# Electromagnetic absorption in a superconductor material

Today i'm trying to define a suitable Electromagnetic Absorption Index for a superconductive material.

If the material is NORMAL, i can evaluate the Absorption ratio using Ohm's law and thinking of the absorption as the ohmic losses in the material [1], but in the superconductor i have some problem to identify the role of various quantities.

The Power absorbed by the material will be used to break Cooper pairs. So there is a loss energy in the pairs recombination mechanism (for radiation frequency $h\nu_{rad} \geq 2\Delta$, where $\Delta$ is the pairs gap energy).

QUESTION: The quantities to know are:

• Some macroscopic quantities that link to the recombination rate of the Cooper Pairs?
• There is also a ohmic losses due to the non-bounding electrons?
• The ohmic losses are present only in a thin length of London's penetration length?

[1] J. D. Jackson - Classical Electrodynamics pag. 356

• Define a good model of volume density current in the superconductor. Let us consider a free electron gas composed by $N_s$ electron in superconductive state and $N_n$ normal electrons. Using Ohm's law for the $N_n$ electrons and London's current density for the $N_s$ supercurrent carriers. So total density is given by $\vec{J}=\vec{J}_s+\vec{J}_n=\frac{N_ne^2\tau}{m}\vec{E}-\frac{N_s e^2\mu}{m}\vec{A} = -i\frac{N e^2}{m\omega}\left[\frac{N_s}{N}+i\omega\tau\frac{N_n}{N}\right]\vec{E}$ How can i use it to obtain information about energy Absorption? It's a good path? – Algebrato Jan 12 '17 at 9:47

The problem of electromagnetic energy absorption ratio in a superconductive thin is the problem of KID (Kinetic Inductance Detector).

The KIDs are bolometer that permit to evaluated the energy of incident radiation.

Is possible to define an absorption ratio taking into account that part of energy has been used to:

• Broke Cooper pairs;
• Ohmic dissipation of unpaired electrons in a London's depth skin.

As we see in [1] [2] [3] a good model that represent the total density current in the superconductive thin is the Two-Fluid Model. So the Ohmic losses term is due to the surface resistance.

The energy used in the pairs recombination mechanism is strictly link to the pairs energy gap.

The absorption start when $h\nu > 2\Delta$, the change of quasi particle density produce a Ohmic losses in the London's skin depth.

A complete Absorptio ratio need to take into account all this effect:

• Ohmic losses due to unpair electron in the London skin depth;
• Pairs recombination;

Reference:

[2] - Basic Principles of RF Superconductivity and Superconducting Cavities - Peter Schmuser

[3] - Surface Resistance of a Superconductor - H. Safa