Floating of extended states in a random magnetic field with a finite mean

Effects of a uniform magnetic field on two-dimensional (2D) electrons subject to a random magnetic field (RMF) are studied by a multifractal scaling analysis. For sufficiently strong uniform field ((B) over bar deltab), the RMF system is equivalent to a quantum Hall system (QHS), namely, the spectral density of states splits into subbands, and states only at the subband centers are extended with the localization-length exponent nu =2.31 +/-0.01, where B is the averaged magnetic field and deltab is the characteristic amplitude of the spatially fluctuating field. In the case of (B) over bar less than or similar to deltab, subbands overlap each other and energies of extended states shift upwards with keeping its universality class. This behavior conflicts with a recent theoretical prediction and demonstrates that 2D systems in RMF's even with small finite means are rather close to QHS's.