In general a superconducting state breaks multiple symmetries and, therefore, is characterized by several different coherence lengths i = 1,..., N. Moreover in multiband material even superconducting states that break only a single symmetry are nonetheless described, under certain conditions by multi component theories with multiple coherence lengths. As a result of that there can appear a state where some coherence lengths are smaller and some are larger than the magnetic field penetration length A: xi(1) <= xi(2)...<root 2 lambda < xi(M) <=... (N). That state was recently termed "type-1.5" superconductivity. This breakdown of type-1/type-2 dichotomy is rather generic near a phase transition between superconducting states with different symmetries. The examples include the transitions between U(1) and U(1) x U(1) states or between U(1) and U(1) x Z(2) states. The later example is realized in systems that feature transition between s-wave and s + is states. The extra fundamental length scales have many physical consequences. In particular in these regimes vortices can attract one another at long range but repel at shorter ranges. Such a system can form vortex clusters in low magnetic fields. The vortex clustering in the type 1.5 regime gives rise to many physical effects, ranging from macroscopic phase separation in domains of different broken symmetries, to unusual transport properties. Prepared for the proceedings of Vortex IX conference, Rhodes 12-17 September 2015.

KTH, School of Engineering Sciences (SCI), Physics, Statistical Physics.

Carlström, J.

Silaev, Mihail

KTH, School of Engineering Sciences (SCI), Physics, Statistical Physics.

Speight, J. M.

Type-1.5 superconductivity2017In: Superconductors at the Nanoscale: From Basic Research to Applications, Walter de Gruyter GmbH , 2017, p. 133-164Chapter in book (Other academic)

Starting with the generic Ginzburg-Landau expansion from a microscopic N-band model, we focus on the case of a 3-band model which was suggested to be relevant to describe some iron-based superconductors. This can lead to the so-called s + is superconducting state that breaks time-reversal symmetry due to the competition between different pairing channels. Of particular interest in that context, is the case of an interband dominated pairing with repulsion between different bands. For that case we consider in detail the relevant reduced two-component Ginzburg-Landau theory. We provide detailed analysis of the ground state, length scales and topological properties of that model. Prepared for the proceedings of Vortex IX conference in Rhodes (Sept. 2015).

We investigate the phase diagram of dirty two-band superconductors. This paper primarily focuses on the properties and observability of the time-reversal symmetry-breaking s + is superconducting states, which can be generated in two-band superconductors by interband impurity scattering. We show that such states can appear in two distinct ways. First, according to a previously discussed scenario, the s + is state can form as an intermediate phase at the impurity-driven crossover between s(+/-) and s(++) states. We show that there is a second scenario where domains of the s + is state exists in the form of an isolated dome inside the s(+/-) domain, completely detached from the transition between s(+/-) and s(++) states. We demonstrate that in both cases the s + is state generated by impurity scattering exists in an extremely small interval of impurity concentrations. Although this likely precludes direct experimental observation of the s + is state formation due to this mechanism, this physics leads to the appearance of a region inside both the s(+/-) and s(++) domains with unusual properties due to softening of normal modes.

The conductivity of vortex lattices in multiband superconductors with high concentration of impurities is calculated based on microscopic kinetic theory at temperatures significantly smaller than the critical one. Both the limits of high and low fields are considered, when the magnetic induction is close to or much smaller than the critical field strength IIc2, respectively. It is shown that in contrast to single-band superconductors, the resistive properties are not universal but depend on the pairing constants and ratios of diffusivities in different bands. The low-field magnetoresistance can strongly exceed the Bardeen-Stephen estimation in a quantitative agreement with experimental data for the two-band superconductor MgB2.