Strongly anharmonic current-phase relation in ballistic graphene Josephson junctions

Motivated by a recent experiment directly measuring the current-phase relation (CPR) in graphene under the influence of a superconducting proximity effect, we here study the temperature dependence of the CPR in ballistic graphene SNS Josephson junctions within the the self-consistent tight-binding Bogoliubov-de Gennes (BdG) formalism. By comparing these results with the standard Dirac-BdG method, where rigid boundary conditions are assumed at the SN interfaces, we show on a crucial importance of both proximity effect and depairing by current for the CPR. The proximity effect grows with temperature and reduces the skewness of the CPR towards the harmonic result. In short junctions ($L<\xi$) current depairing is also important and gives rise to a critical phase $\phi_c<\pi/2$ over a wide range of temperatures and doping levels.Comment: 7 pages, 4 figures. v2 contains very minor change

Current fluctuations in composite conductors: Beyond the second cumulant

Employing the non-linear $\sigma$-model we analyze current fluctuations in coherent composite conductors which contain a diffusive element in-between two tunnel barriers. For such systems we explicitly evaluate the frequency-dependent third current cumulant which also determines the leading Coulomb interaction correction to shot noise. Our predictions can be directly tested in future experiments.Comment: 6 pages, 1 figur

Proximity effect in normal metal-multiband superconductor hybrid structures

A theory of the proximity effect in normal metal¿multiband superconductor hybrid structures is formulated within the quasiclassical Green's function formalism. The quasiclassical boundary conditions for multiband hybrid structures are derived in the dirty limit. It is shown that the existence of multiple superconducting bands manifests itself as the occurrence of additional peaks in the density of states in the structure. The interplay between the proximity effect and the interband coupling influences the magnitudes of the gaps in a superconductor in a nontrivial way and can even give rise to an enhancement of multiband superconductivity by the proximity to a superconductor with a lower transition temperature. The developed theory is applied to the calculation of supercurrent in multiband superconductor¿normal metal¿superconductor Josephson junctions with low-transparent interfaces, and the results are compared with the predictions for multiband tunnel junctions

Crossed Andreev reflection in diffusive contacts

Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to contribute equally to the nonlocal current, which is of relevance to the use of normal metal-superconducting heterostructures as sources of entanglement

Properties of tunnel Josephson junctions with a ferromagnetic interlayer

We investigate superconductor/insulator/ferromagnet/superconductor (SIFS) tunnel Josephson junctions in the dirty limit, using the quasiclassical theory. We formulate a quantitative model describing the oscillations of critical current as a function of thickness of the ferromagnetic layer and use this model to fit recent experimental data. We also calculate quantitatively the density of states (DOS) in this type of junctions and compare DOS oscillations with those of the critical current.Comment: 9 pages, 8 figures, to be published in Phys. Rev.

Nonmonotonic temperature dependence of critical current in diffusive d-wave junctions

We study the Josephson effect in D/I/DN/I/D junctions, where I, DN and D denote an insulator, a diffusive normal metal and a d-wave superconductor, respectively.The Josephson current is calculated based on the quasiclassical Green's function theory with a general boundary condition for unconventional superconducting junctions. In contrast to s-wave junctions, the product of the Josephson current and the normal state resistance is enhanced by making the interface barriers stronger. The Josephson current has a nonmonotonic temperature dependence due to the competition between the proximity effect and the midgap Andreev resonant states.Comment: 5 pages, 4 figure

Angular dependence of Josephson currents in unconventional superconducting junctions

Josephson effect in junctions between unconventional superconductors is studied theoretically within the model describing the effects of interface roughness. The particularly important issue of applicability of the frequently used Sigrist-Rice formula for Josephson current in d-wave superconductor / insulator / d-wave superconductor junctions is addressed. We show that although the SR formula is not applicable in the ballistic case, it works well for rough interfaces when the diffusive normal metal regions exist between the d-wave superconductor and the insulator. It is shown that the SR approach only takes into account the component of the d-wave pair potential symmetric with respect to an inversion around the plane perpendicular to the interface. Similar formula can be derived for general unconventional superconductors with arbitrary angular momentum l.Comment: 4 pages, 4 figure

Properties of superconductor/ferromagnet structures with spin-dependent scattering

We investigate superconductor/ferromagnet (S/F) hybrid structures in the dirty limit, described by the Usadel equations. More precisely, the oscillations of the critical temperature and critical current with the thickness of the ferromagnetic layers are studied. We show that spin-flip and spin-orbit scattering lead to the decrease of the decay length and the increase of the oscillation period. The critical current decay is more sensitive to these pair-breaking mechanisms than that of the critical temperature. These two scattering mechanisms should be taken into account to get a better agreement between experimental results and theoretical descriptions. We also study the influence of the interface transparency on the properties of S/F structures

Josephson φ\varphi-junctions based on structures with complex normal/ferromagnet bilayer

We demonstrate that Josephson devices with nontrivial phase difference $0<\varphi_g <\pi$ in the ground state can be realized in structures composed from longitudinally oriented normal metal (N) and ferromagnet (F) films in the weak link region. Oscillatory coupling across F-layer makes the first harmonic in the current-phase relation relatively small, while coupling across N-layer provides negative sign of the second harmonic. To derive quantitative criteria for a $\varphi$-junction, we have solved two-dimensional boundary-value problem in the frame of Usadel equations for overlap and ramp geometries of S-NF-S structures. Our numerical estimates show that $\varphi$-junctions can be fabricated using up-to-date technology.Comment: 14 pages, 9 figure