- Page 1 and 2: Theory of Superconductivity Carsten
- Page 3 and 4: Contents 1 Introduction 5 1.1 Scope
- Page 5 and 6: 1 Introduction 1.1 Scope Supercondu
- Page 7 and 8: 2 Basic experiments In this chapter
- Page 9 and 10: Superconductivity with rather high
- Page 11 and 12: • In 1979, Frank Steglich et al.
- Page 13 and 14: 3 Bose-Einstein condensation In thi
- Page 15 and 16: We note the identity g n (y) = ∞
- Page 17 and 18: We find a phase transition at T c ,
- Page 19 and 20: gives a reasonable approximation fo
- Page 21 and 22: We now consider the force F = −eE
- Page 23 and 24: 5 Electrodynamics of superconductor
- Page 25 and 26: Thus the supercurrent flows in the
- Page 27: where φ j is the polar angle of el
- Page 31 and 32: N s is the total number of particle
- Page 33 and 34: 6.2 Ginzburg-Landau theory for neut
- Page 35 and 36: scope of this course, though. The i
- Page 37 and 38: As above, we keep only terms up to
- Page 39 and 40: Within the mean-field theories we h
- Page 41 and 42: Including the superconducting contr
- Page 43 and 44: The Gibbs free energy of the domain
- Page 45 and 46: The magnetic flux Φ through this l
- Page 47 and 48: Another useful quantity is the free
- Page 49 and 50: We obtain e −ik yy (− 2 2m ∗
- Page 51 and 52: has a simple interpretation: It is
- Page 53 and 54: This is a Gaussian average since F
- Page 55 and 56: Note that in two dimensions the cur
- Page 57 and 58: Thus the energy is ∫ E 2 = 2E cor
- Page 59 and 60: The energy of an isolated vortex-an
- Page 61 and 62: Next, we have to express Z ′ in t
- Page 63 and 64: quasi−long−range order free vor
- Page 65 and 66: which is valid within the film and
- Page 67 and 68: attraction of the magnetic monopole
- Page 69 and 70: Finally, the voltage measured for a
- Page 71 and 72: In this case it is useful to expand
- Page 73 and 74: It will be useful to write the elec
- Page 75 and 76: (the minus sign is conventional) an
- Page 77 and 78: Note that summing up the more and m
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8.4 Effective interaction between e
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Re RPA, R V eff V c ( ) RPA q 0 Re
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diagrams describing this situation.
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where |0⟩ is the vacuum state wit
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This is called the BCS gap equation
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10 BCS theory The variational ansat
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we obtain ( ) 2ξ k |u k | |v k | e
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1 0 2 u k v 2 k k F k We also find
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10.2 Isotope effect How can one che
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and expanding for small ∆T and sm
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For tunneling between two normal me
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In the limit k B T → 0 this becom
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tant. The first one is (u k ′u k
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for quasiparticle creation and anni
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11 Josephson effects Brian Josephso
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Ginzburg-Landau theory also gives u
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Equation (11.25) can be used to stu
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The averaged current is just Ī = I
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where = 1. In the superconductor,
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with ˜k 1 := (−k 1x , k 1y , k 1
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S N S 2∆ 0 2eV eV In particular,
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But now the right-hand side is alwa
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The fact that the gap closes at som
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where τ is the imaginary time, T
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At lower temperatures, details beco
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Also note that spin fluctuations st
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k y Γ X’ M hole−like Q 2 elect
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Thus ∆ τσ (−k) = − 1 N or,
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It is plausible that in a crystal t