We study peculiarities of proximity effect in clean superconductor -ferromagnet structures caused by either spatial or momentum dependence of the exchange field. Even a small modulation of the exchange field along the quasiparticle trajectories is shown to provide a long range contribution to the supercurrent due to the specific interference of particle-and hole-like wave functions. The momentum dependence of the exchange field caused by the spin -orbit interaction results in the long -range superconducting correlations even in the absence of ferromagnetic domain structure and can explain the recent experiments on ferromagnetic nanowires.The exchange field h in ferromagnetic (F) metals is well known to destroy Cooper pairs resulting, thus, in a strong decay of superconducting (S) correlations in the F material and suppression of Josephson current in SFS junctions (see Refs. 1, 2 for review). Considering the quantum mechanics of quasiparticle excitations this destructive effect of the exchange field can be viewed as a consequence of a phase difference γ ∼ L/ξ h = 2Lh/ V F gained between the electron-and hole-like parts of the total wave function at the path of the length L. Both in the clean and dirty limits the measurable quantities should be calculated as superpositions of fast oscillating contributions e iγ from different trajectories and, thus, rapidly vanish with the increasing distance from the SF boundary.This textbook physical picture appears to be in sharp contrast with a number of recent experiments [3-8] which point to an anomalously large length of decay of superconducting correlations inside the F metal. As we can judge from the observation [8] of a noticeable supercurrent through a Co nanowire, this decay length can be of the order of half a micrometer which well exceeds typical coherence lengths in ferromagnets both in the clean and dirty limits. In the dirty limit such strong proximity effect can hardly be explained even taking account of long-range triplet correlations [2] induced by the exchange field inhomogeneity.Naturally, the inhomogeneity of the field h caused by the ferromagnetic domain structure can improve the conditions of Cooper pair survival in the clean limit as well. To suppress the destructive trajectory interference mentioned above the domain structure should cancel the phase gain γ for a certain group of quasiparticle trajectories. A simple example of such phase gain compensation can be realized in a clean junction consisting of two F layers with opposite orientations of magnetic moment [9,10]. On the other hand in the diffusive limit this compensation effect vanishes [11]. Note, that the exchange field inhomogeneity along the quasiclassical trajectory experiencing multiple reflections from the ferromagnet surface can appear even in the absence of the spatial domain structure. Indeed, the exchange field acting on band electrons in a solid with a finite spin -orbit interaction should obviously depend on the quasiparticle momentum [12]: h = h(k). The normal quasiparticle reflection...

Aptamers are nucleic acid analogues of antibodies with high affinity to different targets, such as cells, viruses, proteins, inorganic materials, and coenzymes. Empirical approaches allow the design of in vitro aptamers that bind particularly to a target molecule with high affinity and selectivity. Theoretical methods allow significant expansion of the possibilities of aptamer design. In this study, we review theoretical and joint theoretical-experimental studies dedicated to aptamer design and modeling. We consider aptamers with different targets, such as proteins, antibiotics, organophosphates, nucleobases, amino acids, and drugs. During nucleic acid modeling and in silico design, a full set of in silico methods can be applied, such as docking, molecular dynamics (MD), and statistical analysis. The typical modeling workflow starts with structure prediction. Then, docking of target and aptamer is performed. Next, MD simulations are performed, which allows for an evaluation of the stability of aptamer/ligand complexes and determination of the binding energies with higher accuracy. Then, aptamer/ligand interactions are analyzed, and mutations of studied aptamers made. Subsequently, the whole procedure of molecular modeling can be reiterated. Thus, the interactions between aptamers and their ligands are complex and difficult to understand using only experimental approaches. Docking and MD are irreplaceable when aptamers are studied in silico.

We show that a wide class of layered superconductor-ferromagnet (S/F) hybrids demonstrates the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase well below the superconducting transition temperature. By decreasing the temperature, one can switch the system from uniform to the FFLO state which is accompanied by the damping of the diamagnetic Meissner response down to zero and also by the sign change in the curvature of the current-velocity dependence. Our estimates show that an additional layer of the normal metal (N) covering the ferromagnet substantially softens the conditions required for the predicted FFLO instability, and for existing S/F/N systems, the temperature of the transition into the FFLO phase can reach several kelvins.

The electronic structure of a vortex line trapped by an insulating columnar defect in a type-II superconductor is analysed within the Bogolubov-de Gennes theory. For quasiparticle trajectories with small impact parameters defined with respect to the vortex axis the normal reflection of electrons and holes at the defect surface results in the formation of an additional subgap spectral branch. The increase in the impact parameter at this branch is accompanied by the decrease of the excitation energy. When the impact parameter exceeds the radius of the defect this branch transforms into the Caroli-de Gennes-Matricon one. As a result, the minigap in the quasiparticle spectrum increases with the increase in the defect radius. The scenario of the spectrum transformation is generalized for the case of arbitrary vorticity.

The distinctive features of equilibrium vortex structures in thin films of anisotropic superconductors in tilted magnetic fields are studied for the limits of moderate and strong anisotropy. The energetically favorable shape of isolated vortex lines is found in the framework of two particular models describing these limiting cases: London theory with an anisotropic mass tensor and London-type model for a stack of Josephson-decoupled superconducting layers. The increase of the field tilting is shown to result in qualitative changes in the vortex-vortex interaction potential: the balance between long-range attractive and repulsive forces occurs to be responsible for a formation of a minimum of the interaction potential vs the intervortex distance. This minimum appears to exist only for a certain restricted range of the vortex tilting angles which shrinks with the decrease of the system anisotropy parameter. Tilted vortices with such unusual interaction potential form clusters with the size depending on the field tilting angle and film thickness or/and can arrange into multiquanta flux lattice. The magnetic flux through the unit cells of the corresponding flux line lattices equals to an integer number M of flux quanta. Thus, the increase in the field tilting should be accompanied by the series of the phase transitions between the vortex lattices with different M .PACS numbers:

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In structures made up of alternating superconducting and ferromagnet layers (S/F/S heterostructures), it is known that the macroscopic quantum wavefunction of the ground state changes its phase difference across the F-layer from 0 to π under certain temperature and geometrical conditions, whence the name "0 − π" for this crossover. We present here a joint experimental and theoretical demonstration that the 0 − π is a true thermodynamic phase transition: microwave measurements of the temperature dependence of the London penetration depth in Nb/Pd0.84Ni0.16/Nb trilayers reveal a sudden, unusual decrease of the density of the superconducting condensate (square modulus of the macroscopic quantum wavefunction) with decreasing temperature, which is predicted by the theory here developed as a transition from the 0− to the π−state. Our result for the jump of the amplitude of the order parameter is the first thermodynamic manifestation of such temperature-driven quantum transition.

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