The Nature of the Cooper Pair - University of Liverpool

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At temperature T , we would expect thermal energies of the order of k BT , either in the form of phonons or excited electrons. If this energy is more than ∆, then there is enough energy to break the Cooper pairs. If this happens, the metal returns to being normal conducting, with resistance. The transition temperature Tc is therefore related to the binding energy by k BTc ≈ ∆. The complete BCS theory gives the more accurate relation of 1.76k BTc = ∆ which agrees well with measured values of Tc and ∆. Superconductivity 31
APPENDIX: Solving for the Cooper pair wavefunction Superconductivity 32
Page 1 and 2: Statistical and Low Temperature Phy
Page 3 and 4: When an electron passes in between
Page 5 and 6: Using the small change approximatio
Page 7 and 8: The attractive force is the Coulomb
Page 9 and 10: Recall that the Debye frequency ω
Page 11 and 12: The displacement then gives us the
Page 13 and 14: We shall approximately represent th
Page 15 and 16: We have seen that two electrons mus
Page 17 and 18: ... recall the quantisation conditi
Page 19 and 20: The Schrodinger equation is then of
Page 21 and 22: Here, we just state the solution to
Page 23 and 24: They will start interfering destruc
Page 25 and 26: Using ∆k.ρ = π we can solve for
Page 27 and 28: The bound pair of electrons is the
Page 29 and 30: The number of Cooper pairs is there
Page 31: So, as in superfluid helium-4, we m
Page 35 and 36: The attractive potential is very sm
Page 37 and 38: Therefore and sin(kR) = 0, k = nπ
Page 39 and 40: The product of the waves sin(kr) an
Page 41 and 42: Return to the Schrodinger’s equat
Page 43 and 44: So in energy variable, the density
Page 45 and 46: However, ε is 2�ω D, then the u
Page 47 and 48: We have found both aε and ∆. Thi

The Nature of the Cooper Pair - University of Liverpool

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