arXiv subjects

V. G. Kogan

Publications and source records attributed to V. G. Kogan.

At least 19 recordsLinked to original sources

arXiv2023

Vortex in superconducting thin-film strips of arbitrary width

The currents and field distributions of a vortex in a thin superconducting strip of a width $W$ is considered. It is shown that unlike infinite films where the vortex field crosses the film only in one direction (say, from the half-space under the film to the half-space above it), in strips (as well as in finite size film samples of any shape) the field lines go back to the lower half-space not only out of the sample but also through certain strip parts. The strip patches where the magnetic lines ``dive" back to the space under the strip are situated mostly near the strip edges at the strip and out of it. The magnetic flux through the strip associated with the vortex is shown to be less than the flux quantum and depends on the vortex position. The suppression of the vortex flux is strong in narrow strips with $W<<Λ=2λ^2/d$ where $λ$ is the bulk London penetration depth and $d$ is the film thickness. The vortex energy scales roughly with $W/Λ$ and depends on vortex position.

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arXiv2023

Slope of the upper critical field at $T_{c}$ in two-band superconductors with non-magnetic disorder: $s_{++}$ superconductivity in $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$

A recent theory of the disorder-dependent slope of the upper critical field, $H_{c2}$, at the superconducting transition temperature, $T_{c}$, is extended to multiband superconductors aiming at iron-based superconductors, considering two constant gaps of different magnitude and, potentially, different signs. The result shows that there is only a narrow domain inside the $s_{\pm}$ pairing state where the slope increases with the increase of transport (non-magnetic) scattering rate, $P$. In most phase space, the slope should decrease in an $s_{\pm}$ state and increase in the $s_{++}$ pairing state. The experiment shows that in an archetypal iron-based superconductor, $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$ (BaK122), non-magnetic disorder induced by electron irradiation increases the slope $S$ across the superconducting ``dome,'' at different $x$. This implies that $\textrm{Ba}_{1-x}\textrm{K}_{x}\textrm{Fe}_{2}\textrm{As}_{2}$ is likely an $s_{++}$ superconductor with two (or more) gaps of different magnitudes. This work reopens a decade-long discussion of the nature of the superconducting order parameter in iron pnictides.

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arXiv2023

Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors

We study the slopes of the upper critical field $\partial_{T}H_{c2}|_{T_{c}}\equiv\partial H_{_{c2}}/\partial T$ at $T_{c}$ in anisotropic superconductors with transport (non-magnetic) scattering employing the Ginzburg-Landau theory, developed for this situation by S. Pokrovsky and V. Pokrovsky, Phys. Rev. B 54, 13275 (1996). We found unexpected behavior of the slopes for a $d-$wave superconductor and in a more general case of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes $\partial_{T}H_{c2}|_{T_{c}}$ to decrease with increasing non-magnetic scattering parameter $P$, unlike the nodeless case where the slope increases. In a pure $d-$wave case, the slope $\partial H_{c2}|_{T_{c}}$ changes from decreasing to increasing when scattering parameter approaches $P\approx0.91\,P_{\rm crit}$, where $P_{\rm crit}\approx0.2807$ at which $T_{c}\to0$ that implies the the existence of a gapless state in $d-$wave superconductors with transport scattering in the interval, $0.91\,P_{\rm {crit}}<P<P_{\rm crit}$. Furthermore, we have considered the mixed $s+d$ order parameter that has 4 nodes on a cylindrical Fermi surface when a $d-$part is dominant, or no nodes at all when an $s-$phase is the major one. We find that presence of nodes causes the slope $\partial_{T}H_{c2}|_{T_{c}},$ to decrease initially with increasing $P$, whereas in the nodeless state, $\partial_{T}H_{c2}|_{T_{c}}$ monotonically increases. Therefore, fairly straightforward experiments make it possible to decide whether or not the order parameter of a superconductor has nodes by measuring the disorder-dependence of the slope of $H_{c2}$ at $T_{c}$.

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arXiv2022

Effects of scattering on the field-induced Tc enhancement in thin superconducting films in a parallel magnetic field

The problem of a thin superconducting film in a parallel magnetic field, first discussed in the classical paper by Ginzburg and Landau for temperatures close to the critical, is revisited with the help of the microscopic BCS theory for arbitrary temperatures taking pair-breaking and transport scattering into account. While confirming experimental findings of the $T_c$ enhancement by the magnetic field, we find that the transport scattering pushes the phase transition curve to higher fields and higher temperatures for nearly all practical scattering rates. Still, the $T_c$ enhancement disappears in the dirty limit. We also consider intriguing changes, such as re-entrant superconductivity, caused to the phase boundary by pair-breaking magnetic ions spread on one of the film faces. These features await experimental verification.

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arXiv2022

Critical fields of superconductors with magnetic impurities

The upper critical field $H_{c2} $, the field $H_{c3}$ for nucleation of the surface superconductivity, and the thermodynamic $H_c $ are evaluated within the weak-coupling theory for the isotropic s-wave case and arbitrary transport and pair-breaking scattering. We find that for the standard geometry of a half-space sample in a magnetic field parallel to the surface, the ratio ${\cal R}=H_{c3}/H_{c2}$ is within the window $1.55\lesssim {\cal R}\lesssim 2.34$, regardless of temperature, magnetic or non-magnetic scattering. While the non-magnetic impurities tend to flatten the ${\cal R}\left(T\right)$ variation, the magnetic scattering merely shifts the maximum of ${\cal R}\left(T\right)$ to lower temperatures. Surprisingly, while reducing the transition temperature, magnetic scattering has a milder impact on ${\cal R}$ than the non-magnetic scattering. The surface superconductivity is quite robust; in fact, the ratio ${\cal R}\approx 1.7$ even in the gapless state. We used Eilenberger's energy functional to evaluate the condensation energy $F_c$ and the thermodynamic critical field $H_c$ for any temperature and scattering parameters. By comparing $H_{c2} $ and $H_{c}$, we find that unlike the transport scattering, the pair-breaking pushes materials toward type-I behavior. We find a peculiar behavior of $F_c$ as a function of the pair-breaking scattering parameter at the low-$T$ transition from gapped to gapless phases, which has recently been associated with the topological transition in the superconducting density of states.

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arXiv2022

Superconductivity and phase diagrams of CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ single crystals

Members of the CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ series have been synthesized in single crystalline form and characterized by elemental analysis, thermodynamic and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K. For $x$-values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kink-like features allow for the determination of the transition temperature, $T^*$, that increases as Mn substitution increases. A temperature-composition ($T$-$x$) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, $T^*$, appearing near 26 K for $x$ $\sim$ 0.017 and rising slowly up to 33 K for $x$ $\sim$ 0.036. Specific heat data are used to track the jump in specific heat at $T_c$; The CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$ data does not follow the scaling of $Δ$$C_{p}$ with $T_{c}^3$ as many of the other Fe-based superconducting systems do. Elastoresistivity coefficients, $2m_{66}$ and $m_{11}-m_{12}$, as a function of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. This may indicate that the magnetic order in Mn substituted system may be still the same as CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. A clear change in $H^\prime_{c2}$($T$)/$T_c$, where $H^\prime_{c2}$($T$) is d$H_{c2}$($T$)/d$T$, at $x$ $\sim$ 0.015 is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also shows the changes near $x$ = 0.015.

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arXiv2021

Multi-band $s_{++}$ superconductivity in $\textrm{V}_{3}\textrm{Si}$ determined from the response to a controlled disorder

The London penetration depth, $λ(T)$, was measured in a single crystal V$_{3}$Si. The superfluid density obtained from this measurement shows a distinct signature of two almost decoupled superconducting gaps. This alone is insufficient to distinguish between $s_{\pm}$ and $s_{++}$ pairing states, but it can be achieved by studying the effect of a controlled non-magnetic disorder on the superconducting transition temperature, $T_{c}$. For this purpose, the same $\text{V}_{3}\text{Si}$ crystal was sequentially irradiated by 2.5 MeV electrons three times, repeating the measurement between the irradiation runs. A total dose of 10 C/cm$^{2}$ ($6.24\times10^{19}$ electrons/$\textrm{cm}^{2}$) was accumulated, for which $T_{c}$ has changed from 16.4 K in a pristine state to 14.7 K (9.3 $\%$). This substantial suppression is impossible for a single isotropic gap, but also it is not large enough for a sign-changing $s_{\pm}$ pairing state. Our electronic band-structure calculations show how five bands crossing the Fermi energy can be naturally grouped to support two effective gaps, not dissimilar from the iron pnictides physics. We analyze the results using two-gap models for both, $λ(T)$ and $T_{c}$, which describe the data very well. Thus, the experimental results and theoretical analysis provide strong support for an $s_{++}$ superconductivity with two unequal gaps, $Δ_{1}\left(0\right)\approx2.53\;\textrm{meV}$ and $Δ_{2}\left(0\right)\approx1.42\;\textrm{meV}$, and a very weak inter-band coupling in $\text{V}_{3}\text{Si}$ superconductor.

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arXiv2021

Dissipation of moving vortices in thin films

Moving vortices in thin superconducting films are considered within the time-dependent London description. The dissipation due to out-of-core normal excitations for two vortices moving together turns out to have a minimum for the separation vector $\bm a$ parallel to the velocity and equal to $a_m \approx 2.2\, Λ$, where $Λ$ is the Pearl length. The minimum entropy production suggests that moving vortices should have a tendency to form chains along the velocity with a period of the order $a_m$.

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arXiv2021

Pearl vortices in anisotropic superconducting films

The magnetic field of vortices in anisotropic superconducting films is considered in the framework of anisotropic London approach. It is found that at distances large relative to the core size, the magnetic field normal to the film surface may change sign. We find that the magnetic field attenuates at large distances as $1/r^3$ as it does in isotropic films, but the anisotropy induces an angular dependence to the supercurrents which causes the sign of the field to change for anisotropy parameters $γ=λ_2/λ_1>\sqrt{2}$ in some parts of the $(x,y)$ plane.

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arXiv2021

Moving vortices in anisotropic superconductors

The magnetic field of moving vortices in anisotropic superconductors is considered in the framework of time-dependent London approach. It is found that at distances large relative to the core size, the field may change sign that alludes to a non-trivial intervortex interaction which depends on the crystal anisotropy and on the speed and direction of motion. These effects are caused to the electric fields and corresponding normal currents which appear due to the moving vortex magnetic structure. We find that the motion related part of the magnetic field attenuates at large distances as $1/r^3$ unlike the exponential decay of the static vortex field. The electric field induced by the vortex motion decreases as $1/r^2$.

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arXiv2021

Current distributions by moving vortices in superconductors

We take account of normal currents that emerge when vortices move. Moving Abrikosov vortices in the bulk and Pearl vortices in thin films are considered. Velocity dependent distributions of both normal and persistent currents are studied in the frame of time-dependent London equations. In thin films near the Pearl vortex core, these distributions are intriguing in particular.

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arXiv2021

Moving Pearl vortices in thin-film superconductors

The magnetic field $h_z$ of a moving Pearl vortex in a superconducting thin-film in $(x,y)$ plane is studied with the help of time-dependent London equation. It is found that for a vortex at the origin moving in $+x$ direction, $h_z(x,y)$ is suppressed in front of the vortex, $x>0$, and enhanced behind ($x<0$). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

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arXiv2020

Temperature dependence of London penetration depth anisotropy in superconductors with anisotropic order parameters

We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $γ_λ(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $Δ(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $Δ(T)/Δ(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {\bf 131}, 1 (2003), which simplifies considerably the evaluation of $γ_λ(T)$. Of particular interest is mixed order parameters of two symmetries for which $γ_λ(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $Δ_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $Δ$.

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arXiv2020

Anisotropic time-dependent London approach

The anisotropic London equations taking into account the normal currents are derived and applied to the problem of the surface impedance in the Meisner state of anisotropic materials. It is shown that the complex susceptibility of anisotropic slab depends on the orientation of the applied microwave field relative to the crystal axes. In particular, the anisotropic sample in the microwave field is subject to a torque, unless the field is directed along with one of the crystal principle axes.

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arXiv2020

Interaction between moving Abrikosov vortices in type-II superconductors

The self-energy of a moving vortex is shown do decrease with increasing velocity. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term $\propto v^2$; the "slow" motion is defined as having the velocity $v v_c(T)$, the interaction energy of two vortices situated along the velocity direction is enhanced and along the perpendicular direction is suppressed compared to the static case.

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arXiv2020

Vortex cores in narrow thin-film strips

We study vortex current distributions in narrow thin-film superconducting strips. If one defines the vortex core ``boundary" as a curve where the current reaches the depairing value, intriguing features emerge. Our conclusions based on the London approach have only qualitative relevance since the approach breaks down near the core. Still, the main observation which might be useful is that the core size near the strip edges is smaller than in the rest of the strip. If so, the Bardeen-Stephen flux-flow resistivity should be reduced near the edges. Moreover, at elevated temperatures, when the depairing current is small, the vortex core may extend to the whole strip width, thus turning into an edge-to-edge phase-slip line.

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arXiv2020

London penetration depth at zero temperature and near superconducting transition

A simple relation is established between the zero-$T$ penetration depth $λ(0)$ and the slope of $λ^{-2}(T)$ near $T_c$, similar to Helfand-Werthamer's relation for $H_{c2}(0)$ and the slope of $H_{c2}(T)$ at $T_c$ for the isotropic s-wave case with non-magnetic scattering.\cite{HW} When the scattering parameter $ρ=\hbar v/2πT_c\ell$ ($v$ is the Fermi velocity and $\ell$ is the mean-free path) varies from 1 to 10, the coefficient of proportionality between $λ^{-2}(0)$ and $T_c (dλ^{-2}/dT)_{T_c}$ changes from 0.43 to 0.38. Combining this relation with the Rutgers thermodynamic identity, one can express $λ(0)$ in terms of the slope $(dH_{c2}/dT)_{T_c}$ and the density of states.

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arXiv2019

Elastic fields in superconductors caused by moving vortices

Strains in superconductors due to moving vortices and vortex lattices are discussed. It is shown that the energy stored in elastic strains increases with vortex velocity. For moving vortex lattices, the elastic energy depends on velocity orientation relative to the lattice having minimum for the velocity directed along one of the unit cell vectors of the moving lattice. It is shown that for supersonic motion, the vortex induced stress field has a shape similar to supersonic shock waves.

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