Butterfly spectrum and quantum Hall effect in three-dimensional FISDW

By extending the two-dimensional (2D) model for Bechgaard salts, we explore field-induced spin-density wave (FISDW) in three-dimensional (3D) systems. We show that a series of FISDW phases peculiar to 3D do exist for quasi-1D systems (rather than quasi-2D ones such as Bechgaard salts). The 3D FISDW is characterized by the quantum Hall effect with σxy and σzx being quantized and the quasi-particle spectrum that is fractal as in the Hofstadter butterfly. This state may be regarded as one realization of the general theory for the 3D butterfly [Phys. Rev. Lett. 86 (2001) 1062].