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16/ Finally, one can turn to the semiconductors: objects which do not conduct electricity at low temperature in their native state, due to gaps between electron bands.
17/ The poster child for the value of reconsidering old semiconductors is the crystal STRONTIUM TITANATE ("STO"). STO is a synthetic gemstone (you can buy it cheap online), which happens to have an enormous dielectric constant.
18/ This huge dielectric constant arises from a ferroelectric phase transition (a buckling-type instability within the atomic cell) that _almost_ happens, but is aborted by quantum fluctuations of the atom positions.
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.
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.
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.
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.
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.
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.
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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