Theoretical Study Of Transport Properties Of Low-dimensional Disordered Systems

In this thesis, we study the transport properties in a tight-binding one-dimensional system with long-range correlated disorder, including correlation of diagonal disorder and off-diagonal disorder. We investigate the competition between the disorder and correlation by computing the values of participation ratio, inverse participation ratio and the length of the localization, and consider mainly about the relevant result of the metal-insulator transition, especially the critical parameter, e.g. mobility edges, critical exponents.In chapter one, we introduce the evolution of the disordered system, and the subject matter in this work.In chapter two, we present the 1-D disorder model with long-range correlation, in whichthe random sequences have a power-law spectral density S(k)∝k^-α withα＞0. Wediscuss the localization of the whole system and the single eigenstate with inverse participation ratio and participation ratio, respectively. Using the general renormalization-group technique and the transfer-matrix method, we also calculate the localization lengthξwith which the accurate results are obtained. In the case of the diagonal disorder with on-site energies {ε_n} within [-W/2,W/2], we find that the critical disorder strength W_c=4|t|-2|E|at fixed energy E, the effective bandwidth of extended states B=4|t|-W at fixed W, and the mobility edges are at±E_c=±|2|t|-W/2| with t the nearest-neighbor hopping amplitude forα＞2, which is similar as the case of the off-diagonal disorder; whereas all the electron stay on localized states forα＞2 or W＞W_c, except for the quasi-delocalized state at the bandcenter E = 0 for off-diagonal correlated disorder.In chapter three, we adopt the numerical fitting method to get the values of criticalparameters W_c or E_c and v_W or v_E in light of the finite-size scaling analysis, and find out the critical exponent v of localization length to be v=1+1.4e^2-α. Our results indicate that the nature of a long-range correlated disordered system is somehow between that of the pure random (without any correlation) and pseudo-random (quasi-periodic) systems. Interestingly, the disorder strength W determines the mobility edges and the degree ofcorrelationαdetermines the critical exponents forα＞2 and W＜W_c, i.e. the situation ofboth occurrence of extended state and localized state. Also, we correct some errors in the past work.In chapter four, we summarize the main work of this thesis and give the next step's work.