Critical current vs critical temperature at different fields

[aleksson]

Hi,

I am trying to figure out whether there is a way to express the ratio of the critical current of a superconductor at zero and finite magnetic fields [denoted as Ic(0) and Ic(B)] as a function of the ratio of corresponding critical temperatures [denoted as Tc(0) and Tc(B)].

According to Tinkham, the critical current of a thin film is given by Ic∝(1-T/T_C)^(3/2).

I appreciate any comments.

Thanks,

-aleksson

 

[eljose79]

Hello aleksson,

Thank you for your question. The ratio of the critical current at zero and finite magnetic fields can indeed be expressed as a function of the ratio of corresponding critical temperatures. This relationship is known as the Ginzburg-Landau equation, which was first proposed by Lev Landau and Vitaly Ginzburg in 1950.

The Ginzburg-Landau equation states that the ratio of the critical current at a finite magnetic field (Ic(B)) to the critical current at zero field (Ic(0)) is equal to the ratio of the corresponding critical temperatures (Tc(B) and Tc(0)), raised to the power of 3/2. This can be expressed mathematically as:

Ic(B)/Ic(0) = (Tc(B)/Tc(0))^(3/2)

This equation holds true for all type II superconductors, which includes most commonly used superconducting materials.

It is important to note that this equation is valid only for temperatures close to the critical temperature (Tc). At lower temperatures, the critical current can deviate significantly from this relationship due to the presence of vortices in the material.

I hope this helps answer your question. If you have any further inquiries, please don't hesitate to ask.