A detailed theoretical interpretation of the Josephson interference experiment between Sr$_2$RuO$_4$ and Pb reported by Kidwingira \textit{et al} is given. Assuming chiral p-wave pairing symmetry a Ginzburg-Landau theory is derived in order to investigate the structure of domain walls between chiral domains. It turns out that anisotropy effects of the Fermi surface and the orientation of the domain walls are essential for their internal structure. Introducing a simple model for a Josephson junction the effect of domain walls intersecting the interface between Sr$_2$RuO$_4$ and Pb is discussed. It is shown that characteristic deviations of the Fraunhofer interference pattern for the critical Josephson current as a function of the magnetic field occurs in qualitative agreement with the experimental finding. Moreover the model is able also to account for peculiar hysteresis effects observed in the experiment.
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and…
Eutectic Sr$_2$RuO$_4$-Ru samples with $μ$m-sized Ru-metal inclusions support inhomogeneous superconductivity above the bulk transition of Sr$_2$RuO$_4$ in the so-called 3-Kelvin phase. In Pb/Ru/Sr$_2$RuO$_4$ Josephson junctions as realized by Maeno et al., a Pb film is indirectly coupled to the superconductor Sr$_2$RuO$_4$ mediated by the proximity-induced superconducting Ru-inclusions, yielding an extended Josephson contact through the interface between Ru and Sr$_2$RuO$_4$. Motivated by this experimental setup, we formulate a sine-Gordon model for the Josephson phase of the interface, assum…
Clarifying the chiral domains structure of superconducting Sr$_{2}$RuO$_{4}$ has been a long-standing issue in identifying its peculiar topological superconducting state. We evaluated the critical current $I_{c}$ versus the magnetic field $H$ of Nb/Sr$_{2}$RuO$_{4}$ Josephson junctions, changing the junction dimension in expectation of that the number of domains in the junction is controlled. $I_{c}(H)$ exhibits a recovery from inversion symmetry breaking to invariance when the dimension is reduced to several microns. This inversion invariant behavior indicates the disappearance of domain wall…
The critical current modulation and the spontaneous flux of the vortex states in corner Josephson junctions between Sr$_2$RuO$_4$ and a conventional s-wave superconductor are calculated as a function of the crystal orientation, and the magnetic field. For Sr$_2$RuO$_4$ we assume two nodeless p-wave pairing states. Also we use the nodal $f$-wave states $B_{1g}\times E_u$ and $B_{2g} \times E_u$, and one special p-wave state having line nodes. It is seen that the critical current depends solely on the topology of the gap.
Superconductivity in Sr$_{2}$RuO$_{4}$ is unconventional, believed to be of $p_{x}\pm ip_{y}$ pairing symmetry. These two degenerate order parameters allow the formation of chiral domains separated by domain walls. In a Josephson junction formed on the edge of a single crystal of Sr$_{2}$RuO$_{4}$, the chiral domains can create a variation of the phase in the tunneling direction causing interference effects which suppress and modulate the critical current of the junction. Cooling the junction in a magnetic field lifts the degeneracy between the order parameter states and induces a preferential…
The superconducting state of Sr$_2$RuO$_4$ was once thought to be a leading candidate for $p$-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a $π$ phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are described by $p$-wave states. However, with recent experiments observing a significant decrease in the Knight shift below the transition temperature, signifying a spin-singlet state, the odd-parity results are left to be reconciled. In this work, we show tha…
We study Josephson current between s-wave/spin-triplet superconductor junctions by taking into account details of band structures in Sr$_{2}$RuO$_{4}$ such as three conduction bands, spin-orbit interaction in the bulk and that at the interface. We assume five superconducting order parameters in Sr$_{2}$RuO$_{4}$: a chiral p-wave symmetry and four helical p-wave symmetries. We calculate current-phase relationship $I(φ)$ in these junctions, where $φ$ is the macroscopic phase difference between two superconductors. The results for a chiral p-wave pairing symmetry show that $\cos(φ)$ term appears …
The chiral p-wave order parameter in Sr$_\mathsf{2}$RuO$_\mathsf{4}$ would make it a special case amongst the unconventional superconductors. A consequence of this symmetry is the possible existence of superconducting domains of opposite chirality. At the boundary of such domains, the locally supressed condensate can produce an intrinsic Josephson junction. Here, we provide evidence of such junctions using mesoscopic rings, structured from Sr$_\mathsf{2}$RuO$_\mathsf{4}$ single crystals. Our order parameter simulations predict such rings to host stable domain walls across their arms. Thisis ve…
It is widely believed that the perovskite Sr$_2$RuO$_4$ is an unconventional superconductor with broken time reversal symmetry. It has been predicted that superconductors with broken time reversal symmetry should have spontaneously generated supercurrents at edges and domain walls. We have done careful imaging of the magnetic fields above Sr$_2$RuO$_4$ single crystals using scanning Hall bar and SQUID microscopies, and see no evidence for such spontaneously generated supercurrents. We use the results from our magnetic imaging to place upper limits on the spontaneously generated supercurrents a…
We present direct imaging of magnetic flux structures in the anisotropic, spin-triplet superconductor Sr$_{2}$RuO$_{4}$ using a scanning $μ$SQUID microscope. Individual quantized vortices were seen at low magnetic fields. Coalescing vortices forming flux domains were revealed at intermediate fields. Based on our observations we suggest that a mechanism intrinsic to the material stabilizes the flux domains against the repulsive vortex-vortex interaction. Topological defects like domain walls can provide this, implying proof for unconventional chiral superconductivity.
We have studied the Josephson coupling between a conventional s-wave superconductor (In) and Sr2RuO4 and found that the coupling is allowed in the in-plane direction, but not along the c axis. This selection rule indicates that the symmetry of superconducting order parameter of Sr2RuO4 is either p- or alternatively, purely d-wave. If Sr2RuO4 is a p-wave superconductor, as strongly favored by other experimental evidence, our result suggests that the pairing state of Sr2RuO4 is Gamma5 with d(k) = z(kx +/- iky), a nodeless state in which the spins of the superconducting electrons lie in the RuO2 …
We present scanning SQUID microscopy data on the superconductors Sr2RuO4 (Tc = 1.5 K) and PrOs$_4$Sb$_{12}$ (Tc = 1.8 K). In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However in neither Sr$_2$RuO$_4$ nor PrOs$_4$Sb$_{12}$ do we observe spontaneous superconductivity-related magnetization. In Sr$_2$RuO$_4$, many experimental results have been interpreted on the basis of a $px \pm ipy$ superconducting order parameter. This order parameter is expected to…
We have measured interlayer current transport in small sized RuSr2GdCu2O8 single crystals. We find a clear intrinsic Josephson effect showing that the material acts as a natural superconductor-insulator-ferromagnet-insulator-superconductor superlattice. So far, we detected no unconventional behavior due to the magnetism of the RuO2 layers.
We describe resistive states of the system combining two types of orderings - superconducting and ferromagnetic one. It is shown that in the presence of magnetization dynamics such systems become inherently dissipative and in principle cannot sustain any amount of the superconducting current because of the voltage generated by the magnetization dynamics. We calculate generic current-voltage characteristics of a superconductor/ferromagnet/superconductor Josephson junction with an unpinned domain wall and find the low-current resistance associated with the domain wall motion. We suggest the fini…
A stationary Josephson effect in point contacts between triplet superconductors is analyzed theoretically for most probable models of the order parameter in UPt_{3} and Sr_{2}RuO_{4}. The consequence of misorientation of crystals in superconducting banks on this effect is considered. We show that different models for the order parameter lead to quite different current-phase dependences. For certain angles of misorientation a boundary between superconductors can generate the parallel to surface spontaneous current. In a number of cases the state with a zero Josephson current and minimum of the …
The Josephson current between an s-wave and a spin-triplet superconductor Sr$_2$RuO$_4$ (SRO) is studied theoretically. In spin-singlet / spin-triplet superconductor junctions, there is no Josephson current proportional to $\sin ϕ$ in the absence of the spin-flip scattering near junction interfaces, where $ϕ$ is a phase-difference across junctions. Thus a dominant term of the Josephson current is proportional to $\sin 2ϕ$ . The spin-orbit scattering at the interfaces gives rise to the Josephson current proportional to $\cosϕ$, which is a direct consequence of the chiral paring symmetry in SRO.
Exotic superconducting properties of Sr$_{2}$RuO$_{4}$ have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of Sr$_{2}$RuO$_{4}$ and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet p…
Single crystals of the Sr$_2$RuO$_4$-Ru eutectic system are known to exhibit enhanced superconductivity at 3~K, in addition to the bulk superconductivity of Sr$_2$RuO$_4$ at 1.5~K. The 1.5-K phase is believed to be a spin-triplet, chiral $p$-wave state with the multi-component order parameter, giving rise to chiral domain structure. In contrast, the 3-K phase is attributable to enhanced superconductivity of Sr$_2$RuO$_4$ in the strained interface region between Ru inclusion of a few to tens of micrometers in size and the surrounding Sr$_2$RuO$_4$. We investigate the dynamic behavior of a topol…
We consider s-wave pairing in a double layer of two chiral metals due to Coulomb interaction, and study the Josephson effect near a domain wall, where the sign of the order parameter jumps. The domain wall creates two zero energy modes, whose superposition is associated with a current that flows in different direction in the two layers. Assuming a toroidal geometry, the effective Josephson currents winds around the domain walls, whose winding number is determined by the coefficients of the superimposed zero energy modes. This result can be understood as a competition of the conventional Joseph…
Domain walls in a tetragonal chiral p-wave superconductors with broken time reversal symmetry are analyzed in the framework of the Ginsburg-Landau theory. The energy and the jump of the magnetic induction on the wall were determined for different types of walls as functions of the parameters of the Ginzburg-Landau theory and orientation of the domain wall with respect to the crystallographic axes. We discuss implications of the analysis for $Sr_{2}RuO_{4}$, where no stray magnetic fields from domain walls were detected experimentally.
It is identified numerically that the resistivity of a fully-frustrated Josephson-junction array is due to motion of domain walls in vortex lattice rather than to motion of single vortices.
The Josephson effect is theoretically studied in two types of SQUIDs consisting of $s$ wave superconductor and Sr$_2$RuO$_4$. Results show various response of the critical Josephson current to applied magnetic fields depending on the type of SQUID and on the pairing symmetries. In the case of a $p_x+ip_y$ wave symmetry, the critical current in a corner SQUID becomes an asymmetric function of magnetic fields near the critical temperatures. Our results well explain a recent experimental finding [Nelson et. al, Science \textbf{306}, 1151 (2004)]. We also discuss effects of chiral domains on the c…
Supposing the spin-triplet superconducting state of Sr$_2$RuO$_4$, the spin-orbit (SO) coupling associated with relative motion in Cooper pairs is calculated by extending the method for the dipole-dipole coupling given by Leggett in the superfluid $^{3}$He. It is shown that the SO coupling works only in the equal-spin pairing (ESP) state to make the pair angular momentum $\hbar{\vec L}$ and the pair spin angular momentum ${\rm i}{\vec d}\times{\vec d}^{*}$ parallel with each other. The SO coupling gives rise to the internal Josephson effect in a chiral ESP state as in superfluid A-phase of $^3…
We study theoretically the properties of SIFS type Josephson junctions composed of two superconducting (S) electrodes separated by an insulating layer (I) and a ferromagnetic (F) film consisting of periodic magnetic domains structure with antiparallel magnetization directions in neighboring domains. The two-dimensional problem in the weak link area is solved analytically in the framework of the linearized quasiclassical Usadel equations. Based on this solution, the spatial distributions of the critical current density, $J_{C},$ in the domains and critical current, $I_{C},$ of SIFS structures a…
We analyze the presence of non-reciprocal critical currents, the so-called superconducting diode effect, in chiral superconductors within a generalized Ginzburg-Landau framework. After deriving its key symmetry conditions we illustrate the basic mechanism for two examples, the critical current in a thin film and a Josephson junction. The appearance of spontaneous edge currents and the energy bias for the formation of Josephson vortices play an essential part in establishing a splitting of the critical currents running in opposite directions. Eventually, this allows us to interpret a supercondu…
Recent experiments suggest that the superconducting order parameter of Sr$_2$RuO$_4$ has two components. A two-component order parameter has multiple degrees of freedom in the superconducting state that can result in low-energy collective modes or the formation of domain walls -- a possibility that would explain a number of experimental observations including the smallness of the time reversal symmetry breaking signal at T$_\mathrm{c}$ and telegraph noise in critical current experiments. We perform ultrasound attenuation measurements across the superconducting transition of Sr$_2$RuO$_4$ using…
Considering s-wave pairing in an electron-hole double layer of two chiral metals, we study the Josephson effect generated by a domain wall. The latter, which is caused by a jump of the order parameter phase, creates two independent evanescent zero-energy modes at an exceptional point. A unique solution is found by coupling the quasiparticle currents to the supercurrents via the continuity equation. This leads to a superposition of the zero-energy modes, where the relative phases of the coefficients are linked to the direction of the macroscopic supercurrents. Assuming a toroidal geometry, the …
Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（材料与固体物理中心（CSIC-巴斯克国立大学混合中心））；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
We theoretically propose a principle for precise measurement of oscillatory domain wall (DW) by a ferromagnetic Josephson junction, which is composed of a ferromagnetic wire with DW and two superconducting electrodes. The current-voltage curve exhibits stepwise structures, only when DW oscillates in the ferromagnetic wire. The voltage step appears at V = n(\hbar/2e)ω_DW with the fundamental constant \hbar/e, integer number n, and the DW frequency ω_DW. Since V can be determined in the order of 10^9 accuracy, the oscillatory DW will be measured more precisely than present status by conventional…
A Josephson junction is made of two superconductors sandwiching an insulator, and a Josephson vortex is a magnetic vortex (flux tube) absorbed into the Josephson junction, whose dynamics can be described by the sine-Gordon equation. In a field theory framework, a flexible Josephson junction was proposed, in which the Josephson junction is represented by a domain wall separating two condensations and a Josephson vortex is a sine-Gordon soliton in the domain wall effective theory. In this paper, we propose a Josephson junction of non-Abelian color superconductors, that is described by a non-Abel…
Multi-layered Josephson junctions are modeled in the context of a field theory, and dynamics of Josephson vortices trapped inside insulators are studied. Starting from a theory consisting of complex and real scalar fields coupled to a U(1) gauge field which admit parallel $N-1$ domain-wall solutions, Josephson couplings are introduced weakly between the complex scalar fields. The $N-1$ domain walls behave as insulators separating $N$ superconductors, where one of the complex scalar fields has a gap. We construct the effective Lagrangian on the domain walls, which reduces to a coupled sine-Gord…
The order parameter of superconducting pairs penetrating an inhomogeneous magnetic material can acquire a long range triplet component (LRTC) with non-zero spin projection. This state has been predicted and generated recently in proximity systems and Josephson junctions. We show using an analytically derived domain wall of an exchange spring how the LRTC emerges and can be tuned with the twisting of the magnetization. We also introduce a new kind of Josephson current reversal, the triplet $0-π$ transition, that can be observed in one and the same system either by tuning the domain wall or by v…
We investigate macroscopic behaviors of fluctuating domain walls in nonequilibrium open systems with the help of the effective field theory based on symmetry. Since the domain wall in open systems breaks the translational symmetry, there appears a gapless excitation identified as the Nambu-Goldstone (NG) mode, which shows the non-propagating diffusive behavior in contrast to those in closed systems. After demonstrating the presence of the diffusive NG mode in the $(2+1)$-dimensional dissipative Josephson junction, we provide a symmetry-based general analysis for open systems breaking the one-d…
A magnetic domain wall (DW) behaves as a massive particle with elasticity. Sliding and oscillation of the DW have been observed experimentally, whereas vibration of a width in the DW, "breathing mode", has not been measured so far. We theoretically propose how to observe the breathing mode by the Josephson junction having a ferromagnetic layer between superconducting electrodes. The current-voltage (I-V) curve is calculated by an equivalent circuit of the resistively shunted junction model. The breathing mode is identified by stepwise structures in the I-V curve, which appear at the voltages V…
We consider a SFS Josephson junction made of two superconductors S and a multidomain ferromagnet F with an in-plane magnetization. We assume that the neighboring domains of the ferromagnet are separated by Neel domain walls. An odd-frequency triplet long-range component of superconducting correlations arises in the domain walls and spreads into the domains over a long distance of the order $ξ_T = \sqrt{D / 2 πT}$, where $D$ is the diffusion coefficient (dirty limit is implied). We calculate the contribution of this component to the Josephson current in the situation when conventional short-ran…
We have contacted single wall carbon nanotubes grown by chemical vapor deposition to superconducting Ti/Al/Ti electrodes. The device, we here report on is in the Kondo regime exhibiting a four-fold shell structure, where a clear signature of the superconducting electrodes is observed below the critical temperature. Multiple Andreev reflections are revealed by sub-gap structure and a narrow peak in the differential conductance around zero bias is seen depending on the shell filling. We interpret the peak as a proximity induced supercurrent and examine its interplay with Kondo resonances.
Chiral superconductors are two-fold degenerate and domains of opposite chirality can form, separated by domain walls. There are indications of such domain formation in the quasi two-dimensional putative chiral $p$-wave superconductor Sr$_2$RuO$_4$, yet no experiment has explicitly resolved individual domains in this material. In this work, $c$-axis domain walls lying parallel to the layers in chiral $p$-wave superconductors are explored from a theoretical point of view. First, using both a phenomenological Ginzburg-Landau and a quasiclassical Bogoliubov-deGennes approach, a consistent qualitat…
We present experimental results on a Josephson parametric amplifier tailored for readout of ultra-sensitive thermal microwave detectors. In particular, we discuss the impact of fabrication details on the performance. We show that the small volume of deposited dielectric materials enabled by the side-wall passivated spacer niobium junction technology leads to robust operation across a wide range of operating temperatures up to 1.5 K. The flux-pumped amplifier has gain in excess of 20 dB in three-wave mixing and its center frequency is tunable between 540 MHz and 640 MHz. At 600 MHz, the amplifi…
We study theoretically the impact of an applied DC-current on a mesoscopic chiral $p$-wave superconductor. Performing quasiclassical calculations on a two-dimensional system, with an external magnetic flux to generate a DC current, we show that the current can trigger a transition to a state with a domain wall between regions of different chiralities. The system shows an hysteretic behavior, as different domain wall configurations are possible for a given current. This domain wall creation mechanism can give new insights on recent experiments observing anomalous current variations in Sr${}_2$R…
We present a structure and a fabrication method for superconducting tunnel junctions down to the dimensions of 200 nm using i-line UV lithography. The key element is a side-wall-passivating spacer structure (SWAPS) which is shaped for smooth crossline contacting and low parasitic capacitance. The SWAPS structure enables formation of junctions with dimensions at or below the lithography-limited linewidth. An additional benefit is avoiding the excessive use of amorphous dielectric materials which is favorable in sub-Kelvin microwave applications often plagued by nonlinear and lossy dielectrics. …
We study chiral interface Andreev bound states and their influence on the Josephson current between clean superconductors. Possible examples are superconducting Sr2RuO4 and the B-phase of the heavy-fermion superconductor UPt3. We show that, under certain conditions, the low-energy chiral surface states enhance the critical current of symmetric tunnel junctions at low temperatures. The enhancement is substantially more pronounced in quantum point contacts. In classical junctions dispersive chiral states result in a logarithmic dependence of the critical current. This logarithmic behavior contai…
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 nonze…
Exotic superconductors, such as high T$_C$, topological, and heavy-fermion superconductors, require phase sensitive measurements to determine the underlying pairing. Here we investigate the proximity-induced superconductivity in nanowires of SnTe, where an $s\pm is^{\prime}$ superconducting state is produced that lacks the time-reversal and valley-exchange symmetry of the parent SnTe. This effect, in conjunction with a ferroelectric distortion of the lattice at low temperatures, results in a marked alteration of the properties of Josephson junctions fabricated using SnTe nanowires. This work e…
Transport measurements are carried out on dice Josephson-junction arrays with the frustration index $f=1/3$ and 1/2 which possess, within the limit of the $XY$ model, an accidental degeneracy of the ground states as a consequence of the formation of zero-energy domain walls. The measurements demonstrate that both the systems undergo a phase transition to a superconducting vortex-ordered state at considerably high temperatures. The experimental findings are in apparent contradiction with the theoretical expectation that frustration effects in the $f=1/3$ system are particularly strong enough to…
We investigate the influence of domain walls on the vortex dynamics in superconductors with multi-component order parameters. We show that, due to their complex structure domain walls can carry vortices with fractional flux quanta. The decay of conventional vortices into fractional ones on domain walls is examined. This decay presents an extraordinarily strong pinning mechanism for vortices and turns domain walls occupied with pinned fractional vortices into efficient barriers for the vortex motion. Therefore, domain walls can act as fences for the flux flow, preventing the decay of the remnan…
It has been proposed that the superconductivity of Sr$_2$RuO$_4$ is characterized by pairing that is unconventional and, furthermore, spontaneously breaks time-reversal symmetry. However, one of the key expected consequences, viz., that the ground state should exhibit chiral charge currents localized near the boundaries of the sample, has not been observed, to date. We explore an alternative implication of time-reversal symmetry breaking: the existence of walls between domains of opposing chirality. Via a general phenomenological approach, we derive an effective description of the superconduct…
We investigate several factors controlling the physics of hybrid structures involving ferromagnetic domain walls (DWs) and superconducting (S) metals. We discuss the role of non collinear magnetizations in S/DW junctions in a spin $\otimes$ Nambu $\otimes$ Keldysh formalism. We discuss transport in S/DW/N and S/DW/S junctions in the presence of inelastic scattering in the domain wall. In this case transport properties are similar for the S/DW/S and S/DW/N junctions and are controlled by sequential tunneling of spatially separated Cooper pairs across the domain wall. In the absence of inelastic…
The recent experimental demonstration of spin-polarized supercurrents offer a venue for establishment of a superconducting analogue to conventional spintronics. Whereas domain wall motion in purely magnetic structures is a well-studied topic, it is not clear how domain wall dynamics may influence superconductivity and if some functional property can be harnessed from such a scenario. Here, we demonstrate that domain wall motion in superconducting systems offers a unique way of controlling the quantum state of the superconductor. Considering both the diffusive and ballistic limits, we show that…
We study theoretically the dc Josephson effect between two volumes of superfluid 3He-B. We first discuss how the calculation of the current-phase relationships is divided into a mesoscopic and a macroscopic problem. We then analyze mass and spin currents and the symmetry of weak links. In quantitative calculations the weak link is assumed to be a pinhole, whose size is small in comparison to the coherence length. We derive a quasiclassical expression for the coupling energy of a pinhole, allowing also for scattering in the hole. Using a selfconsistent order parameter near a wall, we calculate …
We study a diffusive superconductor--ferromagnet--superconductor (SFS) junction with in-plane ferromagnetic domains. Close to the superconducting transition temperature, we describe the proximity effect in the junction with the linearized Usadel equations. We find that properties of such a junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the $π$ state, similarly to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is alwa…
We study the thermodynamic properties of a dirty ferromagnetic S$\mid$F$\mid$S Josephson junction with s-wave superconducting leads in the low-temperature regime. We employ a full numerical solution with a set of realistic parameters and boundary conditions, considering both a uniform and non-uniform exchange field in the form of a Bloch domain wall ferromagnetic layer. The influence of spin-active interfaces is incorporated via a microscopic approach. We mainly focus on how the electronic specific heat and density of states (DOS) of such a system is affected by the \textit{proximity effect}, …
Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the topologically-protected stability of such defects driven by strong external forces. We focus on Josephson vortices that appear at planar weak links of suppressed superconductivity which have attracted much attention for electronic applications, new sources of THz radiation, and low-dissipative computing. Our numerical simulations show that a rapidly moving vortex driven by…
We present a theoretical study of the Josephson coupling of two s-wave superconductors which are connected through a diffusive contact consisting of noncollinear ferromagnetic domains. First, we consider a contact with two domains with magnetization vectors misoriented by an angle $θ$. Using the quantum circuit theory, we find that in addition to the charge supercurrent, a spin supercurrent, which is even in $ϕ$ and odd in $θ$, with a spin polarization normal to the magnetization vectors flows between the domains. Furthermore, with asymmetric insulating barriers at the interfaces of the juncti…
We study the proximity effect in superconductor-ferromagnet (SF) structure with a narrow domain wall (DW) at the SF interface. The width of the domain wall is assumed to be larger than the Fermi wave length, but smaller than other characteristic lengths (for example, the ''magnetic'' length). The transmission coefficient is supposed to be small so that we deal with a weak proximity effect. Solving the linearized Eilenberger equation, we find analytical expressions for quasiclassical Green's functions. These functions describe the short-range (SR) condensate components, singlet and triplet with…
We consider the charge and spin effects in low dimensional superconducting weak links. The first part of the review deals with the effects of electron-electron interaction in Superconductor/Luttinger liquid/Superconductor junctions. The experimental realization of this mesoscopic hybrid system can be the individual single wall carbon nanotube that bridges the gap between two bulk superconductors. The dc Josephson current through a Luttinger liquid in the limits of perfectly and poorly transmitting junctions is evaluated. The relationship between the Josephson effect in a long SNS junction and …
