Conductivity of a superconductor is a complex quantity which can be described by two fluid model. The imaginary part of the complex conductivity is responsible

for unique superconducting properties of such material (supercurrent) . Formally it is equivalent to a negative permittivity. The imaginary part of conductivity is

frequency dependent and at THz frequencies would become very small. This is

the main reason why superconductors are not used in this frequency range.

More details about the complex coductivity of YBCO at microwave frequencies

can be found in the following bublication: IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 23, NO. 2, 1501011, 2013

follow

Thanks Dr Jerzy Antoni for your answer.

According to your answer I can neglect the imaginary part of conductivity?

And because the real part is described by Drude model, I can use this model in cst for superconducting ?

It depends on frequency. Note that at 13 GHz the imaginary part of

conductivity of YBCO is about 10^8 S/m while the real part is two orders of

magnitude smaller. At 1.3 THz the real and the imaginary part of conductivity

will be similar (the imaginary part vary with frequency as f^-(1), while the real part

can be consider as a constant value).

Also when you use Drude model for the real part of conductivity it is necessary

to know plasma frequency for YBCO.

Thanks but I'm working on NbN at THz. So I dont know what to do for its conductivity.

Note that you can find in literature the surface resistance and the London

penetration depth for NbN films from which you can evaluate the complex

conductivity of this material in the same way as for YBCO.

Surface resistance: Physica C 378–381 (2002) 1295–1300

London penetration depth: Applied Physics Letters 68(4):562 - 563

Thanks a lot dear Dr Jerzy Antoni