Inhomogeneous superconductivity and the “pseudogap” state of novel superconductors

Many novel superconducting compounds such as the high T c oxides are intrinsically inhomogeneous systems by virtue of the superconductivity being closely related to the carrier density which is in turn provided in most cases by doping. An inhomogeneous structure is thus created by the statistical nature of the distribution of dopants. At the same time doping also leads to pair-breaking and, consequently, to a local depression of T c . This is a major factor leading to inhomogeneity. As a result, the critical temperature is spatially dependent: T c ≡ T c ( r ) . seudogap” state is characterized by several energy scales: T * , T c * , and T c . The highest energy scale ( T * ) corresponds to phase separation (at T < T * ) into a mixed metallic-insulating structure. Especially interesting is the region T c * > T > T c where the compound contains superconducting “islands” embedded in a normal metallic matrix. As a result, the system is characterized by a normal conductance along with an energy gap structure, anomalous diamagnetism, unusual a.c. properties, an isotope effect, and a “giant” Josephson proximity effect. An energy gap may persist to temperatures above T c * caused by the presence of a charge density wave (CDW) or spin density wave (SDW) in the region T > T c * but less than T * , whereas below T c * superconducting pairing also makes a contribution to the energy gap ( T c * is an “intrinsic” critical temperature). The values of T * , T c * , T c depend on the compound and the doping level. The transition at T c into the dissipationless ( R = 0 ) macroscopically coherent state is of a percolation nature.