A review of two-band superconductivity: materials and effects on the thermodynamic and reversible mixed-state properties

Two-band superconductivity has become an important topic over the past ten years. Extensive experimental and theoretical studies started with MgB2 and are now focused on iron-based and other new superconductors. In this review, I describe how important thermodynamic, reversible mixed-state, and other superconducting properties are changed by two-band superconductivity and, for comparison, by other effects such as anisotropy in a single-band material or an energy-gap structure different from the conventional s-wave symmetry. The work consists of three main parts, in which I review (i) theoretical models and what they predict for experimentally accessible properties in the two-band and other scenarios, (ii) experimental methods applied for investigating superconducting properties and the results obtained in potential two-band materials, and (iii) materials, for which two- or multi-band superconductivity has been suggested. It is shown that two-band effects appear in most of the analyzed properties and that they can be quite significant but usually fade away as interband interactions increase. Anisotropy often leads to similar modifications in single-band superconductors, which is why the distinction of two-band and anisotropy effects is usually difficult, particularly when the temperature dependence of the quantities is examined. In contrast, the field-dependent effects are more often different and thus more often allow a reliable distinction between the models.