臺灣博碩士論文加值系統

在這論文中,我們研究安德生晶體模型(Anderson Lattice Model), 因為
這個模型能夠有效的解釋在重費米子材料(heavy fermions comppound)與
近滕絕緣體(Kondo insulators)的一些物理性質。我們利用了不同的平均
場近似去解決模型問題,並考慮了高階的修正。第一章,是有關重費米子材
料與近滕絕緣體的性質介紹,在這我們閱觀一些有關這些強耦合電子系
統的實驗與理論的工作。第二章,我們研究在磁場下,重費米子材料的異常
的霍爾電阻 (Hall resistance)效應。我們知道在磁場下,能階會因
Zeeman效應而分裂為二, 我們採用了這二能帶模型,去研究這異常的霍爾
電阻效應。我們從Anderson Lattice Model出發,考慮混層交互作用的各
向異性,利用infinite-U one slave boson平均場方法來解決問題。我們
發現唯有考慮混層交互作用 (hybridization interaction)的各向異性,
才能得到正確的解果。第三章,我們研究一維的Anderson Lattice Model
在對庫侖力的二階微擾 作用下的性質。庫侖力的二階微擾作用一般相信
在重費米子材 料中是很重 要的。在這我們從Hartree- Fock平均場出
發去做庫侖力的二階微擾,我們 發現在二階微擾作用下的到的順磁磁矩大
於只做Hartree-Fock平均場的結果。第四章,我們研究電子聲子交互作用
對於Anderson Lattice的影響,而這聲譜來自f電子軌道因混層交互作用產
生的呼吸模 (breathing mode)。在我們的計算發現,電子聲子交互作用會
減少系統的混層交互作用,並且會降低磁性態的穩定性。第五章,我們研究
半填滿時Anderson Lattice在一維,二維與無窮維時的磁性性質。在這
我們利用Kotliar與Ruckenstein slave boson(K.R)方法來處理有限庫侖
力的問題。與量子蒙地卡羅(quantum Monte Carlo)結果比較發現K.R在低
維度時高估了磁性因為低估了混層交互作用,而在無窮維時量子蒙地卡羅
結果吻合。第六章,我們研究有關鈾合金的重費米子材料的超導性與反鐵
磁性共存的性質。方法上我們是先在infinite-U two slave boson方法求
得順磁能帶解然後在讓反鐵磁與超導交互作用相互耦合。在我們計算結果
發現反鐵磁只存在於反鐵交互作用常數一段範圍內,而且反鐵磁具有穩定
超導與增加超導臨界溫度的能力。

we study the anomalous Hall resistance of heavy- fermion
compound in the presence of magnetic field., We use the
standard large-degeneracy expansion for the slave-boson
technique. Second order perturbation in the Coulomb energy, U,
is believed to be able to describe the roperties of the heavy
fermion systems. The magnetic moment is found to be larger than
the Hartree-Fock results without the second order perturbation
in U. In studying the electron-phonon coupling effect to
Anderson lattice. We find that the electron-phonon coupling
effect reduces the hybridization interaction and stabilizes the
paramagnetic state. we use the symmetric Periodic Anderson
model at half-filling to study the magnetic properties of the
Kondo insulatorsis. We employ a special kind of slave-boson
mean-field approximation in one dimension. We also determine
the phase boundary between antiferromagnetic and paramagnetic
states in two dimensions. For simplicity, we extend the
Periodic Anderson Model to infinite dimensions. In studying the
superconductivity coexistes with antiferromagnetism, especially
for the Uranium-based compounds. Only a finite range of the
staggered field is able to stabilize the magnetism. We find
that the superconducting transition temperature, TC, is always
enhanced by the antiferromagnetism.

Cover
Abstrac
1 Introduction
2 Field dependence of the anomalous Hall resistance of the heavy-fermion compounds
2.1 Introduction
2.2 Model and Calculation
2.3 Results and Conclusion
3 The perturbation in U for the Anderson lattice in magnetic field
3.1 Introduction
3.2 Model and Calculations
3.3 Results and Conclusion
Influence of electron-phonon interaction to the Periodic Anderson Lat tice
4.1 Introduction
4.2 Model and Calculations
4.3 Results and Conclusion
5 Magnetic properties of the symmetric periodic Anderson lattice
5.1 Slave-boson mean-field theory versus variational-wave-function approach for the one dimensional periodic Anderson model
5.1.1 Introduction
5.1.2 Model and Calculations
5.1.3 Results and Discussion
5.1.4 Conclusion
5.2 Phase Diagram of the Two-Dimensional Periodic Anderson Model at Half-Filling
5.2.1 Introduction
5.2.2 Model and Calculations
5.2.3 Results and Discussion
5.3 Magnetic properties of the symmetric periodic Anderson model in infinite dimensions
5.3.1 Introduction
5.3.2 Model and Calculations
5.3.3 Results and Dicsussion
5.3.4 Conclusion
6 Antiferromagnetism and Superconductivity in Heavy-Fermion Compounds
6.1 Introduction
6.2 Model and Calculations
6.3 Results and Discussion
6.4 Conclusion
7 References
8 PUBLICATION LIST