We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions. The talk is based on the paper [1].

[1] A.S. Osin and Ya.V. Fominov, arXiv:2105.05786

The multifractality provides a way of ergodicity breaking in term of chaotization and equipartitioning over degrees of freedom. On the other hand, in quantum information theory it is the entanglement entropy which represents the main measure of ergodicity and thermalization. In this talk I will represent an exact relation between the above measures, showing that the fractal dimension of the non-ergodic wave function puts an upper bound on its entanglement entropy [A]. I will also provide a couple of explicit examples demonstrating that the entanglement entropy may reach its ergodic (Page) value when the wave function is still highly non-ergodic and occupies a zero fraction of the total Hilbert space. If time permits I will briefly discuss some other possible deviations from ergodicity relevant for the chaotic many-body systems [B-E].

[A] G. De Tomasi, I. M. K., “Multifractality meets entanglement: relation for non-ergodic extended states”, Phys. Rev. Lett. 124, 200602 (2020) [arXiv:2001.03173]
[B] I. M. K., M. Haque, and P. McClarty, “Eigenstate Thermalization, Random Matrix Theory and Behemoths”, Phys. Rev. Lett. 122, 070601 (2019) [arXiv:1806.09631].
[C] M. Haque, P. A. McClarty, I. M. K. , “Entanglement of mid-spectrum eigenstates of chaotic many-body systems—deviation from random ensembles.” [arXiv:2008.12782].
[D] A. Bäcker, I. M. K., M. Haque,, “Multifractal dimensions for chaotic quantum maps and many-body systems”, Phys. Rev. E 100, 032117 (2019) [arxiv:1905.03099].
[E] G. De Tomasi, I. M. K. , "Ergodic Entanglement of many-body multifractal states in quadratic Hamiltonians", in preparation

Video

Superconductor-ferromagnet heterostructures hosting vortices and skyrmions are new area of an interplay between superconductivity and magnetism. We study [1] an interaction of a Neel-type skyrmion and a Pearl vortex in thin heterostructures due to stray fields. Surprisingly, we find that it can be energetically favorable for the Pearl vortex to be situated at some nonzero distance from the center of the Neel-type skyrmion. The presence of a vortex-antivortex pair is found to result in increase of the skyrmion radius. Our theory predicts that a spontaneous generation of a vortex-anti-vortex pair is possible under some conditions in the presence of a Neel-type skyrmion that is in agreement with recent experiment [2].
[1] E.S. Andriyakhina. and I.S. Burmistrov “Interaction of a Néel–type skyrmion and a superconducting vortex” // arXiv: https://arxiv.org/abs/2102.05434.
[2] A.P. Petrović et al. “Skyrmion-(Anti)vortex coupling in a chiral magnet-superconductor heterostructure” // Phys.Rev. Lett.126, 117205 (2021).

We investigate the structure of the quasiparticle states localized in a superconducting vortex core in the vicinity of a planar defect. It is shown that even a highly transparent defect leads to a significant modification of the excitation spectrum, with the opening of a minigap at the Fermi energy. The magnitude of the minigap exceeds the mean level spacing for a clean vortex already for small values of the reflection coefficient off the defect. It is maximal for the vortex sitting right at the defect, decreases with increasing the distance from the defect and closes at some point. We then generalize the problem for various configurations of several linear defects (periodic structures, two crossing lines, stars). Though the minigap remains, a strong commensurability effect is observed. For two crossing linear defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational number.

We consider a Rosenzweig-Porter (RP) random matrix model with broad distribution of off-diagonal matrix elements which emerge as a model equivalent to the Anderson model on random regular graph. In this work we study the survival probability of a quantum particle with wave function initially localized on one site described by such type of model and show that the strongly non-Gaussian, broad distribution of hopping leads to the stretch-exponential decay of survival probability with time. We show that the ergodic phase with the stretch-exponential behavior of survival probability emerges in this model exactly where on a finite Bethe lattice there is a multifractal phase and relate the stretch exponent $\kappa$ with the kernel \epsilon_{\beta} of the transfer-matrix equation on a Bethe lattice.
We also consider the extension of this RP model relaxing the symmetry inherited from the Bethe lattice and find lines of phase transitions from the exponential to the stretch exponential behavior of survival probability.

We consider an interferometer based on artificially induced topological superconductivity and chiral 1D Majorana fermions. The (non-topological) superconducting island inducing the superconducting correlations in the topological substrate is assumed to be floating. This allows probing the physics of interfering Majorana modes via microwave response, i.e., the frequency dependent impedance between the island and the earth. Namely, charging and discharging of the island is controlled by the time-delayed interference of chiral Majorana excitations in both normal and Andreev channels. We argue that microwave measurements provide a direct way to observe the physics of 1D chiral Majorana modes.

In a quasi-one-dimensional system (a tube) with low concentration of defects $n$ the resistivity $\rho$ has peaks (van-Hove singularities) as a function of Fermi-energy. We show that due to non-Born scattering effects a deep narrow gap should appear just in the center of each peak. The resistivity at the bottom of a gap ($\rho_{\min}\propto n^2$) is dominated by scattering at rare ``twin-pairs'' of close defects, while scattering at solitary defects is suppressed. This effect is characteristic for multi-channel systems, it can not be observed in strictly one-dimensional one.