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Abstract: In this thesis we have discussed two kinds of two-dimensional electron system (2DES) in spatially modulated magnetic fields. We first studied the high-mobility semiconductor 2DES in spatially modulated magnetic field (MMF), with special interest in random magnetic field (RMF). In order to produce MMFs in a controlled fashion, micropatterened film of non-hysteretic magnetic alloy, DyCu, was fabricated on 2DES Hall bars. With the introduction of RMF, the resistance of the 2DES showed an increase with a quadratic dependence on the modulation amplitude. A cross-coil magnet system enabled us to study the magnetoresistance of a 2DES with fixed MMF component $\dB(\vect{r})$ as a function of uniform field component $\bar{B}$. A 2DES with RMF showed a large positive magnetoresistance which look very similar to those observed around the half-filled Landau level state of unmodulated 2DES. This supports the idea of mapping composite fermion in random potential to electron in random magnetic field. Our data also suggests that the characteristic structure of the magnetoresistance curve is of classical nature associated to the cyclotron motion of electron. Analysis of Shubnikov-de Haas oscillation implies that the RMF does not significantly alter the electron effective mass and therefore is not likely to account for the reported mass enhancement of the composite fermion. Introduction of randomness to one-dimensional MMF smears out the well-known commensurability oscillation in the magnetoresistance and changes it to a broad positive one, similar to that seen in two-dimensional RMF systems. However the temperature dependence of the resistance of 2DES with one-dimensional and two-dimensional MMF showed a qualitative difference that the $T^2$-dependent term observed in the former did not show up in the latter. In Chapter \ref{chap-Bfly}, we have explored a different limit of modulated magnetic field sturcture. We have calculated the energy spectra (Hofstadter butterfly) for a checkerboard patterned flux configuration. The result provides a basis for understanding the recent experimental result in a superconducting network.
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