Koshino M, Aoki H, Kuroki K, Kagoshima S, Osada T
Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan.
Phys Rev Lett. 2001 Feb 5;86(6):1062-5. doi: 10.1103/PhysRevLett.86.1062.
For a three-dimensional (3D) lattice in magnetic fields we have shown that the hopping along the third direction, which normally smears out the Landau quantization gaps, can rather give rise to a Hofstadter's butterfly specific to 3D when a criterion is fulfilled by anisotropic (quasi-one-dimensional) systems. In 3D the angle of the magnetic field plays the role of the field intensity in 2D, so that the butterfly can occur in much smaller fields. We have also calculated the Hall conductivity in terms of the topological invariant in the Kohmoto-Halperin-Wu formula, and each of sigma(xy),sigma(zx) is found to be quantized.
对于处于磁场中的三维（3D）晶格，我们已经表明，通常会使朗道量子化能隙模糊的沿第三方向的跳跃，当各向异性（准一维）系统满足一个判据时，反而会产生特定于三维的霍夫施塔特蝴蝶。在三维中，磁场的角度起着二维中场强的作用，这样蝴蝶可以在小得多的场中出现。我们还根据小本 - 哈珀林 - 吴公式中的拓扑不变量计算了霍尔电导率，并且发现(\sigma_{xy})、(\sigma_{zx})中的每一个都是量子化的。
