Understanding the Singlet State of Cooper Pairs in Conventional Superconductors

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Conventional superconductors predominantly feature Cooper pairs in the singlet state due to the lower energy eigenvalue associated with their even spatial and odd spin wave functions when analyzed with the Hamiltonian. BCS theory suggests that while singlet pairs are more favorable, it does not exclusively predict them, as other states like triplet pairs can exist under certain conditions. The anti-parallel spin configuration of Cooper pairs arises from the Pauli exclusion principle and the resulting lower expectation values. The prevalence of singlet states in most superconductors is influenced by material properties, but exceptions exist, such as in ruthenates, where a single state is not favored. Ultimately, the ground state symmetry in superconductors is determined by various factors, making the definition of "favorable" context-dependent.
.J.
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Can anyone help me, I am some what unclear on the reason why "conventional" superconductors have cooper pairs only in the singlet state. Is it something to do with the expectation values given for the separate states calculated from their spatial and spin wave functions? For example does the singlet state with an even spatial wave function and an odd spin wave function give a lower Energy eigenvalue when operated on using the Hamiltonian compared to the triplet (spin anti parallel) state?

Does BCS theory only predict singlet cooper pairs or just state that it is the more favorable ?

I know that cooper pairs have a zero center of mass momentum and anti parallel spins. Is the the anti parallel spin due to the Pauli principle (would that matter as the cooper pair is essentially a composite boson?) or due to a lower expectation value given by the Hamiltonian?
 
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I might be wrong here, but I don't think there is a "general" reason. You canuse whatever symmetry you want in the BCS theory, it just happens to be that s-wave is the most common type in conventional superconductors, but this is presumably due to the materials themselves and not due to the theory as such.
Note that for example P-wave superconductors etc are -usually- referred to as conventional and are described by the BCS theory.
 
Surely if the majority of superconductors only have a singlet amplitude, it must be in general more favorable to have a singlet state rather than a spin anti parallel or spin parallel triplet.
 
.J. said:
Surely if the majority of superconductors only have a singlet amplitude, it must be in general more favorable to have a singlet state rather than a spin anti parallel or spin parallel triplet.

But in the ruthenates, it is NOT favorable to have a single state!

Again, a lot of factors influence the ground state symmetry. So it depends on what you mean by "favorable". It is more favorable to have more Type II superconductors?

Zz.
 
Is there a dominant factor that influences the singlet state in most superconductors?
 

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