Odd-frequency pairing in normal metal/superconductor junctions

We study the induced odd-frequency pairing states in ballistic normal metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has even-parity pair potential (spin-singlet s-wave state), the odd-frequency pairing component with odd-parity is induced near the N/S interface, while in the case of odd-parity pair potential (spin-triplet $p_{x}$-wave or spin-singlet $d_{xy}$-wave) the odd-frequency component with even-parity is generated. We show that in conventional s-wave junctions, the amplitude of the odd-frequency pairing state is enhanced at energies corresponding to the peaks in the local density of states (LDOS). In $p_x$- and $d_{xy}$-wave junctions, the amplitude of the odd-frequency component on the S side of the N/S interface is enhanced at zero energy where the midgap Andreev resonant state (MARS) appears due to the sign change of the pair potential. The odd-frequency component extends into the N region and exceeds the even-frequency component at energies corresponding to the LDOS peak positions, including the MARS.Comment: 27 pages, 12 figure

Multiple Andreev Reflections in Weak Links of Superfluid 3He-B

We calculate the current-pressure characteristics of a ballistic pinhole aperture between two volumes of B-phase superfluid 3He. The most important mechanism contributing to dissipative currents in weak links of this type is the process of multiple Andreev reflections. At low biases this process is significantly affected by relaxation due to inelastic quasiparticle-quasiparticle collisions. In the numerical calculations, suppression of the superfluid order parameter at surfaces is taken into account self-consistently. When this effect is neglected, the theory may be developed analytically like in the case of s-wave superconductors. A comparison with experimental results is presented.Comment: 12 pages, 9 figures, RevTeX

Classical and quantum magnetisation reversal studied in single nanometer-sized particles and clusters using micro-SQUIDs

Recent progress in experiment on quantum tunnelling of the magnetic moment in mesoscopic systems will be reviewed. The emphasis will be made on measurements of individual nanoparticles. These nanomagnets allow one to test the border between classical and quantum behaviour. Using the micro-SQUID magnetometer, waiting time, switching field and telegraph noise measurements show unambiguously that the magnetisation reversal of small enough single crystalline nanoparticles is described by a model of thermal activation over a single-energy barrier. Results on insulating BaFeO nanoparticles show strong deviations from this model below 0.4 K which agree with the theory of macroscopic quantum tunnelling in the low dissipation regime.Comment: 6 pages, 2 figures, conference proceedings of LT22-Helsink

Lifetime of metastable states in resonant tunneling structures

We investigate the transport of electrons through a double-barrier resonant-tunneling structure in the regime where the current-voltage characteristics exhibit bistability. In this regime one of the states is metastable, and the system eventually switches from it to the stable state. We show that the mean switching time grows exponentially as the voltage across the device is tuned from the its boundary value into the bistable region. In samples of small area we find that the logarithm of the lifetime is proportional to the voltage (measured from its boundary value) to the 3/2 power, while in larger samples the logarithm of the lifetime is linearly proportional to the voltage.Comment: REVTeX 4, 5 pages, 3 EPS-figure

Effect of point-contact transparency on coherent mixing of Josephson and transport supercurrents

The influence of electron reflection on dc Josephson effect in a ballistic point contact with transport current in the banks is considered theoretically. The effect of finite transparency on the vortex-like currents near the contact and at the phase difference $\phi =\pi ,$ which has been predicted recently \cite{KOSh}, is investigated. We show that at low temperatures even a small reflection on the contact destroys the mentioned vortex-like current states, which can be restored by increasing of the temperature.Comment: 6 pages, 8 Figures, Latex Fil

Penetration of hot electrons through a cold disordered wire

We study a penetration of an electron with high energy E<<T through strongly disordered wire of length L<<a (a being the localization length). Such an electron can loose, but not gain the energy, when hopping from one localized state to another. We have found a distribution function for the transmission coefficient t. The typical t remains exponentially small in L/a, but with the decrement, reduced compared to the case of direct elastic tunnelling. The distribution function has a relatively strong tail in the domain of anomalously high t; the average ~(a/L)^2 is controlled by rare configurations of disorder, corresponding to this tail.Comment: 4 pages, 5 figure

Binary Tree Approach to Scaling in Unimodal Maps

Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We consider the scaling behavior in a modified tree which takes into account the self-similarity of the window structure. A non-universal geometric convergence of the associated superstable parameter values towards a Misiurewicz point is observed for almost all binary sequences with periodic tails. There are an infinite number of exceptional sequences, however, which lead to superexponential scaling. The origin of such sequences is explained.Comment: 25 pages, plain Te

Pinhole calculations of the Josephson effect in 3He-B

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 the current-phase relationships in several cases. In the isotextural case, the current-phase relations are plotted assuming a constant spin-orbit texture. In the opposite anisotextural case the texture changes as a function of the phase difference. For that we have to consider the stiffness of the macroscopic texture, and we also calculate some surface interaction parameters. We analyze the experiments by Marchenkov et al. We find that the observed pi states and bistability hardly can be explained with the isotextural pinhole model, but a good quantitative agreement is achieved with the anisotextural model.Comment: 20 pages, 21 figures, revtex

Thermally assisted magnetization reversal in the presence of a spin-transfer torque

We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin transfer torques. Since the spin transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill-defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high energy barriers, the law of thermal agitation is derived. We find that the N\'{e}el-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent of the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.Comment: 5 figure

Josephson effect in point contacts between ''f-wave'' superconductors

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 free energy corresponds to a spontaneous phase difference. This phase difference depends on the misorientation angle and may possess any value. We conclude that experimental investigations of the current-phase dependences of small junctions can be used for determination of the order parameter symmetry in the mentioned above superconductors.Comment: 11 pages, 8 figure