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In general a superconducting state breaks multiple symmetries and, therefore, is characterized by several different coherence lengths $xi_i$, $i=1,...,N$. 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 larger and some are smaller than the magnetic field penetration length $lambda$: $xi_1leq xi_2... < sqrt{2}lambda<xi_Mleq...xi_N$. 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 $U(1)times U(1)$ states or between $U(1)$ and $U(1)times Z_2$ 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.
Usual superconductors are classified into two categories as follows: type-1 when the ratio of the magnetic field penetration length (lambda) to coherence length (xi) with Ginzburg-Landau parameter kappa=lambda/xi <1/sqrt{2} and type-2 when kappa >1/s
In the usual Ginzburg-Landau theory the critical value of the ratio of two fundamental length scales in the thery $kappa_c=1/sqrt{2}$ separates regimes of type-I and type-II superconductivity. The latter regime possess thermodynamically stable vortex
In contrast to single-component superconductors, which are described at the level of Ginzburg-Landau theory by a single parameter kappa and are divided in type-I kappa<1/sqrt{2} and type-II kappa>1/sqrt{2} classes, two-component systems in general po
A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth lambda and the coherence length xi. Their ratio kappa determines the response of a supe
We demonstrate the existence of a novel superconducting state in high quality two-component MgB2 single crystalline superconductors where a unique combination of both type-1 (kappa_1 < 0.707) and type-2 (kappa_2 > 0.707) superconductor conditions is