B ∼ few tens of T. [1] M. Kohmoto, B. I. Halperin, and Y. Wu, Phys. Rev. B 45, 13488 (1992). [2] M. Koshino, H. Aoki, K. Kuroki, S. Kagoshima, and T. Osada, Phys. Rev. Lett. 86, 1062 (2001).
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MARV11002K