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
This lesson is part of:
Condensed Matter Physics
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