10/ SmB6 was studied in the 1960s, and there was some puzzle there that was ultimately understood. But going back to this material in the 21st century, we found that the material actually had _topological surface states_.
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19/ This aborted transition was understood in the 1960s, but returning to this material in the 2010s revealed more crazy things. First, STO can be a fairly robustsuperconductor with only a miniscule amount of added electrons. This is well beyond the purview of any theory we know.
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20/ Second, STO can act like a metal even when the apparent mean-free-path of electrons (the distance electrons can travel before scattering off something) is even shorter than the inter-atomic distance. This is a violation of both quantum mechanics and common sense.
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21/ Finally, I'll end with the most studied-to-death material on earth: SILICON. We can do just about everything with silicon at this point, but there is one big thing we don't understand: its transition from insulating to conducting as a function of added ("dopant") atoms.
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22/ Roughly speaking, this "Mott transition" happens when the concentration of dopants becomes high enough that it is easier energetically for electrons to be hybridized (in a quantum sense) between atoms than it is for them to each sit on one atom.
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23/ Near the transition point electrons are somehow like a thick liquid: technically flowing, but poorly, and with their properties somehow arising from an interplay between their repulsion and the quantum hybridization between atom-centered wavefunctions.
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24/ Modern experiments are getting better and better about probing this soupy-liquid at nanometer length scales and femtosecond time scales. These better "movies" might finally allow us to figure out what happens, in a huge class of "strongly correlated electron" situations.
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25/25 Thank you for coming to my TED Talk. Here is a grainy photo of me haranguing other workshop participants about the virtue of boring materials.pic.twitter.com/8fqz7yEQu2
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No, it's a violation of thinking Fermi's golden rule is the be all and end all: it's the semiclassical Drude model that doesn't fit here (which of course is based on a classical gas picture of electrons), you need to use a fully quantum mobility theory.
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Thanks; I am being a bit sloppy with language. But I don't know of any theory that can successfully reproduce the resistivity in STO: For example, the T^2 resistivity (despite apparent absence of umklapp scattering) that has the same dependence at T << E_F and T >> E_F
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