Why is it called fluctuation conductivity in superconductors?

[AJS2011]

Why is it called "fluctuation conductivity" in superconductors?

Hello,

In the work of Aslamazov-Larkin and many more, conductivity of a superconductor is calculated from the time dependent Ginzburg-Landau (TDGL) theory. They call it "fluctuation conductivity" bellow and above critical temperature. Then, this fluctuation conductivity must be added to the conductivity that comes from BCS theory known as Mattis-Bardeen complex conductivity to give the full conductivity.

Now my question:

Why is not that "fluctuation conductivity" the full conductivity?

Should not TDGL be able to give the full conductivity? Of course, considering the limitation of TDGL as an approximation. It seems that TDGL just gives the correction. Why?

Thank you!

 

[eljose79]

Thank you for your question regarding the use of the term "fluctuation conductivity" in superconductors. The reason for this terminology lies in the underlying physics of superconductors and the theoretical framework used to study them.

Superconductivity is a phenomenon where certain materials can conduct electricity with zero resistance when cooled below a critical temperature. This behavior is described by the BCS theory, which explains that electrons in a superconductor form pairs and move together without any loss of energy. However, this theory does not fully account for the behavior of superconductors near the critical temperature, where fluctuations in the order parameter (a measure of the superconducting state) become significant. These fluctuations can cause temporary disruptions in the superconducting state, leading to a non-zero resistance.

To account for these fluctuations, the TDGL theory is used, which takes into account the time-dependent behavior of the superconducting order parameter. This theory predicts a "fluctuation conductivity" that contributes to the overall conductivity of the superconductor. This fluctuation conductivity is only a correction to the conductivity predicted by the BCS theory, and therefore cannot fully account for the behavior of the superconductor. Hence, the term "fluctuation conductivity" is used to differentiate it from the complete conductivity predicted by the BCS theory.

In summary, the TDGL theory gives a more complete picture of the behavior of superconductors near the critical temperature, but it is still an approximation and cannot fully explain all the properties of superconductors. Therefore, the term "fluctuation conductivity" is used to describe the contribution of these fluctuations to the overall conductivity, while the BCS theory gives the complete conductivity. I hope this helps to clarify the terminology used in this field of study.