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Equation 17 · A Strained Crystal Is a Designer Spacetime

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7×105 cm2/V⋅s7\times10^5\,\text{cm}^2/\text{V·s}

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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A tilted cone crossing 1 on a band diagram is not automatically a horizon an electron experiences. For the crossing to be a physical event rather than a line on a chart, a carrier has to travel across it ballistically — without being scattered by disorder — for at least as long as the horizon takes to act on it. Turning that single requirement into arithmetic sets a minimum mobility: too dirty a crystal, and disorder buries the horizon under ordinary resistive scattering before any carrier gets close enough to feel the tipped cone. At the paper’s design point, a tenth-of-a-kelvin horizon demands a mobility on the order of 7×\times10^5\,cm2\text{cm}^2/V⋅s\text{V·s} , with carriers needing to cross…
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A tilted cone crossing 1 on a band diagram is not automatically a horizon an electron experiences. For the crossing to be a physical event rather than a line on a chart, a carrier has to travel across it ballistically — without being scattered by disorder — for at least as long as the horizon takes to act on it. Turning that single requirement into arithmetic sets a minimum mobility: too dirty a crystal, and disorder buries the horizon under ordinary resistive scattering before any carrier gets close enough to feel the tipped cone. At the paper’s design point, a tenth-of-a-kelvin horizon demands a mobility on the order of 7×\times10^5\,cm2\text{cm}^2/V⋅s\text{V·s} , with carriers needing to cross roughly fourteen micrometres without scattering to register it.

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