Abrikosov vortex contains magnetic field and circulating currents that decay at a short range $λ\sim 100$ nm. However, the vortex can induce a long range Josephson phase shift at distances $r\simμ$m$\ggλ$. The mechanism of this puzzling phenomenon is not clearly understood. Here we present a systematic study of vortex-induced phase shift in planar Josephson junctions. We make two key observations: (i) The cutoff effect: although vortex-induce phase shift is a long-range phenomenon, it is terminated by the junction and does not persists beyond it. (ii) A crossover from linear to superlinear dependence of the phase shift on the vortex polar angle occurs upon approaching of the vortex to the junction. The crossover occurs at a distance comparable with the penetration depth. This, together with theoretical and numerical analysis of the problem, allows unambiguous identification of two distinct and independent mechanisms. The short range mechanism is due to circulating vortex currents {\it inside} superconducting electrodes without involvement of magnetic field. The long range mechanism is due to stray magnetic fields {\it outside} electrodes without circulating vortex currents. We argue that understanding of controlling parameters of vortex-induced Josephson phase shift can be used for development of compact and fast electronic devices with low dissipation power.
From the point of view of time-dependent Ginzburg Landau (TDGL) theory, a Josephson-like relation is derived for an Abrikosov vortex lattice accelerated and deformed by applied fields. Beginning with a review of the Josephson Relation derived from the two ingredients of a lattice-kinematics assumption in TDGL theory and gauge invariance, we extend the construction to accommodate a time-dependent applied magnetic field, a floating-kernel formulation of normal current, and finally lattice deformation due to the electric field and inertial effects of vortex-lattice motion. The resulting Josephson…
We present a theoretical and experimental study of the Fiske resonances in the current-voltage characteristics of "small" Josephson junctions with randomly distributed misaligned Abrikosov vortices. We obtained that in the presence of Abrikosov vortices the resonant interaction of electromagnetic waves, excited inside a junction, with the ac Josephson current manifests itself by Fiske steps in a current-voltage characteristics even in the absence of external magnetic field. We found that the voltage positions of the Fiske steps are determined by a junction size, but the Fiske step magnitudes d…
Abrikosov vortex melting in high-temperature superconductors of ErBa2Cu3O7-δ system is investigated using mechanical contactless method of energy dissipation.
The electronic structure of a vortex line trapped by a planar defect in a type-II superconductor is analyzed within the Bogoliubov-de Gennes theory. The normal reflection of electrons and holes at the defect plane results in the topological transition in the spectrum and formation of a new type of quasiparticle states skipping or gliding along the defect. This topological transition appears to be a hallmark of the initial stage of the crossover from the Abrikosov to the Josephson vortex type revealing in the specific behavior of the quantized quasiparticle levels and density of states. The inc…
We report on dynamics of non-local Abrikosov vortex flow in mesoscopic superconducting Nb channels. Magnetic field dependence of the non-local voltage induced by the flux flow shows that vortices form ordered vortex chains. Voltage asymmetry (rectification) with respect to the direction of vortex flow is evidence that vortex jamming strongly moderates vortex dynamics in mesoscopic geometries. The findings can be applied to superconducting devices exploiting vortex dynamics and vortex manipulation, including superconducting wires with engineered pinning centers.
We formulate the time-dependent Ginzburg-Landau theory, with the assumption of local equilibrium made in the reference frame floating with normal electrons. This theory with floating nucleation kernel is applied to the far infrared (FIR) conductivity in the Abrikosov vortex lattice. It yields better agreement with recent experimental data [PRB {\bf 79}, 174525 (2009)] than the customary time-dependent Ginzburg-Landau theory.
We show that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has different parity with respect to frequency from that in the bulk if m is an odd number and has the same parity if m is an even number. As a result, in a conventional vortex with m=1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in even(odd)-frequency superconductor. We propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.
We show that low-angle grain boundaries (GB) in high-temperature superconductors exhibit intermediate Abrikosov vortices with Josephson cores, whose length $l$ along GB is smaller that the London penetration depth, but larger than the coherence length. We found an exact solution for a periodic vortex structure moving along GB in a magnetic field $H$ and calculated the flux flow resistivity $R_F(H)$, and the nonlinear voltage-current characteristics. The predicted $R_F(H)$ dependence describes well our experimental data on $7^{\circ}$ unirradiated and irradiated $YBa_2Cu_3O_7$ bicrystals, from …
Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a columnar defect with the characteristic size of the cross-section much smaller than the coherence length. We present an extension of the electrostatic analogies method, which proved to be useful for calculations of the pinning force for large cavities, to the case of small defects. The pinning potential for an elliptic cavity is derived analytically. Also, we determine the depinning current for a circular defect.
We examine the question of thermal melting of the triangular Abrikosov vortex solid in two-dimensional superconductors or neutral superfluids. We introduce a model, which combines lowest Landau level (LLL) projection with the magnetic Wannier basis to represent degenerate eigenstates in the LLL. Solving the model numerically via large-scale Monte Carlo simulations, we find clear evidence for a continuous melting transition, in perfect agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young theory and with recent experiments.
We consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg-Landau model. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet (D)-type and Gross-Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magn…
In superconductors penetrated by Abrikosov vortices the magnetic pressure and the inhomogeneous condensate density induce a deformation of the ionic lattice. We calculate how this deformation corrugates the surface of a semi-infinite sample. The effect of the surface dipole is included.
We establish the existence of topologically stable knot in two-gap superconductor whose topology $π_3(S^2)$ is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in Ginzburg-Landau theory of two-gap superconductor which has a non-vanishing condensate at the core, and identify the knot as a twisted magnetic vortex ring made of the helical vortex. We discuss how the knot can be constructed in the recent two-gap $\rm MgB_2$ superconductor.
At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadow-like region extending from the vortex to the boundary. This effect is stable for differ…
We study microscopic scenario of vortex escape from a columnar defect under the influence of a transport current. For defect radii smaller than the superconducting coherence length the depinning process is shown to be a consequence of two subsequent topological electronic transitions in a trapped vortex core. The first transition at a critical current $j_L$ is associated with the opening of Fermi surface segments corresponding to the creation of a vortex--antivortex pair bound to the defect. The second transition at a certain current $j_d > j_L$ is caused by merging of different Fermi surface …
Theory alternative to the vortex lattice melting theories is advertised. The vortex lattice melting theories are science fiction cond-mat/9811051 because the Abrikosov state is not the vortex lattice with crystalline long-range order. Since the fluctuation correction to the Abrikosov solution is infinite in the thermodynamic limit (K.Maki and H.Takayama, 1972) any fluctuation theory of the mixed state should consider a superconductor with finite sizes. Such nonperturbative theory for the easiest case of two-dimensional superconductor in the lowest Landau level approximation is presented in thi…
The manipulation and control of vortex states in superconducting systems are of great interest in view of possible applications, for which mesoscopic materials are good candidates. In this work, we studied the annihilation dynamics and the dissipative aspects of an Abrikosov's vortex-antivortex pair in a mesoscopic superconducting system with a concentric hole. The generalized time-dependent Ginzburg-Landau equations were numerically solved. The main result is the appearance of a phase slip-like line due to the elongation of the vortex and antivortex cores. Under specific circumstances, therma…
We explore the possibility of using the inhomogeneous magnetic field carried by an Abrikosov vortex in a type-II superconductor to localize spin-polarized textures in a nearby magnetic semiconductor quantum well. We show how Zeeman-induced localization induced by a single vortex is indeed possible, and use these results to investigate the effect of a periodic vortex array on the transport properties of the magnetic semiconductor. In particular, we find an unconventional Integer Quantum Hall regime, and predict directly testable experimental consequences due to the presence of the periodic spin…
We study the subgap spectrum of a 2D Abrikosov vortex in an s-wave superconductor in the absence and presence of a point impurity. By solving the Eilenberger equations without impurity for two models of the vortex (including a self-consistent one), we find multiple subgap spectral branches. The number of these branches may be arbitrary large provided that the magnetic field screening length is large enough. The quasiclassical spectrum of the vortex has a local gap with a width of the order of the bulk gap and a spatial extent of several coherence lengths. The existence of such gap is the prere…
Observation of individual vortex penetration in a coplanar superconducting resonator
The University of Tokyo（东京大学）；University of Connecticut（康涅狄格大学）；University of Arizona（亚利桑那大学）；Institute of Science Tokyo（东京科学大学）；National Institute for Materials Science（物质材料研究机构）
Mass of Abrikosov vortices defied experimental observation for more than four decades. We demonstrate a method of its detection in high-temperature superconductors. Similarly to electrons, fluxons circulate in the direction given by the magnetic field, causing circular dichroism. We report the magneto-transmittance of a nearly optimally doped thin YBaCuO film, measured using circularly polarized submillimeter waves. The circular dichroism emerges in the superconducting state and increases with dropping temperature. Our results confirm the dominant role of quasiparticle states in the vortex cor…
The dynamical response of the Abrikosov vortex lattice in the presence of an oscillating driving field is calculated by constructing an analytical solution of the time-dependent Ginzburg-Landau equation. The solution is steady-state, and work done by the input signal is dissipated through vortex cores, mainly by scattering with phonons. The response is nonlinear in the input signal, and is verified for consistency within the theory. The existence of well-defined parameters to control nonlinear effects is important for any practical application in electronics, and a normalised distance from the…
Within the framework of the time-dependent Ginzburg-Landau theory we show that circularly polarized THz or far-infrared radiation induces a dc supercurrent that influences the dynamics of vortex-antivortex pair formation in a mesoscopic superconductor undergoing rapid thermal quenching. The Lorentz force arising from the supercurrents promotes vortex-antivortex separation and allows survival of the vortex polarity defined by the helicity of light. Based on this idea, we propose a two-stage irradiation scheme that provides a powerful method for controlled all-optical generation of Abrikosov vor…
We calculate the local density of states of a vortex in a two-dimensional s-wave superconductor, in the presence of a uniform applied supercurrent. The supercurrent induces changes in the electronic structure for the isolated vortex as well as the vortex lattice, which agree with the recent measurements in 2H-NbSe2 [Maldonado et al., Phys. Rev. B 88, 064518 (2013)]. We find that the supercurrent polarizes the core states when the vortices are pinned. This shows that the transfer of momentum from the supercurrent to the bound states and the rigidity of the wave functions must be considered for …
We study the impact of the non-analytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure). Similar instability may be also observable in clean superconducting films.
Abrikosov vortex lattice dynamics in a superconductor with weak defects is studied taking into account gyroscopic (Hall) properties. It is demonstrated that interaction of the moving lattice with weak defects results in appearance of the additional drag force, $F$, which is $F(V)\propto \sqrt V$ at small velocities, while at high velocities $F(V)\propto 1/\sqrt V$. Thus, the total drag force can be a nonmonotonic function of the lattice translational velocity. It leads to the velocity dependence of the Hall angle and a nonlinear current-voltage characteristic of the superconductor. Due to the …
We report theoretical and experimental work on the development of a Josephson vortex qubit based on a confocal annular Josephson tunnel junction (CAJTJ). The key ingredient of this geometrical configuration is a periodically variable width that generates a spatial vortex potential with bistable states. This intrinsic vortex potential can be tuned by an externally applied magnetic field and tilted by a bias current. The two-state system is accurately modeled by a one-dimensional sine-Gordon like equation by means of which one can numerically calculate both the magnetic field needed to set the v…
We study the spatial distribution of supercurrent circulated around an Abrikosov vortex in an SF bilayer in perpendicular magnetic field. Within the dirty limit regime and circular cell approximation for the vortex lattice, we derive the conditions when the Usadel equations the F layer can be solved analytically. Using the obtained solutions, we demonstrate the possibility of reversal of direction of proximity induced supercurrents around the vortex in the F layer compared to that in the S-layer. The direction of currents can be controlled either by varying transparency of the SF interface or …
Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50 ξ). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ~ 230 vor…
We show that periodic lattice of Abrikosov vortices in chiral $p$ wave superconductor in general supports fermionic states with zero energy provided the intervortex distance is smaller than the critical one. The zero modes appear at the intersection with the Fermi level of electronic magnetic Bloch bands formed by the overlapping vortex core states. The Bloch bands are robust against lattice disorder induced by fluctuations of vortex positions and can transmit the energy flow across the lattice. The hallmark of zero modes on Bloch bands in electronic heat conductivity is discussed.
A quantum-mechanical model for the interaction of Josephson vortices (fluxons) embedded in superconducting transmission line is presented. The vortices interact through emission and absorption of linear waves (electromagnetic cavity modes). We show that in a classical regime this peculiar type of interaction is determined by the product of instantaneous velocities of fluxons. In a quantum regime, this property provides tunable coupling between vortices which can be used for entanglement of vortex qubits. The physical mechanism of the vortex interaction is similar to that proposed for qubits ba…
Five years ago the talk "The vortex lattice melting theory as example of science fiction" cond-mat/9811051 was presented. Nevertheless this theory predominates up to now and very many people devote oneself to it. It is explained in the present paper why the only first order phase transition observed on the way from the Abrikosov state in the normal state should be interpreted as phase coherence disappearance. The false concept of vortex lattice melting appeared because of some causes main of them are erroneous interpretation of direct observation of the Abrikosov state and the use by theorists…
We show that the strain-induced attraction between Abrikosov vortices has a non-core contribution overlooked up until now. This contribution is an example of the universal mechanism of soliton attraction in solids revealed in [Phys. Rev. B {\bf 66}, 14111 (2002)]. The resulting interaction energy is larger than that due to the vortex cores at least by a factor $\ln ^2 κ$. Consequently, the non-core contribution must be included, for instance, in discussions about the orientation of vortex lattices with respect to the crystal axes. It is shown to be also important when interpreting the thermal …
Many practical applications of high T$_c$ superconductors involve layered materials and magnetic fields applied on an arbitrary direction with respect to the layers. When the anisotropy is very large, Cooper pair currents can circulate either within or perpendicular to the layers. Thus, tilted magnetic fields lead to intertwined lattices of Josephson and Abrikosov vortices, with quantized circulation across and within layers, respectively. Transport in such intertwined lattices has been studied in detail, but direct observation and manipulation of vortices remains challenging. Here we present …
The resistive properties of thin amorphous NbO_{x} films with weak pinning were investigated experimentally above and below the second critical field H_{c2}. As opposed to bulk type II superconductors with weak pinning where a sharp change of resistive properties at the transition into the Abrikosov state is observed at H_{c4}, some percent below H_{c2} (V.A.Marchenko and A.V.Nikulov, 1981), no qualitative change of resistive properties is observed down to a very low magnetic field, H_{c4} < 0.006 H_{c2}, in thin films with weak pinning. The smooth dependencies of the resistivity observed in t…
Vortex lattices, arising from repulsive inter-vortex interactions, are a canonical example of emergent phenomena. Recent studies on the cuprates have drawn attention to the appearance of competing correlations within vortex cores. This gives internal structure to each vortex and changes the nature of inter-vortex interactions, especially at short range. This can have significant consequences for vortex lattices wherein vortices are in close proximity to one another. We consider the attractive Hubbard model, a prototypical model for phase competition, with checkerboard charge density wave order…
We study the instability of the superconducting state in a mesoscopic geometry for the low pinning material Mo$_3$Ge characterized by a large Ginzburg-Landau parameter. We observe that in the current driven switching to the normal state from a nonlinear region of the Abrikosov flux flow, the mean critical vortex velocity reaches a limiting maximum velocity as a function of the applied magnetic field. Based on time dependent Ginzburg-Landau simulations we argue that the observed behavior is due to the high velocity vortex dynamics confined on a mesoscopic scale. We build up a general phase diag…
Using low-temperature Magnetic Force Microscopy (MFM) we provide direct experimental evidence for spontaneous vortex phase (SVP) formation in EuFe$_2$(As$_{0.79}$P$_{0.21}$)$_2$ single crystal with the superconducting $T^{\rm 0}_{\rm SC}=23.6$~K and ferromagnetic $T_{\rm FM}\sim17.7$~K transition temperatures. Spontaneous vortex-antivortex (V-AV) pairs are imaged in the vicinity of $T_{\rm FM}$. Also, upon cooling cycle near $T_{\rm FM}$ we observe the first-order transition from the short period domain structure, which appears in the Meissner state, into the long period domain structure with …
It is argued that only a single spontaneous long-range order, namely the phase coherence exists in the Abrikosov state, and the prediction of the crystalline long-range order of vortex lattice does not correspond to the facts.
In systems combining type-II superconductivity and magnetism the non-stationary magnetic field of moving Abrikosov vortices may excite spin waves, or magnons. This effect leads to the appearance of an additional damping force acting on the vortices. By solving the London and Landau-Lifshitz-Gilbert equations we calculate the magnetic moment induced force acting on vortices in ferromagnetic superconductors and superconductor/ferromagnet superlattices. If the vortices are driven by a dc force, magnon generation due to the Cherenkov resonance starts as the vortex velocity exceeds some threshold v…
We confirmed the existence of the collective transverse plasma modes excited by the motion of the Josephson vortex lattice in stacked intrinsic Josephson junctions of Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ by observing the multiple subbranches in the Josephson-vortex-flow current-voltage characteristics. We also observed the symptom of the microwave emission from the resonance between the Josephson vortex lattice and the collective transverse plasma modes, which provides the possibility of developing Josephson-vortex-flow electromagnetic oscillators.
We report the experimental confirmation of the collective transverse plasma modes excited by the Josephson vortex lattice in stacks of intrinsic Josephson junctions in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ single crystals. The excitation was confirmed by analyzing the temperature ($T$) and magnetic field ($H$) dependencies of the multiple sub-branches in the Josephson-vortex-flow region of the current-voltage characteristics of the system. In the near-static Josephson vortex state for a low tunneling bias current, pronounced magnetoresistance oscillations were observed, which represented a trian…
Abrikosov fluxonics, a domain of science and engineering at the interface of superconductivity research and nanotechnology, is concerned with the study of properties and dynamics of Abrikosov vortices in nanopatterned superconductors, with particular focus on their confinement, manipulation, and exploitation for emerging functionalities. Vortex pinning, guided vortex motion, and the ratchet effect are three main fluxonic ``tools'' which allow for the dynamical (pinned or moving), the directional (angle-dependent), and the orientational (current polarity-sensitive) control over the fluxons, res…
We theoretically study Josephson vortex structures in Josephson junctions which have multiple tunneling channels caused by multiple superconducting gaps. Deriving "coupled sine-Gordon equations" from the free-energy taking account of the multiple tunneling channels, we examine two typical situations, a heterotic junction composed of multigap-superconductor, insulator, and single-gap superconductor, and a grain-boundary junction formed by two identical multigap superconductors. Then, we reveal in both situations that the magnetic field distribution of the Josephson vortex for $\pm s$-wave super…
The Josephson-plasma and vortex modes in layered superconductors have been studied theoretically for low magnetic fields parallel and perpendicular to layers. The two modes belong to the same lowest-frequency branch of collective-mode spectrum localized near vortices. This is the Josephson-plasma resonance if pancakes are strongly pinned and cannot move. Otherwise the lowest-frequency mode is a vortex mode governed by pancake pinning and the vortex mass. The latter is strongly enhanced by wandering of a vortex line around its average direction. The recently observed jump of the magnetoabsorpti…
The voltage shift RfIc with respect to the flux flow ohmic behavior of the current-voltage characteristic in type II superconductors is ascribed to the irreversible processes occurring when a vortex crosses defects. We include irreversible effects of the vortices-defects interaction into an effective law of motion. The obtained current-voltage characteristic at finite temperature is in agreement with experimental data.
The Josephson vortex formed in a superconductor-insulator-superconductor (SIS) junction can affect the quantum mechanics of quasiparticles by creating an effective adiabatic potential determined by the inhomogeneous distribution of the phase difference of the order parameter along the junction. Starting from the quasiclassical version of the Bogoliubov-de Gennes (BdG) theory, we found the quasiparticle spectrum and the local density of states (DOS) both for the isolated Josephson vortex and the vortex chain. The spatially resolved DOS reveals a peculiar two-peak structure for each Josephson vo…
Equidistant resonance jumps in superconducting coplanar resonators driven by Abrikosov vortices
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Physics of Microstructures, Russian Academy of Sciences（俄罗斯科学院微结构物理研究所）；Dukhov Research Institute of Automatics (VNIIA)（杜霍夫自动仪器科学研究院）
We present an analysis of the magnetic field distribution in the Abrikosov lattice of high-$κ$ superconductors with singlet pairing in the case where the critical field is mainly determined by the Pauli limit and the superfluid currents partly come from the paramagnetic interaction of electron spins with the local magnetic field. The derivation is performed in the frame of the generalized Clem variational method which is valid not too close to the critical field and furthermore with the Abrikosov type theory in the vicinity of it. The found vortex lattice form factor increases with increasing …
We present experimental evidence for a new behavior which involves discrete breathers and vortices in a Josephson Ladder. Breathers can be visualized as the creation and subsequent annihilation of vortex/anti-vortex pairs. An externally applied magnetic field breaks the vortex/anti-vortex symmetry and causes the breather to split apart. The motion of the vortex or anti-vortex creates multi-site breathers, which are always to one side or the other of the original breather depending on the sign of the applied field. This asymmetry in applied field is experimentally observed.
