Superconductor-insulator transition and the anomalous metal

6 problems

• Nature of the Cooper-pair insulator beyond the transition

  Contested

  On the insulating side, some films such as amorphous indium oxide and titanium nitride show a giant resistance peak in a magnetic field and signs that electrons are still bound in pairs. How paired electrons form an insulator, and what sets its conduction, is open.

• Are critical resistance and exponents at the 2D superconductor-insulator transition universal?

  Contested

  Theory predicted that at the switch between superconductor and insulator the film resistance takes a universal value set by Planck constant and the electron charge, with simple scaling laws. Experiments find different values and exponents in different films.

• What dissipates current in an anomalous metal at low temperature?

  Open

  If the anomalous metal is real, something must let current lose energy even though the film is nearly superconducting. Candidates include quantum tunneling of magnetic vortices and superconducting islands coupled through normal metal.

• Is the anomalous metal a true zero-temperature phase?

  Contested

  Some thin superconducting films stop losing resistance on cooling and level off at a small value. The dispute is whether this is a genuine state of matter or a result of electrical noise and stray radiation that keep the electrons warmer than the thermometer.

• Does multifractality of electron states raise $T_{c}$ in disordered superconductors?

  Open

  Near the point where disorder traps electrons, their wavefunctions become patchy at every length scale (multifractal) and overlap strongly in hot spots, which theory predicts can strengthen pairing and raise the superconducting transition temperature. Whether this happens in real materials, and by how much, is not settled.

• What decides whether disorder destroys pairing or only phase coherence?

  Open

  Disorder can end superconductivity in two ways: by breaking the electron pairs, or by leaving the pairs intact but stopping them from moving together in step. Some films, such as amorphous indium oxide and titanium nitride, keep a pairing gap into the insulator, while in others the gap seems to close together with the transition temperature, and what selects the route is not known.