van Hove 奇異點模型與在釔鋇銅氧高溫超導體中氧含量相關之轉變溫度及其加壓改變率之影響

Abstract

本論文之研究目的在於了解氧化物高溫超導體釔鋇銅氧之超導機制，而最 近實驗與理論都一再的指出銅氧面為高溫超導的轉變所在，因此我們採用 描述銅氧類高溫超導體的銅氧面的準二維的模型來探討釔鋇銅氧之含氧量 、結構和壓力對超導轉變溫度之影響。由最近對不同含氧量的釔鋇銅氧的 中子散射結構分析與隨壓力變化的實驗數據中，顯示在釔鋇銅氧中的氧含 量的變化或壓力的變化將導至銅氧面上的超導載子的數目的變化。我們採 用了銅氧面是超導體的轉變機制、氧含量及壓力將導至銅氧面上的載子數 目發生變化和不同含氧量之銅氧面上的載子隨壓力的變化率為一常數等三 點假設及運用 van Hove 奇異點模型，以數值方法求出含氧量對超導轉變 溫度、含氧量對超導轉變溫度隨壓力的變化量等的關係曲線，並與實驗上 的數據作比較，其比較結果是相當吻合的，因此採用 van Hove 奇異點模 型能合理的描述釔鋇銅氧隨氧含量及壓力變化的超導行為。 This study is proposed to understand the superconducting state of the cuprate superconductor YBa2Cu3Ox and the scenario of the van Hove singularity model. First, we study the picture drawn by van Hove singularity model. We simplify the CuO2 plane in YBa2Cu3Ox (6.4<x<7) to be a square lattice and use the dispersion relation estimated by the tight- binding method to calculate the density of state. Second, we use the BCS theorem associated with this density of state to calculate the Fermi energy (Ef) dependence of the transition temperature (Tc). We assume the dopant (x) dependence on the change of charge density (n) on the CuO2 plane is linear and the change of n(x) on the pressure (0 to 20 kbar) is constant. We then calculate Tc(x) and dTc(x)/dP in numerical method. Our results of Tc(x) and dTc(x)/dP by using the van Hove singularity model are agreeable with the experimental data.