臺灣博碩士論文加值系統

本論文主旨要探討在熱微擾下二類超導體在大磁場下的物理性質，以增廣超導應用上的知識。主要研究的材料是針對高溫超導和新的非傳統超導，此類材料在空間上的異向性很強，強烈的影響到費米面的不對偁性，使得材料在超導態的物理性質與傳統超導體有很大的不同。在磁場下超導所形成的奈米級的『渦旋物質』，它們可以大小彼此間的影響力是可以由調變溫度和磁場所控制，此外它們的活動深深影響在臨界區的物理現象。超導態的相變屬於二類相變的範疇, 因此我
們採用Ginzburg – Landau理論作為基本模型，根據不同的系統加以變化，並以統計力學的技巧考慮高溫效應和雜質的影響在一項性強的材料下的物理性質。
材料在空間異相性可以分為ｘｙ平面上的異相性和ｚ軸上層狀結構。在ｘｙ平面上的異相性我們探討了四方長柱形底材的渦旋物質之結構相變。根據我們的計算發現可以藉由調變磁場強度控制渦旋物質結構使其產生由菱形到矩形的相變。在此研究中我們分別考慮了純系統和無序系統下對此結構相變的影響，結果顯示雜質影響下原本為第二類相變結構相變成為第一類相變，同時雜質也影響了結構相變曲線的溫度相依性等其他現象。
在研究ｚ軸上層狀結構我們探討此異性相對超導反磁性的影響。所採用的模型有Laerence-Doniach 模型和準二維的Ginzburg – Landau模型。一般勻稱的材料在Hc2(T)附近的強磁場區裡物理量在不同磁場下的溫度特性曲線會有最低Landau能級的scaling行為,我們發現底材層狀結構和在準二維系統強大的熱擾動皆會破壞這個scaling行為,尤其在臨界曲線附近一般常用的最低Landau能級的近似法無法使用描述具有強熱效應的準二維系統。我們將理論的結果與很多實驗比照得到很好的應證。

Vortex matter plays an important role in superconductivity state especially for high-Tc cuprate superconductors with layered structure. For an homogeneous system, the isotropic repelled vortices form the Abrikosov lattice. It was first proposed by Abrikosov for temperatures close to Tc, and then it was extended to all temperatures [56]. These theories ignore the fluctuations of the order parameter, called mean-filed theory. It is a very good approximation for the conventional superconductors.
However, under fluctuations influence 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 most efficient way to study the mesoscopic phenomena is the effective Ginzburg-Landau (GL) functional. Unfortunately, because of the nonlinear term, even having the effective functional one can hardly calculate the free energy exactly. It is a typical problem for the critical phenomena. Lowest
Landau level approximation (LLL) is a common way to simplify the question and its practical region is valid all the way down to H = Hc2(T)/13 [89]. The LLL degeneracy results in a high field scaling was observed in many experiments. For various physical quantities (static quantities such as magnetization curves, specific heat etc. and dynamic quantities such as electrical conductivity etc.) as function of temperature will collapse to a scaling function for various fields. However, recent experiments show the failure of high field scaling behavior and the GL model is under examination. To understand them, in this thesis, we consider two cases in liquid phase: For strongly quasi 2D system, higher landau levels contribution is taken into account. For the layered superconductors, the coupling between layers which changes the dimensionality of the system is considered. Our results show a good agreement with several experiments.

In the second part of this dissertation, the structural transition of vortex solid state is discussed. For a 4-
fold symmetric system, it transpires that the coupling between magnetic flux and underlying crystal lattice influences the vortex lattice configuration in a complicate way. The distortion of vortex lattice from hexagonal lattice to square lattice depends on an external magnetic field which enhances the effect of anisotropy and temperature. At a sufficient high field, the configuration is a perfect square
lattice.
Temperature dependency of the structural phase transition is under debate. Experiments shows that even for small Gi materials, the structural phase transition has a strong temperature dependency which is inconsistent with theoretical prediction base on the thermal fluctuations influences. It is found that quenched disorder is responsible for the departure from the mean field result in clean sample. Thermal fluctuations merely smear the anisotropy effect at the vicinity of its melting line.

1 Introduction 1
1.1 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Spontaneous Symmetry Breaking and Phase Transitions . . . . . . . . . 10
1.3 Thermal fluctuations in anisotropic/ disordered superconductors . . . . 12
2 Mesoscopic description of superconductor in magnetic field 17
2.1 Landau Expansion of the Free Energy in homogeneous Superconductors . 18
2.2 Landau Expansion of the Free Energy in
Anisotropic Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Applicability of Lowest Landau level approximation within the mean field
approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Optimized perturbation approach and the Bore-Pad′e approximation . . . 26
2.5 Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Magnetization in Layered Superconductors 33
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Basic equations and assumptions . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Dimensionality effects of layered superconductors . . . . . . . . . . . . . 40
3.4 Sum of contributions of all Landau levels in quasi-2D systems. The 1st
OPA method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 All Landau level contributions in quasi-2D systems. An effective LLL model 45
3.6 Results and Comparisons with Experiments 48
3.7 Discussion 52
4 Structural Phase transition in Fourfold Symmetric Superconductors 54
4.1 Introduction 54
4.2 Basic equations and symmetries 56
4.3 Structure of the vortex lattice in the clean system and its phase transition 57
4.4 Effects of weak disorder on structural phase transition 60
4.5 Spectrum of rhombic lattice in a clean system 63
4.6 Hartree-Fock-like approximation and Replica trick in disordered system 66
4.7 Results 71
4.8 Discussion 74
5 Summary 79
Bibliography 81

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