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

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