Superconductivity at very low carrier density

6 problems

• How semimetallic bismuth superconducts at half a millikelvin

  Open

  Bismuth crystals, with roughly one mobile electron per hundred thousand atoms, become superconducting at about half a thousandth of a kelvin. Standard theory gives no reliable prediction at such low density with such light carriers.

• Does ferroelectric quantum criticality raise the $T_{c}$ of $\mathrm{SrTiO_3}$?

  Open

  $\mathrm{SrTiO_3}$ is close to becoming ferroelectric, meaning its ions almost shift to create a permanent electric dipole. Pushing it closer, by replacing oxygen-16 with oxygen-18 or adding calcium, raises its superconducting temperature, and the reason is debated.

• Is superconducting $\mathrm{FeSe}1-x\mathrm{S}x$ in the BCS-BEC crossover regime?

  Contested

  In FeSe the energy needed to break a pair is comparable to the energy of the fastest electrons, which is unusual. This hints that its pairs are small and tightly bound, between ordinary weakly bound pairs and molecule-like bosons.

• Origin of the superconducting dome at $\mathrm{LaAlO_3}$/$\mathrm{SrTiO_3}$ interfaces

  Open

  Where $\mathrm{LaAlO_3}$ meets $\mathrm{SrTiO_3}$, a thin conducting sheet forms that superconducts below about $0.3\,\mathrm{K}$, and a gate voltage tunes its transition temperature up and then down. What causes this dome-shaped curve is unresolved.

• What pairs electrons in doped $\mathrm{SrTiO_3}$ at Fermi energies below phonons?

  Open

  Strontium titanate with very few added electrons superconducts below about 0.4 K. Its electrons have less kinetic energy than the lattice vibrations that should pair them, so standard theory does not apply.

• Pairing state of total angular momentum $3/2$ fermions in YPtBi

  Open

  In the half-Heusler compound YPtBi, the electrons near the Fermi level carry total angular momentum $3/2$ instead of the usual $1/2$, so a pair can have total angular momentum 0, 1, 2 or 3, not only the usual 0 or 1. Experiments indicate lines of zero gap, but which pairing state forms is unknown.