# Superconductivity: Current and Magnetic Field Limitations

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• VictorMedvil
In summary, the destruction of superconductivity in a material occurs when the energy of the electrons is increased, preventing the formation of Cooper pairs. This can be achieved through thermal energy or by exceeding the critical current density or critical field. To increase these values, the critical temperature must also be increased through methods such as electrically driving the electrons.
VictorMedvil
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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It's the same effect, basically. The current inside the superconductor produces a magnetic field that needs to be canceled (which effectively means the current flows on the surface, approximately), that only works up to some point.

VictorMedvil
mfb said:
It's the same effect, basically. The current inside the superconductor produces a magnetic field that needs to be canceled (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.

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.”

VictorMedvil
Lord Jestocost said:
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.

## 1. What is superconductivity?

Superconductivity is a phenomenon in which certain materials exhibit zero electrical resistance when cooled below a certain temperature, known as the critical temperature. This allows for the flow of electric current without any energy loss, making superconductors highly efficient for various applications.

## 2. What are the current limitations of superconductivity?

One of the main limitations of superconductivity is the need for extremely low temperatures to maintain the superconducting state. This requires expensive and complex cooling systems. Additionally, the critical temperature of superconductors is limited, with most materials only exhibiting superconductivity at temperatures below -200°C.

## 3. How does magnetic field affect superconductivity?

Magnetic fields can disrupt the superconducting state in materials, causing them to lose their zero resistance properties. This is known as the Meissner effect, and the strength of the magnetic field required to disrupt superconductivity is known as the critical magnetic field. Different materials have different critical magnetic fields, with some superconductors able to withstand stronger fields than others.

## 4. What are the applications of superconductivity?

Superconductors have various practical applications, including in medical imaging devices such as MRI machines, in particle accelerators, and in power transmission systems. They are also being researched for use in high-speed trains, energy storage systems, and quantum computing.

## 5. What are the current challenges in advancing superconductivity?

One of the main challenges in advancing superconductivity is finding materials that exhibit superconductivity at higher temperatures, making them more practical and cost-effective to use. Another challenge is developing superconductors that can withstand higher magnetic fields, allowing for more diverse applications. Researchers are also working on improving the stability and durability of superconducting materials for long-term use.

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