# Superconductivity: Current and Magnetic Field Limitations

## Main Question or Discussion Point

Why when a certain current limit is breached is superconductivity destroyed in a material, what atomically causes this effect when J > Jc? Secondary question what causes H0's value to be higher or lower atomically and chemically for a given material?

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mfb
Mentor
It's the same effect, basically. The current inside the superconductor produces a magnetic field that needs to be cancelled (which effectively means the current flows on the surface, approximately), that only works up to some point.

It's the same effect, basically. The current inside the superconductor produces a magnetic field that needs to be cancelled (which effectively means the current flows on the surface, approximately), that only works up to some point.
But why? I understand that part of it.

Lord Jestocost
Gold Member
According to the BCS theory, superconducting phenomena occur when two electrons couple to form a Cooper pair (http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html).

Kevin A. Delin and Terry P. Orlando in Chapter 122 „Superconductivity“ in „The Engineering Handbook“ (ed. Richard C. Dorf):

“If we prevent the Cooper pairs from forming by ensuring that all the electrons are at an energy greater than the binding energy, we can destroy the superconducting phenomenon. This can be accomplished, for example, with thermal energy. In fact, according to the BCS theory, the critical temperature, $T_c$, associated with this energy is

$$\frac {2\Delta} {k_BT_c} \approx 3.5$$

where $k_B$ is Boltzmann’s constant. For low critical temperature (conventional) superconductors, $2Δ$ is typically on the order of $1 meV$, and we see that these materials must be kept below temperatures of about $10 K$ to exhibit their unique behavior. Superconductors with high critical temperature, in contrast, will superconduct up to temperatures of about $100 K$, which is attractive from a practical view because the materials can be cooled cheaply using liquid nitrogen. A second way of increasing the energy of the electrons is electrically driving them. In other words, if the critical current density, $J_c$, of a superconductor is exceeded, the electrons have sufficient kinetic energy to prevent the formation of Cooper pairs. The necessary kinetic energy can also be generated through the induced currents created by an external magnetic field. As a result, if a superconductor is placed in a magnetic field larger than its critical field, $H_c$, it will return to its normal metallic state. To summarize, superconductors must be maintained under the appropriate temperature, electrical current density, and magnetic field conditions to exhibit its special properties.”

According to the BCS theory, superconducting phenomena occur when two electrons couple to form a Cooper pair (http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/coop.html).

Kevin A. Delin and Terry P. Orlando in Chapter 122 „Superconductivity“ in „The Engineering Handbook“ (ed. Richard C. Dorf):

“If we prevent the Cooper pairs from forming by ensuring that all the electrons are at an energy greater than the binding energy, we can destroy the superconducting phenomenon. This can be accomplished, for example, with thermal energy. In fact, according to the BCS theory, the critical temperature, $T_c$, associated with this energy is

$$\frac {2\Delta} {k_BT_c} \approx 3.5$$

where $k_B$ is Boltzmann’s constant. For low critical temperature (conventional) superconductors, $2Δ$ is typically on the order of $1 meV$, and we see that these materials must be kept below temperatures of about $10 K$ to exhibit their unique behavior. Superconductors with high critical temperature, in contrast, will superconduct up to temperatures of about $100 K$, which is attractive from a practical view because the materials can be cooled cheaply using liquid nitrogen. A second way of increasing the energy of the electrons is electrically driving them. In other words, if the critical current density, $J_c$, of a superconductor is exceeded, the electrons have sufficient kinetic energy to prevent the formation of Cooper pairs. The necessary kinetic energy can also be generated through the induced currents created by an external magnetic field. As a result, if a superconductor is placed in a magnetic field larger than its critical field, $H_c$, it will return to its normal metallic state. To summarize, superconductors must be maintained under the appropriate temperature, electrical current density, and magnetic field conditions to exhibit its special properties.”
So the only way to increase Jc and Hc is to increase Tc, thanks for answering this question Lord Jestocost.