The Nature of the Cooper Pair - University of Liverpool

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Putting in the numbers, we would find that the distance D between the Cooper pairs is about 30d, where d is the distance between the ions. Since the size of the Cooper pair wavefunction is around 10 −4 cm, this means that there is a lot of overlap between Cooper pairs. However, there must be a distance below which two Cooper pair wavefunctions cannot come any closer, just as the wavefunctions between two atoms must start repelling if they come too close. According to Victor Weisskopf, the average distance D between Cooper pairs is just this distance. This means that the Cooper pairs are packed in a compact way, just like liquid helium-4. It behaves like a liquid instead of a gas. (Weisskopf(1979)http://cdsweb.cern.ch/record/880131/files/p1.pdf) Superconductivity 29
So, as in superfluid helium-4, we may expect phonons and rotons, and that the critical velocity be determined by the minimum roton excitation. If we think of the rotation as a rotation of two Cooper pairs about each other, we can relate the roton excitation to the minimum rotational energy. The rotational energy is quantised and the minimum is given by 2� 2 /meD 2 . If we put in the numbers, we would find that this is much larger than ∆, the binding energy for the Cooper pair. The Cooper pair would break before any roton gets excited. As long as there is not enough energy to break the Cooper pairs, the Cooper pair condensate flows with zero resistance. This condesate is also called the BCS superfluid. This explains why a superconductor has zero resistance. Superconductivity 30
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: The number of Cooper pairs is there
Page 33 and 34: APPENDIX: Solving for the Cooper pa
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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