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The corrected dependence of the mean depth of the EAS maximum $X_{max}$ on the energy was obtained from the data of the Tunka-133 array for 7 years and the TAIGA-HiSCORE array for 2 years. The parameter $\langle\ln A\rangle$, characterizing the mean mass compositon was derived from these results. The differential energy spectrum of primary cosmic rays in the energy range of $2\cdot 10^{14}$ - $2\cdot 10^{16}$\,eV was reconstructed using the new parameter $Q_{100}$ the Cherenkov light flux at the core distance 100 m.}, Comment: 6 pages, 3 figures, Submitted to SciPost Phys.Proc

Ultrastrong light-matter coupling opens exciting possibilities to generate squeezed quantum states and entanglement. Here we propose a way to achieve this regime in superconducting hybrid nanostructures with ferromagnetic interlayers. Strong confinement of electromagnetic field between superconducting plates is found to result in the existence of magnon-polariton modes with ultrastrong magnon-photon coupling, ultra-high cooperativity and very large group velocities. These modes provide a numerically accurate explanation of recent experiments and have intriguing quantum properties. The magnon-polariton quantum vacuum consists of the squeezed magnon and photon states with the degree of squeezing controlled in wide limits by the external magnetic field. The ground state population of virtual photons and magnons is shown to be very large which can be used for generating correlated magnon and photon pairs. Excited states of magnon-polaritons contain bipartite entanglement between magnons and photons. This property can be used for transferring entanglement between different types of quantum systems.

The physical motivations, present status, main results in study of cosmic rays and in the field of gamma-ray astronomy as well future plans of the TAIGA-1 (Tunka Advanced Instrument for cosmic ray physics and Gamma Astronomy) project are presented. The TAIGA observatory addresses ground-based gamma-ray astronomy and astroparticle physics at energies from a few TeV to several PeV, as well as cosmic ray physics from 100 TeV to several EeV. The pilot TAIGA-1 complex is located in the Tunka valley, ~50 km west from the southern tip of the lake Baikal., Comment: Submission to SciPost Phys. Proc., 10 pages, 2 figures

Anderson-Higgs mechanism of mass generation is a generic concept in high-energy and condensed matter physics. It shows up through the Meissner effect providing the expulsion of static and low-frequency magnetic fields from superconductors. However, it does not affect propagating electromagnetic waves with a spectrum gap determined by the plasma frequency, which is too large to be sensitive to the superconducting transition. Here we demonstrate the spectroscopic manifestation of the Anderson-Higgs mass, showing that it determines the spectrum gap of magnons in superconductor/ferromagnet/superconductor multilayers. Moreover, we show that this effect has been observed in recent experiments as a spontaneous ferromagnetic resonance frequency shift in such systems. Our theory explains many unusual experimental features and suggests effective controls over the magnon spectrum with tunable spectral gap and group-velocity reversal. These findings pave the way to a wide range of advanced functionalities for possible applications in magnonics.

The Tunka-Grande experiment is a scintillation array with about 0.5 sq.km sensitive area at Tunka Valley, Siberia, for measuring charged particles and muons in extensive air showers (EASs). Tunka-Grande is optimized for cosmic ray studies in the energy range 10 PeV to about 1 EeV, where exploring the composition is of fundamental importance for understanding the transition from galactic to extragalactic origin of cosmic rays. This paper attempts to provide a synopsis of the current results of the experiment. In particular, the reconstruction of the all-particle energy spectrum in the range of 10 PeV to 1 EeV based on experimental data from four observation seasons is presented., Comment: 7 pages, 3 figures, submission to SciPost Phys. Proc

The review is devoted to the fundamental aspects and characteristic features of the magnetoelectric effects, reported in the literature on Josephson junctions (JJs). The main focus of the review is on the manifestations of the direct and inverse magnetoelectric effects in various types of Josephson systems. They provide a coupling of the magnetization in superconductor/ferromagnet/superconductor JJs to the Josephson current. The direct magnetoelectric effect is a driving force of spin torques acting on the ferromagnet inside the JJ. Therefore it is of key importance for the electrical control of the magnetization. The inverse magnetoelectric effect accounts for the back action of the magnetization dynamics on the Josephson subsystem, in particular, making the JJ to be in the resistive state in the presence of the magnetization dynamics of any origin. The perspectives of the coupling of the magnetization in JJs with ferromagnetic interlayers to the Josephson current via the magnetoelectric effects are discussed.

Ising superconductivity has been recently discovered in 2D transition metal dichalcogenides. We report that such superconductors have unusual optical properties controlled by the in-plane Zeeman field. First, we find several optical gaps visible as peaks of the conductivity and the Raman susceptibility. Moreover, we find that the Ising spin splitting in the spectrum of Bogolubov quasiparticles enables strong population inversion generated by the time-dependent Zeeman field. Ultimately this leads to the possibility of the superconducting laser with magnonic pumping which can be realized in the van der Waals structures consisting of the Ising superconductor and the ferromagnetic insulator layers.

Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge in highly localized (sub-80 nm) channels at the rim of the ferromagnet, despite its trivial band structure. We show that these robust rim currents arise from the magnetization texture acting as an effective spin-orbit coupling, which results in spin accumulation at the bilayer-vacuum boundary. Lastly, we demonstrate that by altering the spin texture of a single ferromagnet, both $0$ and $\pi$-channels can be realized in the same device.

A wide-angle Cerenkov array TAIGA-HiSCORE (FOV $\sim$0.6 sr), was originally created as a part of TAIGA installation for high-energy gamma-ray astronomy and cosmic ray physics. Array now consist on nearly 100 optical stations on the area of 1 km$^2$. Due to high accuracy and stability ($\sim$1 ns) of time synchronization of the optical stations the accuracy of EAS arrival direction reconstruction is reached 0.1$^\mathrm{o}$. It was proven that the array can also be used to search for nanosecond events of the optical range. The report discusses the method of searching for optical transients using the HiSCORE array and demonstrates its performance on a real example of detecting signals from an artificial Earth satellite. The search for this short flares in the HiSCORE data of the winter season 2018--2019 is carried out. One candidate for double repeater has been detected, but the estimated probability of random simulation of such a transient by background EAS events is not less than 10%, which does not allow us to say that the detected candidate corresponds to a real astrophysical transient. An upper bound on the frequency of optical spikes with flux density of more than $10^{-4} \mathrm{erg/s/cm}^2$ and a duration of more than 5\,ns is established as $\sim 2 \times 10^{-3}$ events/sr/hour., Comment: 15 pages, 6 figures, reported at the conference ISCRA-2021, Accepted for publication in Physics of Atomic Nuclei

We report that spin supercurrents in magnetic superconductors and superconductor/ferromagnetic insulator bilayers can induce the Dzyaloshinskii-Moriya interaction which strength is proportional to the superconducting order parameter amplitude. This effect leads to the existence of inhomogeneous parity-breaking ground states combining the chiral magnetic helix and the pair density wave orders. The formation of such states takes place via the penetration of chiral domain walls at the threshold temperature below the superconducting transition. We find regimes with both the single and the re-entrant transitions into the inhomogeneous states with decreasing temperature. The predicted hybrid chiral states can be found in the existing structures with realistic parameters and materials combinations.

We consider the Higgs mode at nonzero momentum in superconductors and demonstrate that in the presence of Rashba spin-orbit coupling, it couples linearly with an external exchange field. The Higgs-spin coupling dramatically modifies the spin susceptibility near the superconducting critical temperature and consequently enhances the spin pumping effect in a ferromagnetic insulator/superconductor bilayer system. We show that this effect can be detected by measuring the magnon-induced voltage generated by the inverse spin Hall effect.

A conventional superconductor sandwiched between two ferromagnets can maintain coherent equilibrium spin current. This spin supercurrent results from the rotation of odd-frequency spin correlations induced in the superconductor by the magnetic proximity effect. In the absence of intrinsic magnetization, the superconductor cannot maintain multiple rotations of the triplet component but instead provides a Josephson type weak link for the spin supercurrent. We determine the analogue of the current-phase relation in various circumstances and show how it can be accessed in experiments on dynamic magnetization. In particular, concentrating on the magnetic hysteresis and the ferromagnetic resonance response, we show how the spin supercurrent affects the nonequilibrium dynamics of magnetization which depends on a competition between spin supercurrent mediated static exchange contribution and a dynamic spin pumping contribution. Depending on the outcome of this competition, a mode crossing in the system can either be an avoided crossing or mode locking., Comment: 6 pages, 5 figures; Supplementary material 5 pages, 3 figures

The EAS Cherenkov light array Tunka-133, with $\sim$ 3 km$^2$ geometric area, is taking data since 2009.The array permits a detailed study of energy spectrum and mass composition of cosmic rays in the energy range from $6\cdot 10^{15}$ to $10^{18}$ eV. We describe the methods of time and amplitude calibration of the array and the methods of EAS parameters reconstruction. We present the all-particle energy spectrum, based on 7 seasons of operation., Comment: 12 pages,18 figures

We develop a theory of the spin battery effect in superconductor/ferromagnetic insulator (SC/FI) systems taking into account the magnetic proximity effect. We demonstrate that the spin-energy mixing enabled by the superconductivity leads to the enhancement of spin accumulation by several orders of magnitude relative to the normal state. This finding can explain the recently observed giant inverse spin Hall effect generated by thermal magnons in the SC/FI system. We suggest a non-local electrical detection scheme which can directly probe the spin accumulation driven by the magnetization dynamics. We predict a giant Seebeck effect converting the magnon temperature bias into the non-local voltage signal. We also show how this can be used to enhance the sensitivity of magnon detection even up to the single-magnon level., Comment: 6 pages, 4 figures. Supplementary material: 11 pages, 4 figures

We show that the spin pumping from ferromagnetic insulator into the adjacent metallic spin sink can be strongly stimulated by the superconducting correlations. The key physical mechanism responsible for this effect is the presence of quasiparticle surface states at the ferromagnetic insulator/superconductor interface. We consider the minimal model when these states appear because of the suppressed pairing constant within the interfacial normal layer. For thin normal layers we obtain a strongly peaked temperature dependence of the Gilbert damping coefficient which has been recently observed in such systems. For thicker normal layers the Gilbert damping monotonically increases down to the temperatures much smaller than the critical one. The suggested model paves the way to controlling the temperature dependence of the spin pumping by fabricating hybrid normal metal/superconductor spin sinks.

Static spin susceptibility of superconductors with spin-orbit relaxation has been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov. Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the ordinary and spin-orbit scattering. Using the developed formalism we study the linear spin pumping effect between the ferromagnet and the adjacent superconducting film. The consequences for understanding recent experiments demonstrating the modification of Gilbert damping by the superconducting correlations are discussed.

Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling (SOC) and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the SOC, into dynamical s-wave equal-spin triplet correlations. We demonstrate that the critical current of Josephson junctions hosting these states is proportional to the electromagnetic power, supplied either by the external irradiation or by the ac current source. Based on these unusual properties we propose the scheme of a Josephson transistor which can be switched by the ac voltage and demonstrates an even-numbered sequence of Shapiro steps. Combining the photo-active Josephson junctions with recently discovered Josephson phase batteries we find photo-magnetic SQUID devices which can generate spontaneous magnetic fields while being exposed to irradiation., Comment: published version

It has been commonly accepted that magnetic field suppresses superconductivity by inducing the ordered motion of Cooper pairs. We demonstrate that magnetic field can instead provide a generation of superconducting correlations by inducing the motion of superconducting condensate. This effect arises in superconductor/ferromagnet heterostructures in the presence of Rashba spin-orbital coupling. We predict the odd-frequency spin-triplet superconducting correlations called the Berezinskii order to be switched on at large distances from the superconductor/ferromagnet interface by the application of a magnetic field. This is shown to result in the unusual behaviour of Josephson effect and local density of states in superconductor/ferromagnet structures., Comment: 10 pages, 3 figures, published version

Superconductor-ferromagnet-superconductor Josephson junctions are known to exist in the $0$ and $\pi$ states with the transitions between them controlled by the temperature and ferromagnetic interlayer thickness. We demonstrate that these transitions can be controlled also by the external magnetic field directed perpendicular to the layers. By varying the ratio of diffusion coefficients in superconducting and ferromagnetic layers, these field-controlled transitions can be made detectable for arbitrary large value of the exchange energy in the ferromagnet. We also show that the $0$-$\pi$ transitions in the perpendicular field can be observed as the specific features of the flux-flow conductivity dependencies on the ferromagnetic thickness in accordance with recent experimental results., Comment: 5 pages, 4 figures