Ginzburg-Landau 理論對於 Type-II 超導體的傳輸性質與漲落之研究

Abstract

高溫超導的發現有趣地修改了超導體熱擾動性質,尤其是熱力學性質和傳輸性質(尤其是熱流傳輸)。我們在這工作理考慮在磁場下的超導體的擾動效應。在高溫擾動的影響下,特別是對一些非傳統超導體中很強的各向非均勻性的磁特性,系統的熱力學性質和傳輸特性會影響渦流的運動。

高溫超導的 Ginzburg-Landau (GL)現象描述顯著成功地描述各種熱力學和傳輸特性。在平均場近似下,擾動可以忽略的情況下它變得相當容易。然而當擾動不可被忽略時,即使是等效描述也會變的相當複雜。當增加需要的假設時,有些進展已經被達成。額外的假設通常用於解析的計算,只有最低的 Landau 能階顯著的貢獻到我們關注的物理量上。對最近實驗研究的大範疇外來的參數(磁場,溫度),這種近似是無效的,因此必須推廣理論到包含所有的 Landau 能階。

過去只有電性傳輸的理論被發展,然而最近實驗已經能夠觀察到磁熱效應和熱流傳輸現象,像是 Nernst 和熱電功率,我們需要延伸擾動理論去包含這些現象。當只考慮高斯擾動時,熱電阻率和電阻率在平均場的轉換溫度下是被預測會發散,這個理論與實驗結果矛盾。其中一個重要的結論是要符合實驗結果必須要考慮擾動間的交互作用。之前的工作是 S. Ullah 和 A. T. Dorsey 在 GL 方程式中,在最低的 Landau 能階中應用 Hartree-Fock 近似去處理四次方項計算熱流傳輸問題。

在這個論文中,我的工作使用更有系統的高斯近似法去推廣包含所有 Landau 能階,並且計算有趣的物理量,像是橫向熱電阻率和Nernst訊號去描述Nernst效應,也算了在線性響應下的第二類超導體的渦流範疇中之交流電阻率。我們使用包含雜訊的時變 GL(TDGL)方程式。我們的理論數值結果可以吻合數個高溫超導中的實驗數據。

我也使用線性響應研究在外加磁場下層狀第二類超導體中的傳輸特性。使用TDGL 方程式以及熱雜訊可以得到電阻率和霍爾電阻率。我們的理論結果定量上吻合在強電場下高溫導體的實驗數據。

The discovery of high-temperature superconductors (HTSC) has revived interest in thermal fuctuation effects in superconductors, both in thermodynamic properties and in transport properties, with emphasis on the heat transport. In this work we shall be concerned with the effect of fuctuations on the transport properties of a superconductor in a magnetic field. Under the influence of fuctuations at high temperature, the motions of vortices are responsible for the thermodynamic properties and transport properties of systems especially for those unconventional superconductors due to it's strong anisotropic magnetic properties. The Ginzburg-Landau (GL) phenomenological description of high superconductors has been remarkably successful in describing various thermodynamic and transport properties. In the mean field approximation, when the fuctuations are neglected, it is relatively simple. However when fuctuations are not negligible, even this effective description becomes very complicated. Some progress can be achieved when certain additional assumptions are added. An additional assumption, often made in analytical calculations, is that only the lowest Landau level significantly contributes to physical quantities of interest. However, in a large domain of external parameters (magnetic field, temperature) currently under experimental investigation, this approximation is not valid and now there is a need to generalize the theory to include all Landau levels. In the past only electric transport has been thoroughly developed theoretically. However recent experimental advance in observing various magnetocaloric coefficient and heat transport phenomena like the Nernst and thermoelectric power necessitate extension of the fuctuations theory to include these phenomena. When only the Gaussian fuctuations are considered, then the thermoelectric conductivity and the electrical conductivity were predicted to diverge at the mean-field transition temperature, in conflict with the experimental results. One of important conclusions is that interactions between the fluctuations must be considered in order to obtain even qualitative agreement with the experimental results. An early work on this subject was application of the Hartree-Fock approximation to treat the quartic term within the lowest Landau level approximation in the GL Hamiltonian for heat transport current by S. Ullah and A. T. Dorsey. In this thesis I have extended the work to include all Landau level, use more systematic Gaussian approximation and calculate physical quantities of current interest like the transverse thermoelectric conductivity and the Nernst signal, describing the Nernst effect, as well as ac conductivity in linear response in Type-II superconductor in the vortex-liquid regime. The time-dependent Ginzburg-Landau (TDGL) equation with thermal noise is used. Our results show a good agreement with several experiment and numerical simulation on HTSC. I also studied the transport properties in a layered Type-II superconductor under magnetic field beyond the linear response. By using TDGL equation with thermal noise is to obtain electrical conductivity and Hall conductivity. Our results are in good qualitative and even qualitative agreement with experimental data on HTSC in strong electric fields.