Understanding the Singlet State of Cooper Pairs in Conventional Superconductors

Click For Summary

Discussion Overview

The discussion revolves around the nature of Cooper pairs in conventional superconductors, specifically focusing on why these pairs predominantly exist in the singlet state. Participants explore the implications of BCS theory, the role of symmetry, and the influence of material properties on the ground state of superconductors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the singlet state of Cooper pairs is related to the expectation values derived from their spatial and spin wave functions, suggesting that the energy eigenvalue may be lower for the singlet state compared to the triplet state when analyzed through the Hamiltonian.
  • Another participant argues that BCS theory does not impose a general reason for the singlet state dominance, noting that while s-wave symmetry is common in conventional superconductors, it may be more a property of the materials than a theoretical necessity.
  • A different participant asserts that if most superconductors exhibit a singlet amplitude, it implies a general favorability for the singlet state over triplet states, although this is contested.
  • One participant points out that in certain materials, such as ruthenates, the singlet state may not be favorable, indicating that multiple factors can influence the ground state symmetry of superconductors.
  • A participant inquires about the dominant factors that might influence the prevalence of the singlet state in most superconductors.

Areas of Agreement / Disagreement

Participants express differing views on the reasons for the predominance of the singlet state in conventional superconductors. While some suggest it is a favorable condition, others highlight the variability based on material properties and the influence of different symmetries.

Contextual Notes

The discussion highlights the complexity of factors influencing the ground state symmetry in superconductors, including material characteristics and theoretical frameworks, without resolving the underlying uncertainties.

Who May Find This Useful

This discussion may be of interest to those studying superconductivity, condensed matter physics, or the theoretical underpinnings of BCS theory.

.J.
Messages
4
Reaction score
0
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?
 
Physics news on Phys.org
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?
 

Similar threads

Graduate Pairing of electrons in superconductors
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad How do Cooper pairs carry a current with zero net-momentum?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Issues in understanding screening effects in the Jellium model
  • · Replies 0 ·
Replies
0
Views
3K
Graduate Cooper Pairs: Definition and Formation Process
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Theory questions on superconductivity
  • · Replies 6 ·
Replies
6
Views
4K
Spatial Perturbative Hamiltonians In Systems of Identical Particles
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How is spin exchange interaction generalised to many electrons?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Do electrons exist within a Cooper Pair?
  • · Replies 20 ·
Replies
20
Views
8K
Graduate Superconductivity and the BCS Theory
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Fermi function for Superconductors?
  • · Replies 2 ·
Replies
2
Views
3K