Colloquium: High pressure and road to room temperature superconductivity

This Colloquium is concerned with the superconducting state of new high-T-c compounds containing hydrogen ions (hydrides). Recently superconductivity with the record-setting transition temperature of T-c = 203 K was reported for sulfur hydrides under high pressure. In general, high pressure serves as a path finding tool toward novel structures, including those with very high T-c. The field has a rich and interesting history. Currently, it is broadly recognized that superconductivity in sulfur hydrides owes its origin to the phonon mechanism. However, the picture differs from the conventional one in important ways. The phonon spectrum in sulfur hydride is both broad and has a complex structure. Superconductivity arises mainly due to strong coupling to the high-frequency optical modes, although the acoustic phonons also make a noticeable contribution. A new approach is described, which generalizes the standard treatment of the phonon mechanism and makes it possible to obtain an analytical expression for T-c in this phase. It turns out that, unlike in the conventional case, the value of the isotope coefficient (for the deuterium-hydrogen substitution) varies with the pressure and reflects the impact of the optical modes. The phase diagram, that is the pressure dependence of T-c, is rather peculiar. A crucial feature is that increasing pressure results in a series of structural transitions, including the one which yields the superconducting phase with the record T-c of 203 K. In a narrow region near P approximate to 150 GPa the critical temperature rises sharply from T-c approximate to 120 to approximate to 200 K. It seems that the sharp structural transition, which produces the high-Tc phase, is a first-order phase transition caused by interaction between the order parameter and lattice deformations. A remarkable feature of the electronic spectrum in the high-Tc phase is the appearance of small pockets at the Fermi level. Their presence leads to a two-gap spectrum, which can, in principle, be observed with the future use of tunneling spectroscopy. This feature leads to nonmonotonic and strongly asymmetric pressure dependence of T-c. Other hydrides, e.g., CaH6 and MgH6, can be expected to display even higher values of T-c up to room temperature. The fundamental challenge lies in the creation of a structure capable of displaying high T-c at ambient pressure.