Physics » Condensed Matter Physics » Superconductivity

# Summarizing Superconductivity

## Summary

• A superconductor is characterized by two features: the conduction of electrons with zero electrical resistance and the repelling of magnetic field lines.
• A minimum temperature is required for superconductivity to occur.
• A strong magnetic field destroys superconductivity.
• Superconductivity can be explain in terms of Cooper pairs.

## Key Equations

 Electrostatic energy for equilibrium separation distance between atoms $${U}_{\text{coul}}=-\cfrac{k{e}^{2}}{{r}_{0}}$$ Energy change associated with ionic bonding $${U}_{\text{form}}={E}_{\text{transfer}}+{U}_{\text{coul}}+{U}_{\text{ex}}$$ Critical magnetic field of a superconductor $${B}_{\text{c}}(T)={B}_{\text{c}}(0)[1-{\left(\cfrac{T}{{T}_{\text{c}}}\right)}^{2}]$$ Rotational energy of a diatomic molecule $${E}_{r}=l(l+1)\cfrac{{\hslash }^{2}}{2I}$$ Characteristic rotational energy of a molecule $${E}_{0r}=\cfrac{{\hslash }^{2}}{2I}$$ Potential energy associated with the exclusion principle $${U}_{\text{ex}}=\cfrac{A}{{r}^{n}}$$ Dissociation energy of a solid $${U}_{\text{diss}}=\alpha \cfrac{k{e}^{2}}{{r}_{0}}(1-\cfrac{1}{n})$$ Moment of inertia of a diatomic molecule with reduced mass $$\mu$$ $$I=\mu {r}_{0}^{2}$$ Electron energy in a metal $$E=\cfrac{{\pi }^{2}{\hslash }^{2}}{2m{L}^{2}}({n}_{1}^{2}+{n}_{2}^{2}+{n}_{3}^{2})$$ Electron density of states of a metal $$g(E)=\cfrac{\pi V}{2}{\left(\cfrac{8{m}_{e}}{{h}^{2}}\right)}^{3\text{/}2}\;{E}^{1\text{/}2}$$ Fermi energy $${E}_{\text{F}}=\cfrac{{h}^{2}}{8{m}_{e}}{\left(\cfrac{3N}{\pi V}\right)}^{2\text{/}3}$$ Fermi temperature $${T}_{\text{F}}=\cfrac{{E}_{\text{F}}}{{k}_{\text{B}}}$$ Hall effect $${V}_{\text{H}}=uBw$$ Current versus bias voltage across p-n junction $${I}_{\text{net}}={I}_{0}({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1)$$ Current gain $${I}_{c}=\beta {I}_{B}$$ Selection rule for rotational energy transitions $$\text{Δ}l=±1$$ Selection rule for vibrational energy transitions $$\text{Δ}n=±1$$

## Glossary

### BCS theory

theory of superconductivity based on electron-lattice-electron interactions

### Cooper pair

coupled electron pair in a superconductor

### critical magnetic field

maximum field required to produce superconductivity

### critical temperature

maximum temperature to produce superconductivity

### type I superconductor

superconducting element, such as aluminum or mercury

### type II superconductor

superconducting compound or alloy, such as a transition metal or an actinide series element