Abstract
In this thesis, we discuss the magneto-transport properties in quasi-low-dimensional disordered systems under weak localization theory. Two systems are considered in this work. One is the quasi-one-dimensional (Q1D) cylindrical wire, and the other is the quasi-two-dimensional (Q2D) sandwich structure. For the cylindrical wire case, we develop a transfer-matrix method to solve the differential equation in the problem and compare our calculated magnetoconductance (MC) with the one obtained by perturbation method [B. L. Altshuler, A. G. Aronov, 1981a, Pis’ma Zh. Eksp. Teor. Fiz. 33, 515 [JETP Lett. 33, 499 (1981)]]. In general, the two results of different methods agree well with each other at low temperatures and at small magnetic fields. Slight deviations are found at high temperatures and at large magnetic fields when comparing these two results. Our work in this case extends the calculation of MC for cylindrical wire to high temperatures and large magnetic fields. In addition, our method could be applied to investigate the MC of non-uniform disordered cylindrical wires. The sandwich structure consists of a dirty metallic film bounded by relatively clean but nearly insulating layers on the sides, with material parameters chosen so that the structure has classical current transport confined mainly in the metallic layer. Quantum correction of conductance (QC) and MC are calculated for this system. The result shows that QC/MC saturates over a range of low temperatures for a certain range of structural/material parameters of the sandwich structure. Moreover, QC/MC goes divergent at extreme low temperatures eventually. In the bulk-like limit, where the thickness of this system is comparable to its width, our analysis shows that QC saturates even down to zero temperature. Similarly, MC also shows saturation at zero temperature if the system satisfies the requirement of clean-bulk limit where electron’s motion in the nearly insulating layers is ballistic. Our work of sandwich structure could qualitatively explain the observed dephasing time saturation in Q2D films and the upturn of dephasing time at extreme low temperatures [S. M. Huang, T. C. Lee, H. Akimoto, K. Kono, J.-J. Lin, Phys. Rev. Lett. 99, 046601 (2007)]. The calculation can be extended to Q1D non-uniform disordered systems of, i.e., quantum wires.