Non s-wave superconductivity

[nbo10]

In BCS you make the assumption that the effective electron-electron interaction is constant within a small shell around the fermi surface and zero otherwise. From this you get a constant spherical gap.

In non s-wave SC there is a specific form for the gap ie, $$\Delta_0 = [ \cos (k_x a) - \cos (k_y a)]$$. I know that you can calculate the gap parameter using group theory and the underlying symmetry of the crystal lattice. But is there a way to choose an arbitary form for $$k \cdot k^\prime$$, self consistently solve the gap equation and arrive at a d-wave gap or any other non s-wave gap?

How do you choose the effective electron-electron interaction? Is it based on the atomic orbitals that are believed to be responsible for SC? I've done a few searches and all I find is a assumption for the form of the gap. Thanks

 

[ZapperZ]

In BCS you make the assumption that the effective electron-electron interaction is constant within a small shell around the fermi surface and zero otherwise. From this you get a constant spherical gap.

In non s-wave SC there is a specific form for the gap ie, $$\Delta_0 = [ \cos (k_x a) - \cos (k_y a)]$$. I know that you can calculate the gap parameter using group theory and the underlying symmetry of the crystal lattice. But is there a way to choose an arbitary form for $$k \cdot k^\prime$$, self consistently solve the gap equation and arrive at a d-wave gap or any other non s-wave gap?

How do you choose the effective electron-electron interaction? Is it based on the atomic orbitals that are believed to be responsible for SC? I've done a few searches and all I find is a assumption for the form of the gap. Thanks

This isn't an easy question to answer because this is still something being worked on. Something like the t-J method using mean-field approximation can drop the d-wave symmetry onto your lap (this assertion is still controversial). In many instances, the symmetry is inserted by hand because that is the product of experimental observation. There's a persuasive reason why this is having that d-wave symmetry - the valence shell of the Cu in the CuO plane where superconductivity is thought to reside. The transition metals have d-orbitals valence shell.

Note that for the Ruthenates, you have a p-wave symmetry for the pair.

Zz.

 

[charng]

I can understand your curiosity about non s-wave superconductivity and the questions you have raised. Let me provide some insights that might help answer your questions.

First of all, it is important to understand that the BCS theory is based on a simplified model of superconductivity and does not fully capture the complexities of real superconducting materials. In this model, the effective electron-electron interaction is assumed to be constant within a small shell around the Fermi surface and zero otherwise. This assumption is made for mathematical convenience and does not necessarily reflect the true nature of the electron-electron interaction in a material.

Now, in non s-wave superconductors, the gap parameter takes on a specific form that is determined by the underlying symmetry of the crystal lattice. This can be calculated using group theory and is not an arbitrary choice. However, it is possible to choose a different form for the gap parameter and solve the gap equation self-consistently, but this may not represent the actual behavior of the material.

In terms of choosing the effective electron-electron interaction, it is not solely based on the atomic orbitals responsible for superconductivity. It is a complex interplay of various factors such as the electronic band structure, lattice vibrations, and the strength of the electron-electron coupling. This interaction is not a simple quantity that can be determined from a single set of atomic orbitals, but rather it is affected by the overall electronic and structural properties of the material.

In conclusion, while the BCS theory provides a good starting point for understanding superconductivity, it is important to keep in mind that it is a simplified model and may not fully capture the complexities of real materials. The specific form of the gap parameter in non s-wave superconductors is determined by the underlying symmetry of the crystal lattice, and the effective electron-electron interaction is a complex quantity that is influenced by various factors. Further research and experiments are needed to fully understand and characterize non s-wave superconductivity.