臺灣博碩士論文加值系統

In this article we studied the BCS-BEC crossover in two-dimensional d-wave pairing at finite temperature. We would life to calculat the relation between condensate numbers and chemical potential and then find the energy gap in superconductors. We will discuss the attractive seperable potential and the contact (hard core) potential with d-wave form. The main diffrence between d-wave and s-wave is that the d-wave is angle dependent. It will lead to a factor of 1/2 in the perturbation expansion of the hard core potential.

We analyzed the asymptotic property of the two potentials. It is showed that the pair susceptibility will diverge for some kinds of potential. That is, some of potentials is computable in mean field theory but not in the pair susceptibility method.

Abstract

Ch1 Introduction

1.1 From BCS Theory to BE Condensation 1
1.2 The Model 1
1.2.1 Ground State 1
1.2.2 Finite Temperature State 2

Ch2 Finite Temperature Formulation

2.1 Series Expansion of Interaction 3
2.1.1 Green''s Function 3
2.1.2 Frequency Summation 4
2.2 Thermodynamic Potential and Number Equation 5
2.3 D-wave Potential 6
2.3.1 Separable d-wave Potential 6
2.3.2 Pair Susceptibility 7
2.4 The Hard Core Potential 8
2.4.1 Bessel function Expansion of Potential 8
2.4.2 Pair Susceptibility 8

Ch3 Superconductor

3.1 Superconductivity 10
3.2 Energy Gap 10
3.2.1 Derivation for Gap Equation 10
3.2.2 Separable Potential 12
3.2.3 The Hard Core Potential 12

Ch4 The Critical Analysis

4.1 The Real Part of Pair Susceptibility 14
4.1.1 The Property of Separable Potential 14
4.1.2 The Divergence of Real Part 15
4.2 The Real Part of Argument 16
4.3 The Behavior of Hard Core Potential 17
Ch5 Discussions 18

Appendix 19
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