缺陷對低維強關聯電子系統的影響

Abstract

本論文為二維和一維系統的理論研究。我們提出了一個現象學的二維自由能模型，用於描述 Gd1.02Sb0.87Te1.11 中電子的自發對稱破缺相和電荷序的拓撲缺陷。數值結果與掃描隧道顯微鏡的量測顯示令人滿意的一致性，並表明原子替代在穩定拓撲缺陷中起著關鍵作用。一維系統則為帶有雜質的 Luttinger 液體。我們使用密度矩陣重正化群和共形對稱性來研究電荷傳輸。我們發現，在存在兩個雜質和有限尺寸雜質的情況下，電荷傳輸的行為與單一雜質問題不同，這是由於釘住效應的相互抵銷。這一結果通過時間演化計算得到了進一步的確認。

This thesis focuses on the theoretical investigation of two- and one- di mensional systems. The phenomenological two-dimensional free energy is proposed to model the spontaneous symmetry breaking phase of electrons in Gd1.02Sb0.87Te1.11 and the topological defects of the charge order. The nu merical results show a satisfactory agreement with the pattern imaged by a scanning tunnelling microscope and suggest the essential role of atomic sub stitution in stabilizing the topological defects. The one-dimensional system is the Luttinger wires with impurities. The density matrix renormalization group and conformal symmetry are employed to study charge transport. We find that the behavior of charge transport in the presence of two impurities and finite-size impurities can be strikingly different from a single impurity problem since the cancellation of the pinning effect. The result is doubly confirmed by time-evolving calculations.