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Equation 18 · A Strained Crystal Is a Designer Spacetime

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5×103 cm2/V⋅s5\times10^3\,\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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Measured against real crystals, that bar splits the shortlist cleanly in two, and neither half clears it whole. The near-critical type-II hosts that actually carry the tilt — tungsten ditelluride, molybdenum ditelluride, and the strain-tunable tungsten-doped compound — sit at measured mobilities in the low thousands to low tens of thousands of square centimetres per volt-second, with tungsten ditelluride’s magnetotransport mobility around 5×\times10^3\,cm2\text{cm}^2/V⋅s\text{V·s} [ 12 ] , roughly two orders of magnitude below what the design point needs. The crystals that clear the mobility bar with room to spare sit on the other side of the same divide: the Dirac semimetal cadmium arsenide…
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Measured against real crystals, that bar splits the shortlist cleanly in two, and neither half clears it whole. The near-critical type-II hosts that actually carry the tilt — tungsten ditelluride, molybdenum ditelluride, and the strain-tunable tungsten-doped compound — sit at measured mobilities in the low thousands to low tens of thousands of square centimetres per volt-second, with tungsten ditelluride’s magnetotransport mobility around 5×\times10^3\,cm2\text{cm}^2/V⋅s\text{V·s} [ 12 ] , roughly two orders of magnitude below what the design point needs. The crystals that clear the mobility bar with room to spare sit on the other side of the same divide: the Dirac semimetal cadmium arsenide reaches mobilities above 10^7\,cm2\text{cm}^2/V⋅s\text{V·s} below four kelvin [ 5 ] , and the Weyl semimetal niobium phosphide reaches 5×\times10^6\,cm2\text{cm}^2/V⋅s\text{V·s} [ 6 ] — both comfortably ultraclean, and both type-I, with cones that sit upright and carry no tilt to bend into a horizon at all. Even suspended graphene, the two-dimensional mobility champion at roughly 2×\times10^5\,cm2\text{cm}^2/V⋅s\text{V·s} [ 10 ] , fails on both counts at once: short of the threshold, and a two-dimensional Dirac system with no cone tilt in the first place. The property that lets a crystal carry the geometry and the property that lets a carrier survive long enough to see it currently live in different crystals, and no material shortlist entry has both.

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