We develop a microscopic analysis of superconducting and dissipative currents in junctions between superconductors with d-wave symmetry of the order parameter. We study the proximity effect in such superconductors and show that for certain crystal orientations the superconducting order parameter can be essentially suppressed in the vicinity of a nontransparent specularly reflecting boundary. This effect strongly influences the value and the angular dependence of the dc Josephson current j S . At T ∼ T c it leads to a crossover between j S ∝ T c − T and j S ∝ (T c − T ) 2 respectively for homogeneous and nonhomogeneous distribution of the order parameter in the vicinity of a tunnel junction. We show that at low temperatures the current-phase relation j S (ϕ) for SNS junctions and short weak links between d-wave superconductors is essentially nonharmonic and contains a discontinuity at ϕ = 0. This leads to further interesting features of such systems which can be used for novel pairing symmetry tests in high temperature superconductors (HTSC). We also investigated the low temperature I-V curves of NS and SS tunnel junctions and demonstrated that depending on the junction type and crystal orientation these curves show zero-bias anomalies I ∝ V 2 , I ∝ V 2 ln(1/V ) and I ∝ V 3 caused by the gapless behavior of the order parameter in d-wave superconductors. Many of our results agree well with recent experimental findings for HTSC compounds.

We analyze an interplay between the proximity effect and quantum interference of electrons in hybrid structures superconductor-normal metal-superconductor which contain several insulating barriers. We demonstrate that the dc Josephson current in these structures may change qualitatively due to quantum interference of electrons scattered at different interfaces. In junctions with few conducting channels mesoscopic fluctuations of the supercurrent are significant and its amplitude can be strongly enhanced due to resonant effects. In the many channel limit averaging over the scattering phase effectively suppresses interference effects for systems with two insulating barriers. In that case a standard quasiclassical approach describing scattering at interfaces by means of Zaitsev boundary conditions allows to reproduce the correct results. However, in systems with three or more barriers the latter approach fails even in the many channel limit. In such systems interference effects remain important in this limit as well. For short junctions these effects result in additional suppression of the Josephson critical current indicating the tendency of the system towards localization. For relatively long junctions interference effects may -on the contraryenhance the supercurrent with respect to the case of independent barriers.

We analyze current fluctuations in mesoscopic coherent conductors in the presence of electronelectron interactions. In a wide range of parameters we obtain explicit universal dependencies of the current noise on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination n Tn(Tn − 1), where Tn is the transmission of the n-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large voltages we recover two different interaction corrections entering with opposite signs. The net result is proportional to n Tn(Tn − 1)(1 − 2Tn), i.e. Coulomb interaction decreases the shot noise at low transmissions and increases it at high transmissions.