Several physical systems related to two-dimensional electron gas(2DEG) subjected to an electric or a magnetic modulation at various strength have been theoretically studied. In Chapter 3, a quantum transport theory is developed for the calculation of magnetoresistance ρ_xx in a 2DEG subjected to strong one-dimensional periodic potential and at low uniform magnetic field (the Weiss oscillations regime). The theory is based on the exact diagonalization of the Hamiltonian and the constant relaxation time approximation. The theoretical predictions are in good agreement with the experimental results. The discrepancy between the classical calculation and the experiment is removed in our quantum treatment. In particular, the quenching of the Weiss oscillations is understood in this framework. I...[ Read more ]

Several physical systems related to two-dimensional electron gas(2DEG) subjected to an electric or a magnetic modulation at various strength have been theoretically studied. In Chapter 3, a quantum transport theory is developed for the calculation of magnetoresistance ρ_xx in a 2DEG subjected to strong one-dimensional periodic potential and at low uniform magnetic field (the Weiss oscillations regime). The theory is based on the exact diagonalization of the Hamiltonian and the constant relaxation time approximation. The theoretical predictions are in good agreement with the experimental results. The discrepancy between the classical calculation and the experiment is removed in our quantum treatment. In particular, the quenching of the Weiss oscillations is understood in this framework. In Chapter 4, the non-perturbative method for electric modulated system(EMS) is used to calculate the magnetoresistance ρ_xx for a magnetic modulated system(MMS), which is a 2DEG subjected to strong one-dimensional periodic magnetic modulation and at low uniform magnetic field. As the amplitude of magnetic modulation increases we first find a quenching of the low fields oscillations. This is similar to the quenching of the Weiss oscillations in the EMS case. As the strength of the magnetic modulation increases further, a new series of oscillations appears in our calculation. The temperature dependence of these new oscillations shows that the basic mechanism of these oscillations is similar to Weiss oscillations, and the origin can be identified with the extra term in the Hamiltonian for the MMS case. In Chapter 5, a self-consistent quantum transport theory is developed to calculate magnetocoductivities in a 2DEG subjected to strong one-dimensional periodic potential and at high uniform magnetic field(SdH oscillation regime). The theory is based on the self-consistent Born approximation(SCBA) for the randomly distributed short-range impurities together with an exact diagonalization of the Hamiltonian. Quantum oscillations of magnetoconductivities as a function of the amplitude of electric modulation are calculated and the basic mechanism behind these oscillations is discussed. In chapter 6, a tight-binding model is used to discuss the energy spectrum of 2DEG subjected to a strong two-dimensional magnetic modulation and a uniform magnetic field corresponing to a rational value of magnetic flux per unit cell φ=p/qφ₀. Some symmetries broken in the case of one-dimensional magnetic modulation are recovered in the two-dimensional case. Furthermore, when q is even, the magnetic Bloch band is broken into q subbands; while for odd q, the magnetic Bloch band is broken into 2q subbands. This has interesting implication on the magnetotransport properties as one changes φ. Our energy spectrum is similar but more complex than the Hofstadter's butterfly. Some suggestions to observe the new fractal energy spectrum are made.