Upper limits on the superconducting transition temperature

4 problems

• Can any material superconduct at room temperature and ambient pressure

  Open

  The best superconductor at normal pressure works up to about 151 K, roughly minus 120 degrees Celsius; whether any material can reach room temperature without huge pressure is unknown.

• Maximum $T_c$ from purely repulsive electron interactions

  Open

  If electron repulsion alone can make electrons pair, there should be a largest possible transition temperature, measured in units of the energy for an electron to hop between neighboring atoms; in cuprates the transition temperature is only about 3 percent of that hopping energy.

• Is there a rigorous upper bound on phonon-mediated $T_{\mathrm{c}}$

  Open

  For superconductors glued by lattice vibrations, the transition temperature seems to stay below about one tenth of the vibration energy scale, and the vibration energies themselves are capped by fundamental constants; neither statement is proven.

• Do superfluid-stiffness bounds on $T_c$ extend to three dimensions

  Open

  In two-dimensional superconductors the transition temperature is provably limited by how stiff the superconducting phase is, which in turn is limited by how easily electrons move; whether a similar proof works in three dimensions is unknown.