Topological phase transition between the gap and the gapless superconductors

It is demonstrated that the known for a long time transition between the gap and gapless superconducting states in the Abrikosov-Gor'kov theory of superconducting alloy with paramagnetic impurities is of the Lifshitz type, i.e. of the $2\frac12$ order phase transition. We prove that this phase transition has a topological nature and is characterized by the corresponding change of the topological invariant, namely the Euler characteristic. We study the stability of such a transition with respect to the spatial fluctuations of the magnetic impurities critical concentration $n_s$ and show that the requirement for validity of its mean field description is unobtrusive: $\nabla \left( {\ln {n_s}} \right) \ll \xi^{-1}$ (here $\xi$ is the superconducting coherence length) Finally, we show that, similarly to the Lifshitz point, the $2\frac12$ order phase transition should be accompanied by the corresponding singularities, for instance, the superconducting thermoelectric effect has a giant peak exceeding the normal value of the Seebeck coefficient by the ratio of the Fermi energy and the superconducting gap. The concept of the experiment for the confirmation of $2\frac12$ order topological phase transition is proposed.Comment: 7 pages with the supplemental material and 3 figure

Soliton states in mesoscopic two-band-superconducting cylinders

In the framework of the Ginzburg-Landau approach, we present a self-consistent theory of specific soliton states in mesoscopic (thin-walled) two-band-superconducting cylinders in external parallel magnetic fields. Such states arise in the presence of "Josephson-type" interband coupling, when phase winding numbers are different for each component of the superconducting order parameter. We evaluate the Gibbs free energy of the sysyem up to second-order terms in a certain dimensionless parameter $\epsilon\approx\frac{\mathcal{L}_{m}}{\mathcal{L}_{k}}\ll1$, where $\mathcal{L}_{m}$ and $\mathcal{L}_{k}$ are the magnetic and kinetic inductance, respectively. We derive the complete set of exact soliton solutions. These solutions are thoroughly analyzed from the viewpoint of both local and global (thermodynamic) stability. In particular, we show that rotational-symmetry-breaking caused by the formation of solitons gives rise to a zero-frequency rotational mode. Although soliton states prove to be thermodynamically metastable, the minimal energy gap between the lowest-lying single-soliton states and thermodynamically stable zero-soliton states can be much smaller than the magnetic Gibbs free energy of the latter states, provided that intraband "penetration depths" differ substantially and interband coupling is weak. The results of our investigation may apply to a wide class of mesoscopic doubly-connected structures exhibiting two-band superconductivity.Comment: 15 pages, 3 figure

Free-free absorption parameters of Cassiopeia A from low-frequency interferometric observations

Context. Cassiopeia A is one of the most extensively studied supernova remnants (SNRs) in our Galaxy. The analysis of its spectral features with the help of low frequency observations plays an important role for understanding the evolution of the radio source through the propagation of synchrotron emission to observers through the SNR environment and the interstellar medium. Aims. In this paper we present measurements of the integrated spectrum of Cas A to characterize the properties of free-free absorption towards this SNR. We also add new measurements to track its slowly evolving and decreasing integrated flux density. Methods. We use the Giant Ukrainian radio telescope (GURT) for measuring the continuum spectrum of Cassiopeia A within the frequency range of 16-72 MHz. The radio flux density of Cassiopeia A relative to the reference source of the radio galaxy Cygnus A has been measured on May-October, 2019 with two subarrays of the GURT, used as a two-element correlation interferometer. Results. We determine magnitudes of emission measure, electron temperature and an average number of charges of the ions for both internal and external absorbing ionized gas towards in Cassiopeia A. Generally, their values are close to the ones suggested by Arias et al. (2018), although for some there are slight differences. In the absence of clumping we find the unshocked ejecta of M = 2.61 solar mass at the electron density of 15.3 cm^-3 has a gas temperature of T=100 K. If the clumping factor is 0.67, then the unshocked ejecta of 0.96 solar mass the electron density of 18.7 cm^-3. Conclusions. The integrated flux density spectrum of Cassiopeia A obtained with the GURT interferometric observations is consistent with the theoretical model within measurement errors and also reasonably consistent with other recent results in the literature.Comment: 9 pages, 9 figures, 2 table