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Equation 6 · Part 1 · From Origins to Frontier: A History of Quantum and Condensed-Matter Systems

Symbol omega_D

ωD\omega_D
ωD\omega_D

What this part means

the because.

Its job in the formula

omegaDa_D is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

The formula also predicts an upper ceiling: no phonon-mediated superconductor should exceed roughly 30–40 kelvin, because ωD\omega_D for any real lattice is bounded.

The passage around this formula

The exponential is the important feature, not decoration: it says TcT_c depends on the coupling strength in a way that is extraordinarily sensitive at weak coupling and saturates at strong coupling, and it predicts that heavier isotopes of the same element (which lower ωD\omega_D ) should lower TcT_c in a specific, measurable way — the isotope effect, observed before BCS existed and one of the clues that pointed toward a phonon mechanism in the first place. The formula also predicts an upper ceiling: no phonon-mediated superconductor should exceed roughly 30–40 kelvin, because ωD\omega_D for any real lattice is bounded. That ceiling is exactly what shattered in 1986.

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Sources cited in the article section

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