Brian Skinner

12/ Perhaps the most famous semimetal is GRAPHITE (pencil lead), whose electronic structure was mostly understood in the 1940s. But it turns out that putting graphite in a huge magnetic field changes things dramatically.

13/ Newly-developed magnetic field facilities were used to study graphite in fields up to 90 tesla. In such large fields graphite becomes an _excitonic insulator_: free electrons and holes bind to each other and form composite bosons that can undergo Bose Einstein condensation.

14/ BISMUTH is a semimetal with an ultralow concentration of free charges (one per 10^5 bismuth atoms). It was a big surprise, then to see this become a _superconductor_ at low enough temperature. Actually, bismuth holds the record for the lowest-TC superconductor (~ 0.5 mK)

15/ Maybe even more shocking is amorphous bismuth. This is a pile of bismuth atoms with no discernible order. Somehow this becomes a superconductor at ~7K. i.e., it is a 14,000-fold better superconductor than clean, orderly bismuth. What the heck??

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.