arXiv subjects

Anatoly F. Volkov

Publications and source records attributed to Anatoly F. Volkov.

At least 19 recordsLinked to original sources

arXiv2024

Superluminal Propagation of Composite Collective Modes in Superconductor-Ferromagnet Heterostructures

Superconductor/ferromagnet/superconductor Josephson junctions are paradigmatic systems for studying the delicate interplay of superconductivity and magnetism via proximity effects as well as their composite excitations. Here, we analyse the collective modes (CM) in such a heterostructure by taking into account the interplay between the de-magnetisation field $H_{dem}$ and the field caused by the anisotropy of the ferromagnet $H_{an}$, which was previously neglected. It turns out that the spectrum of composite collective modes, $ω(k)$, has a qualitatively different form in the case of $H_{dem} H_{an}$. In the first case, the dependence $ω(k)$ has the same form as in previous studies, whereas in the second case, the spectrum looks completely different. In particular, for moderate or weak anisotropy in ferromagnet the group velocity of collective modes demonstrates inflection point where the group velocity become infinite and is superluminal. Furthermore, this point separates purely real and complex-conjugate solutions for the collective modes and is also {\it exception point}. We show that the difference of the CMs spectra can be revealed by Fiske experiment, i.\,e.\,by measuring the $I-V$ characteristics in the presence of magnetic field and voltage.

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arXiv2023

Nonlinear Response of Diffusive Superconductors to $ac$-electromagnetic Fields

Motivated by the recent experimental progress in studying conventional and unconventional superconductors in a pump-probe setup, we perform a comprehensive theoretical analysis of the nonlinear response of a diffusive BCS conventional superconductor to the action of an alternating electromagnetic field using a generalized Usadel equation. We analyze the response up to the second order of the perturbation in the amplitude of the vector potential $\vec{A}$, the superconducting order parameter $Δ$ and in the third order for the current $\vec{j}$. On the basis of this approach, we derive general expressions for the retarded (advanced) Green's functions, as well as the Keldysh function for an arbitrary number of harmonics of the incident field. Most importantly, we analyze the set of physical observables in a non-equilibrium superconductor, such as frequency and the temperature dependencies of the zero harmonic $δ( Δ)_0$ (Eliashberg effect), the second harmonic $δ( Δ)_{2Ω}$, as well as the third harmonic for the electric current $j(3Ω)$ under the action of a monochromatic irradiation. For the same set of parameters, we also analyze the behavior of the reflectivity and the down-conversion intensity of a thin superconducting film, discussed recently in the context of parametric amplification of superconductivity. We derive these quantities microscopically and show the connection of the down-conversion intensity to the third harmonic generation currents induced by the amplitude mode and the direct action of the electric field on the charge carriers.

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arXiv2022

Triplet odd-frequency superconductivity in hybrid superconductor-ferromagnet structures

We present an overview of the contributions made by Konstantin B. Efetov and the authors to the field of triplet odd-frequency superconductivity in hybrid ferromagnet-superconductor structures and the repercussions they had on experimental and theoretical research. Konstantin B. Efetov passed away in August 2021. We hope the present short review gives a faithful testimony of an important part of his scientific legacy.

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arXiv2022

Charge and Spin Supercurrents in Magnetic Josephson Junctions with Spin Filters and Domain Walls

We analyze theoretically the influence of domain walls (DWs) on the DC Josephson current in magnetic superconducting S$_{m}$/Fl/F/Fl/S$_{m}$ junctions. The Josephson junction consists of two "magnetic" superconductors S$_{m}$ (superconducting film covered by a thin ferromagnetic layer), spin filters Fl and a ferromagnetic layer F with or without DW (DWs). The spin filters Fl allow electrons to pass with one specific spin orientation, such that the Josephson coupling is governed by a fully polarized long-range triplet component. In the absence of DW(s), the Josephson and spin currents are nonzero when the right and left filters, Fl$_{r,l}$, pass electrons with equal spin orientation and differ only by a temperature-independent factor. They become zero when the \textbf{spins} of the triplet Cooper pairs passing through the Fl$_{r,l}$ have opposite directions. Furthermore, for the different chiralities of the injected triplet Cooper pairs the spontaneous currents arise in the junction yielding a diode effect. Once a DW is introduced, it reduces the critical Josephson current $I_{c}$ in the case of equal spin polarization and makes it finite in the case of opposite spin orientation. The critical current $I_{c}$ is maximal when the DW is in the center of the F film. A deviation of the DW from the center generates a force that pushes the DW to the center of the F film. In addition, we consider the case of an arbitrary number $N$ of DW's, with the case $N=2$ corresponding to a model system for a magnetic skyrmion.

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arXiv2021

Signatures of Long-Range Spin-Triplet Component in Andreev Interferometer

We analyze the Josephson,$I_{J}$, and dissipative,$I_{V}$, currents in a magnetic Andreev interferometer in the presence of the long-range spin triplet component (LRSTC). Andreev interferometer has a cross-like geometry and consists of a SF$_{l}$ - F - F$_{r}$S circuit and perpendicular to it a N - F - N circuit, where S, F$_{l,r}$ are superconductors and weak ferromagnets with non-collinear magnetisations $\mathbf{M}_{l,r}$, F is a strong ferromagnet with a high exchange energy. The ferromagnetic wire F can be replaced with a non-magnetic wire n. In the limit of a weak proximity effect (PE), we obtain simple analytical expressions for the currents $I_{J}$ and $I_{V}$. In particular, the critical Josephson current in a long Josephson junction (JJ) is $I_{c}(α,β)=I_{0c}χ(α,β)$, where the function $% χ(α,β)$ is a function of angles $(α,β)_{l,r}$ that characterize the orientations of $\mathbf{M}_{l,r}$. The oscillating part of the dissipative current $I_{osc}(V)=χ(α,β)\cos φI_{0}(V)$ in the N - F(n)- N circuit depends on the angles $(α,β)_{l,r}$ in the same way as the critical Josephson current $I_{c}(α,β)$, but can be much greater than the $I_{c}(α,β)$. At some angles the current $I_{c}(α,β)$ changes sign. We briefly discuss a relation between the negative current $I_{c}$ and paramagnetic response. We argue that the measurements of the conductance in N - F(n) - N circuit can be used as another complementary method to identify the LRSTC in S/F heterostructures.

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arXiv2021

Note on possibility of proximity induced spontaneous currents in superconductor/normal metal heterostructures

We analyse the possibility of the appearance of spontaneous currents in proximated superconducting/normal metal (S/N) heterostructure when Cooper pairs penetrate into the normal metal from the superconductor. In particular, we calculate the free energy of the S/N structure. We show that whereas the free energy of the N film $F_{N}$ in the presence of the proximity effect increases compared to the normal state, the total free energy, which includes the boundary term $F_{B}$, decreases. The condensate current decreases $F_{N}$, but increases the total free energy making the current-carrying state of the S/N system energetically unfavorable.

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arXiv2020

Meissner Currents Induced by Topological Magnetic Textures in Hybrid Superconductor/Ferromagnet Structures

Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing non-trivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray-fields which are therefore essential for the study of these systems. Here, we determine the effective stray-field and the Meissner currents in a Superconductor/Ferromagnet/Superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and Néel-type Sk and also analyze in detail the periodic structures of different types of DW's-- that is Bloch-type DW (BDW) and Néel-type DW (NDW) of finite width with in- and out-of-plane magnetization vector. The spatial dependence of the fields and Meissner currents are shown to be qualitatively different for the case of Bloch- and Néel-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of Néel-type magnetic textures. The depairing factor, which determines the critical temperature and which is related to vector potential of the stray-field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's the maximum is located at a finite distance within the Sk radius. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for Néel-type structures, the critical temperature in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers.

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arXiv2019

Phase-dependent Spin Polarization of Cooper Pairs in Magnetic Josephson Junctions

Superconductor-Ferromagnet hybrid structures (SF) have attracted much interest in the last decades, due to a variety of interesting phenomena predicted and observed in these structures. One of them is the so-called inverse proximity effect. It is described by a spin polarization of Cooper pairs, which occurs not only in the ferromagnet (F), but also in the superconductor (S) yielding a finite magnetic moment $M_{\text{S}}$ inside the superconductor. This effect has been predicted and experimentally studied. However, interpretation of the experimental data is mostly ambiguous. Here, we study theoretically the impact of the spin polarized Cooper pairs on the Josephson effect in an SFS junction. We show that the induced magnetic moment $M_{\text{S}}$ does depend on the phase difference $φ$ and therefore, will oscillate in time with the Josephson frequency $2eV/\hbar$ if the current exceeds a critical value. Most importantly, the spin polarization in the superconductor causes a significant change in the Fraunhofer pattern, which can be easily accessed experimentally.

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arXiv2019

Interaction of Skyrmions and Pearl Vortices in Superconductor-Chiral Ferromagnet Heterostructures

We investigate a hybrid heterostructure with magnetic skyrmions (Sk) inside a chiral ferromagnet interfaced by a thin superconducting film via an insulating barrier. The barrier prevents the electronic transport between the superconductor and the chiral magnet, such that the coupling can only occur through the magnetic fields generated by these materials. We find that Pearl vortices (PV) are generated spontaneously in the superconductor within the skyrmion radius, while anti-Pearl vortices ($\overline{\mathrm{PV}}$) compensating the magnetic moment of the Pearl vortices are generated outside of the Sk radius, forming an energetically stable topological hybrid structure. Finally, we analyze the interplay of skyrmion and vortex lattices and their mutual feedback on each other. In particular, we argue that the size of the skyrmions will be greatly affected by the presence of the vortices offering another prospect of manipulating the skyrmionic size by the proximity to a superconductor.

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arXiv2017

Static and dynamic properties of Josephson weak links with singlet and triplet coupling

We theoretically study static and dynamic properties of short Josephson junctions (JJ) with singlet and triplet Josephson coupling. In singlet Josephson weak links, two singlet superconductors S are connected with each other by a normal film (N) or wire. Triplet JJs, which we denote S$_{\text{m}}$/N(F)/S$_{\text{m}}$, are formed by two singlet BCS superconductors covered by a thin layer of a weak ferromagnet F$_{\text{w}}$. These superconductors S$_{\text{m}}$ are separated from the N (or F) layer by spin filters, which pass electrons with only one spin orientation. The triplet Cooper pairs propagating from the left (right) superconductors S$_{\text{m}}$ differ from each other not only by polarizations, but also by chiralities. The latter is determined by the magnetization orientation in weak ferromagnets F$_{\text{w}}$. We obtain analytical formulas for the critical Josephson current in both types of the JJs. If chiralities of the triplet Cooper pairs penetrating into the N film in S$_{\text{m}}$/N(F)/S$_{\text{m}}$ JJs from the left and right S$_{\text{m}}$ are different, the Josephson current is not zero in the absence of the phase difference (spontaneous Josephson current). We also calculate the admittance $Y(Ω)$ for arbitrary frequencies $Ω$ in the case of singlet JJs and for low frequencies in the case of triplet JJs. At low temperatures $T$, the real part of the admittance $Y^{\prime}(Ω)$ in singlet JJs starts to increase from zero at ${\hbar Ω\geq Δ_{\text{sg}}}$, but at ${T \geq Δ_{\text{sg}}}$, it has a peak at low frequencies the magnitude of which is determined by inelastic processes. The subgap $Δ_{\text{sg}}$ depends on transparencies of the S/N interfaces and on the phase difference $2 χ_{0}$. The low-frequency peak in $Y^{\prime}(Ω)$ in triplet JJs disappears.

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arXiv2017

ac properties of short Josephson weak links

The admittance of two types of Josephson weak links is calculated, i.e., of a one-dimensional superconducting wire with a local suppression of the order parameter, and the second is a short S-c-S structure, where S denotes a superconductor and c---a constriction. The systems of the first type are analyzed on the basis of time-dependent Ginzburg-Landau equations. We show that the impedance $Z(Ω)$ has a maximum as a function of the frequency $Ω$, and the electric field $E_Ω$ is determined by two gauge-invariant quantities---the condensate momentum $Q_Ω$ and the potential $μ$ related to charge imbalance. The structures of the second type are studied on the basis of microscopic equations for quasiclassical Green's functions in the Keldysh technique. For short S-c-S contacts (the Thouless energy ${E_{\text{Th}} = D/L^{2} \gg Δ}$) we present a formula for admittance $Y$ valid at frequencies $Ω$ and temperatures $T$ less than the Thouless energy but arbitrary with respect to the energy gap $Δ$. It is shown that, at low temperatures, the absorption is absent [${\mathrm{Re}(Y) = 0}$] if the frequency does not exceed the energy gap in the center of the constriction (${Ω< Δ\cos φ_{0}}$, where $2 φ_{0}$ is the phase difference between the S reservoirs). The absorption gradually increases with increasing the difference ${(Ω- Δ\cos φ_{0})}$ if $2 φ_{0}$ is less than the phase difference $2 φ_{\text{c}}$ corresponding to the critical Josephson current. In the interval ${2 φ_{\text{c}} < 2 φ_{0} < π}$, the absorption has a maximum. This interval of the phase difference is achievable in phase-biased Josephson junctions. Close to $T_{\text{c}}$ the admittance has a maximum at low $Ω$ which is described by an analytical formula.

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arXiv2017

Amplitude Higgs mode and admittance in superconductors with a moving condensate

We consider the amplitude (Higgs) mode in a superconductor with a condensate flow (supercurrent). We demonstrate that, in this case, the amplitude mode corresponding to oscillations $δ|Δ|_Ω \exp(i Ωt)$ of the superconducting gap is excited by an external ac electric field $\mathbf{E}_Ω \exp(i Ωt)$ already in the first order in $|\mathbf{E}_Ω|$, so that ${δ|Δ|_Ω \propto (\mathbf{v}_{0} \mathbf{E}_Ω)}$, where $\mathbf{v}_{0}$ is the velocity of the condensate. The frequency dependence $δ|Δ|_Ω$ has a resonance shape with a maximum at ${Ω= 2 Δ}$. In contrast to the standard situation without the condensate flow, the oscillations of the amplitude $δ|Δ(t)|$ contribute to the admittance $Y_Ω$. We provide a formula for admittance of a superconductor with a supercurrent. The predicted effect opens new ways of experimental investigation of the amplitude mode in superconductors and materials with superconductivity competing with other states.

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arXiv2016

Excess current in ferromagnet-superconductor structures with fully polarized triplet component

We study the $I$-$V$ characteristics of S$_{\text{T}}$/n/N contacts, where S$_{\text{T}}$ is a BCS superconductor S with a built-in exchange field $h$, n represents a normal metal wire, and N---a normal metal reservoir. The superconductor S$_{\text{T}}$ is separated from the n-wire by a spin filter which allows the passage of electrons with a certain spin direction so that only fully polarized triplet Cooper pairs penetrate into the n-wire. We show that both the subgap conductance $σ_{\text{sg}}$ and the excess current $I_{\text{exc}}$, which occur in conventional S/n/N contacts due to Andreev reflection (AR), exist also in the considered system. In our case, they are caused by unconventional AR that is not accompanied by spin flip. The excess current $I_{\text{exc}}$ exists only if $h$ exceeds a certain magnitude $h_{\text{c}}$. At ${h < h_{\text{c}}}$ the excess current is converted into a deficit current $I_\text{def}$. The dependencies of the differential conductance and the current $I_{\text{exc}}$ are presented as a function of voltage and $h$.

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arXiv2015

Chirality and spin transformation of triplet Cooper pairs upon interaction with singlet condensate

We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current $I_{\text{J}}$ in a multiterminal Josephson contact of the S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ type with "magnetic" superconductors S$_{\text{m}}$ that generate fully polarized triplet components. The superconductors S$_{\text{m}}$ are attached to magnetic insulators (filters) which let to pass electrons with a fixed spin direction only. The filter axes are assumed to be oriented antiparallel to each other. The Josephson current is zero in two-terminal Josephson junction, i.e., in S/n/S$_{\text{m}}$ or in S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ contact. But in the three-terminal Josephson junction, with another S superconductor attached to the normal wire, the finite current $I_{\text{J}}$ appears flowing from the S~superconductor to S$_{\text{m}}$ superconductors. The currents through the right (left) superconductors S$_{\text{m}}$ are opposite in sign, ${I_{\text{R}} \equiv I_{\text{J}} = I_{\text{c}} \sin (χ_{\text{R}} + χ_{\text{L}} - 2 χ) = - I_{\text{L}}}$, where $χ_{\text{L/R}}$ and $χ$ are the phases of superconductors S$_{\text{m}}$, S$_{\text{m}}^{\prime}$, and S, respectively. We discuss possibilities of experimental observation of the effect.

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arXiv2015

Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

We consider two types of magnetic Josephson junctions~(JJ). They are formed by two singlet superconductors~S and magnetic layers between them so that the JJ is a heterostructure of the S$_{\text{m}}$/n/S$_{\text{m}}$ type, where~S$_{\text{m}}$ includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one---the spin filter---is either conducting strong ferromagnet (nematic or N\nobreakdash-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M\nobreakdash-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n~wire and provides the Josephson coupling between the superconductors~S. Although both filters let to pass triplet Cooper pairs with total spin~$\mathbf{S}$ parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents,~$I_{\text{Q}}$ and~$I_{\text{sp}}$, do not depend on mutual orientation of the filter axes, both currents vanish in magnetic~JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for~$I_{\text{Q}}$ and~$I_{\text{sp}}$ show clearly a duality between the superconducting phase~$φ$ and the angle~$α$ between the exchange fields in the weak magnetic layers.

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arXiv2015

Hidden Order as a Source of Interface Superconductivity

Interfacial superconductivity is observed in a variety of heterostructures composed of different materials including superconducting and nonsuperconducting (at appropriate doping and temperatures) cuprates and iron-based pnictides. The origin of this superconductivity remains in many cases unclear. Here, we propose a general mechanism of interfacial superconductivity for systems with competing order parameters. We assume that parameters characterizing the material allow formation of another order like charge- or spin-density wave competing and prevailing superconductivity in the bulk (hidden superconductivity). Diffusive electron scattering on the interface results in a suppression of this order and releasing the superconductivity. Our theory is based on the use of Ginzburg--Landau equations applicable to a broad class of systems. We demonstrate that the local superconductivity appears in the vicinity of the interface and the spatial dependence of the superconducting order parameter~$Δ(x)$ is described by the Gross--Pitaevskii equation. Solving this equation we obtain quantized values of temperature and doping levels at which~$Δ(x)$ appears. Remarkably, the local superconductivity shows up even in the case when the rival order is only slightly suppressed and may arise also on the surface of the sample (surface superconductivity).

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arXiv2015

Spin Current in Junctions composed of Multi-band Superconductors with a Spin-density Wave

We calculate a nondissipative spin current and show that it can flow with or without a charge current. We consider a two-band model which can be applied to the description of Fe-based pnictides in coexistence regime of superconductivity and spin-density wave. Using quasiclassical Green's functions approach and tunneling Hamiltonian method we show that there exists a possibility to switch off the Josephson current while leaving the spin current finite. Moreover, it is possible to have the critical Josephson current and the critical spin current being proportional to each other, thus giving a possibility to measure the spin current via the Josephson current. The underlying mechanism is the interfering hopping of electron--hole pairs between different bands of the superconductors composing the junction. This is an intrinsic property of the system and provides a unique and natural way to utilize junctions made solely of pnictides in promising applications in spintronics devices.

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arXiv2014

Topological Defects in Systems with Two Competing Order Parameters: Application to Superconductors with Charge- and Spin-Density Waves

On the basis of coupled Ginzburg--Landau equations we study nonhomogeneous states in systems with two order parameters~(OP). Superconductors with superconducting OP~$Δ$, and charge- or spin-density wave (CDW or SDW) with amplitude~$W$ are examples of such systems. When one of OP, say~$Δ$, has a form of a topological defect, like, e.g., vortex or domain wall between the domains with the phases~$0$ and~$π$, the other OP~$W$ is determined by the Gross--Pitaevskii equation and is localized at the center of the defect. We consider in detail the domain wall defect for~$Δ$ and show that the shape of the associated solution for~$W$ depends on temperature and doping (or on the curvature of the Fermi surface)~$μ$. It turns out that, provided temperature or doping level are close to some discrete values~$T_{n}$ and~$μ_{n}$, the spacial dependence of the function~$W(x)$ is determined by the form of the eigenfunctions of the linearized Gross--Pitaevskii equation. The spacial dependence of~$W_{0}$ corresponding to the ground state has the form of a soliton, while other possible solutions~$W_{n}(x)$ have nodes. Inverse situation~when~$W(x)$ has the form of a topological defect and~$Δ(x)$ is localized at the center of this defect is also possible. In particular, we predict a surface or interfacial superconductivity in a system where a superconductor is in contact with a material that suppresses~$W$. This superconductivity should have rather unusual temperature dependence existing only in certain intervals of temperature. Possible experimental realizations of such non-homogeneous states of OPs are discussed.

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