van Hove singularity 模型下高溫超導體化學能的變化及穿隧電導的特異性

Abstract

我們研究的主題是以vHs模型來解釋高溫超導體的一些物理性質。主要的 主題有二：在第一個子題中，我們研究此模型下正常態與超導態的化學能 的差值，我們發現其大小可達1meV。相對於費米能而言，1meV是相當小的 ，因此其對能隙與臨界溫度的響影是可忽略的。但1meV的大小在實驗上是 可量測的，我們將計算的結果與實驗數據相比較發現是相當的符合。而在 第二個子題我們以現象學的方式來探討此模型下的穿隧電導係數，我們假 設穿隧機率正比於電子的群速度加上一個小的修正項，在此情形下電導係 數會有雙高峰的情況而且會有不對稱性存在，而這兩個高峰很容易由一些 其他的因素而合成一個較寬的高峰，在此情形下，要由穿隧電導係數判斷 能隙的大小就很容易誤判，這或許就是為何各個實驗上2gap/KTc的值會有 分歧的看法與其大於傳統BCS的結果的理由。 In this thesis we try to use vHs model to explain some physical properties of high temperature superconductor. First we study the chemical potential difference between normal state and superconducting state. It shows that the difference can be as large as 1meV. Compared with Fermi energy, 1meV is small and we can neglect its influence on gap and Tc. Nevertheless we notice that 1meV can be experimentally observed. We find that the tendency of the result of this model is the same as that of experiment. Second we use a phenomenological method to study the tunneling conductance. We assume the tunneling probability is proportional to the group velocity of electron and add a rectifying term. The conductance will display double peaks and asymmetry. And then the double peaks broaden to a broader peak. Hense it is difficult to point out the real value of energy gap. This may be the reason why the value 2gap/KTc of many experiments are scattered and why it does not conform to traditional BCS result.