Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2001-10-10
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
8 pages, 8 figures, eps versions of the figures will be sent on request to koshino@cms.phys.s.u-tokyo.ac.jp
Scientific paper
10.1103/PhysRevB.65.045310
We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a parameter space of the transfer energies and the magnetic field for the appearance of Hofstadter's butterfly spectrum in anisotropic crystals in 3D. (ii) We show that the orientation of the external magnetic field can be arbitrary to have the 3D butterfly. (iii) We show that the butterfly is beyond the semiclassical description. (iv) The required magnetic field for a representative organic metal is estimated to be modest ($\sim 40$ T) if we adopt higher Landau levels for the butterfly. (v) We give a simpler way of deriving the topological invariants that represent the quantum Hall numbers (i.e., two Hall conductivity in 3D, $\sigma_{xy}, \sigma_{zx}$, in units of $e^2/h$).
Aoki Hideo
Kagoshima Seiichi
Koshino Masanori
Kuroki Kazuhiko
Osada Takeshi
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