The analysis of nonclassical rotational response of superfluids and superconductors was performed by Onsager (in 1949) cite{Onsager} and London (in 1950) cite{London} and crucially advanced by Feynman (in 1955) cite{Feynman}. It was established that,
in thermodynamic limit, neutral superfluids rotate by forming---without any threshold---a vortex lattice. In contrast, the rotation of superconductors at angular frequency ${bf Omega}$---supported by uniform magnetic field ${bf B}_Lpropto {bf Omega}$ due to surface currents---is of the rigid-body type (London Law). Here we show that, neglecting the centrifugal effects, the behavior of a rotating superconductor is identical to that of a superconductor placed in a uniform fictitious external magnetic filed $tilde{bf H}=- {bf B}_L$. In particular, the isomorphism immediately implies the existence of two critical rotational frequencies in type-2 superconductors.
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
qrt{2}. The boundary case kappa =1/sqrt{2} is also considered to be a special situation, frequently termed as Bogomolnyi limit. Here we discuss multicomponent systems which can possess three or more fundamental length scales and allow a separate superconducting state, which was recently termed type-1.5. In that state a system has the following hierarchy of coherence and penetration lengths xi_1<sqrt{2}lambda<xi_2. We also briefly overview the works on single-component regime $kappa approx 1/sqrt{2}$ and comment on recent discussion by Brandt and Das in the proceedings of the previous conference in this series.
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
rconductor to an external field, sorting them into two categories as follows; type-I when kappa <1/sqrt{2} and type-II when kappa >1/sqrt{2} . We overview here multicomponent systems which can possess three or more fundamental length scales and allow a separate type-1.5 superconducting state when, e.g. in two-component case xi_1<sqrt{2}lambda<xi_2. In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges. As a consequence the system should form an additional Semi-Meissner state which properties we discuss below. In that state vortices form clusters in low magnetic fields. Inside the cluster one of the component is depleted and the superconductor-to-normal interface has negative energy. In contrast the current in second component is mostly concentrated on the clusters boundary, making the energy of this interface positive. Here we briefly overview recent developments in Ginzburg-Landau and microscopic descriptions of this state.
The recent paper by V. G. Kogan and J. Schmalian Phys. Rev. B 83, 054515 (2011) argues that the widely used two-component Ginzburg-Landau (GL) models are not correct, and further concludes that in the regime which is described by a GL theory there co
uld be no disparity in the coherence lengths of two superconducting components. This would in particular imply that (in contrast to $U(1)times U(1)$ superconductors), there could be no type-1.5 superconducting regime in U(1) multiband systems for any finite interband coupling strength. We point out that these claims are incorrect and based on an erroneous scheme of reduction of a two-component GL theory. We also attach a separate rejoinder on reply by Kogan and Schmalian. In their reply Phys. Rev. B 86, 016502 (2012) to our comment Phys. Rev. B 86, 016501 (2012) Kogan and Schmalian did not refute or, indeed, discuss the main points of criticism in the comment. Unfortunately they instead advance new incorrect claims regarding two-band and type-1.5 superconductivity. The main purpose of the attached rejoinder is to discuss these new incorrect claims.
We demonstrate existence of non-pairwise interaction forces between vortices in multicomponent and layered superconducting systems. That is, in contrast to most common models, the interactions in a group of such vortices is not a universal superposit
ion of Coulomb or Yukawa forces. Next we consider the properties of vortex clusters in Semi-Meissner state of type-1.5 two-component superconductors. We show that under certain condition non-pairwise forces can contribute to formation of very complex vortex states in type-1.5 regimes.
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
ssess three fundamental length scales and have been shown to possess a separate type-1.5 superconducting state. In that state, as a consequence of the extra fundamental length scale, vortices attract one another at long range but repel at shorter ranges, and therefore should form clusters in low magnetic fields. In this work we investigate the appearance of type-1.5 superconductivity and the interpretation of the fundamental length scales in the case of two bands with substantial interband couplings such as intrinsic Josephson coupling, mixed gradient coupling and density-density interactions. We show that in the presence of substantial intercomponent interactions of the above types the system supports type-1.5 superconductivity with fundamental length scales being associated with the mass of the gauge field and two masses of normal modes represented by mixed combinations of the density fields.
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
excitations which interact with each other repulsively and tend to form vortex lattices. It was shown in [5] that this dichotomy in broken in U(1)xU(1) Ginzburg-Landau models which possess three fundamental length scales which results in the existence of a distinct phase with vortex excitations which interact attractively at large length scales and repulsively at shorter distances. Here we briefly review these results in particular discussing the role of interband Josephson coupling and the case where only one band is superconducting while superconductivity in another band is induced by interband proximity effect. The report is partially based on E. Babaev, J. Carlstrom, J. M. Speight arXiv:0910.1607.
We show that in multiband superconductors even small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interac
tion results in unusual response to low magnetic fields leading to phase separation into domains of a two-component Meissner states and vortex droplets.
I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in
these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.
