臺灣博碩士論文加值系統

本論文主要研究由鐵磁金屬，絕緣體與電子滲雜的d波超導體(有反

鐵磁序)所組成之結的點接觸穿隧電導。我們首先推廣了Bogoliubov-de

Gennes方程組，使其加入反鐵磁及自旋極化的效應，從而可以在理論上

分析反鐵磁態與超導態之間的相互作用。我們發現反鐵磁及自旋極化有

反常的點接觸穿隧電導。因此點接觸穿隧方面的實驗可以提供一種途徑

澄清反鐵磁態與超導態是否會共存。另外，我們計算出能隙以下的表面

態的色散關係所滿足的公式，而表面態是造成零電壓峰值的主要原因。

最後，我們提出一條可以利用點接觸穿隧電導的實驗數據準確地計算自

旋極化大小的公式。

This thesis applies the theory of tunneling to study different kinds of metal/insulator/ superconductor (N/I/S) junctions. Chapter 1 gives a brief review of the BCS theory. Chapter 2 mentions some basic properties of high-temperature superconductors (HTSC). Possible coexistence of antiferromagnetic (AF) order and the superconducting order in HTSC is emphasized. In chapter 3, theories of tunneling are presented, namely the Blonder-Tinkham-Klapwijk model approach and the tunneling Hamiltonian approach. In chapter 4, we summarize recent experimental and theoretical works on different kinds of N/I/S junctions. Chapter~5 is based on one of my recent paper to be published. We extend the theory of point-contact spectroscopy [Phys. Rev. B 76, 220504(R) (2007). This paper argued that the splitting of zero-bias conductance peak (ZBCP) in electron-doped cuprate superconductor point-contact spectroscopy is due to the coexistence of AF and $d$-wave superconducting orders.]
to study the ferromagnetic metal/electron-doped cuprate
superconductor (FM/EDSC) junctions. In addition to the AF order, effects of spin polarization, Fermi-wave vector mismatch (FWM) between the FM and EDSC regions, and effective barrier are also considered. They play a crucial role in determining the spin polarization value. It is shown that there exits the midgap surface state (MSS) contribution to the ZBCP in the junction and Andreev
reflections are largely modified due to the exchange field of ferromagnetic metal. A more accurate formula is proposed for determining the spin polarization value in combination with the conductance in point-contact experimental data. Finally in Chapter~6, a brief conclusion and future prospects are given.

Contents
1 BCS Theory 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Cooper Pairs and the Origin of the Attractive Interaction . . . . . . . . 2
1.3 BCS Ground State . . . . . . . . . . . . . . . . . . . . . . . . . . .4
2 Some Basic Properties of Hight-Temperature Superconductors 7
2.1 Structure of Hight-Temperature Superconductors . . . . . . . . . . . . 7
2.2 Phase Diagram of Hight-Temperature Superconductors and AntiferromagneticOrder . . . . . . . . . . . . . . . . . . 8
3 Tunneling Theory 13
3.1 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . .13
3.2 Semiconductor Model . . . . . . . . . . . . . . . . .13
3.3 Formula of Tunneling Current . . . . . . . . . . . . 15
3.4 Andreev Reflection . . . . . .. . . . . . . . . . . .16
3.5 Blonder-Tinkham-Klapwijk Model Approach .. .. . . . . 17
3.6 Tunneling Hamiltonian Approach . . . . .. . . . . . . 22
4 Tunneling in Di®erent Kinds of Metal/Insulator/Superconductor Junctions 25
4.1 Introduction . . . . . . . . . . . . . . . . . . . . 25
4.2 N/I/sSC Junctions . . . . . . . . . . . . . . . . . . 26
4.3 FM/I/sSC Junctions .. . . . . . . . . . . . . . . . . 27
4.4 N/I/HTSC Junctions . . . . . . .. . . . . . . . . . . 33
5 A Detailed Study of FM/I/dSC Junction 37
5.1 Introduction . . . . . . . . . . . . . . . . . . . . 37
5.2 Formalism . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Results and Discussions . . . . . . . . . . . . . . . 45
5.3.1 Midgap Surface States . . . . . . . . .. . . . . . 45
5.3.2 E®ects of Fermi-wave-vector Mismatch . . . . . . . 46
5.3.3 E®ects of Spin Polarization . . . . . . . .. . . . 48
5.3.4 E®ects of E®ective Barrier . . . . . .. ... . . . . 50
5.3.5 A General Formula for Determining the Spin Polarization . . . . . . . .. . . . . . . . . . . . .... .54
6 Conclusions.............................................55

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