Current-voltage relation for superconducting d-wave junctions

We calculate the current-voltage (I-V) relation for planar superconducting d-wave junctions for both arbitrary transmission of the junction and arbitrary orientation of the d-wave superconductors. The midgap states (MGS) present at interfaces/surfaces of a d-wave superconductor influence the I-V relation. In some arrangements we find considerable negative differential conductance and lower threshold voltage for non-zero current due to resonant conduction through MGS.Comment: 4 pages, 2 figure

Discrete conventional signalling of a continuous variable

In aggressive interactions, animals often use a discrete set of signals, while the properties being signalled are likely to be continuous, for example fighting ability or value of victory. Here we investigate a particular model of fighting which allows for conventional signalling of subjective resource value to occur. The result shows that neither perfect nor no signalling are evolutionarily stable strategies (ESSs) in the model. Instead, we find ESSs in which partial information is communicated, with discrete displays signalling a range of values rather than a precise one. The result also indicates that communication should be more precise in conflicts over small resources. Signalling strategies can exist in fighting because of the common interest in avoiding injuries, but communication is likely to be limited because of the fundamental conflict over the resource. Our results reflect a compromise between these two factors. Data allowing for a thorough test of the model are lacking; however, existing data seem consistent with the obtained theoretical results

Resonant transport through midgap states in voltage-biased Josephson junctions of d-wave superconductors

We study theoretically the ac Josephson effect in voltage biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current-voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors.Comment: 10 pages, 5 figures, Submitted to a special volume of "Superlattices and Microstructures

Superconducting d-wave junctions: The disappearance of the odd ac components

We study voltage-biased superconducting planar d-wave junctions for arbitrary transmission and arbitrary orientation of the order parameters of the superconductors. For a certain orientation of the superconductors the odd ac components disappear, resulting in a doubling of the Josephson frequency. We study the sensitivity of this disappearance to orientation and compare with experiments on grain boundary junctions. We also discuss the possibility of a current flow parallel to the junction.Comment: 5 pages, 3 figure

ac Josephson effect in superconducting d-wave junctions

We study theoretically the ac Josephson effect in superconducting planar d-wave junctions. The insulating barrier assumed to be present between the two superconductors may have arbitrary strength. Many properties of this system depend on the orientation of the d-wave superconductor: we calculate the ac components of the Josephson current. In some arrangements there is substantial negative differential conductance due to the presence of mid-gap states. We study how robust these features are to finite temperature and also comment on how the calculated current-voltage curves compare with experiments. For some other configurations (for small barrier strength) we find zero-bias conductance peaks due to multiple Andreev reflections through midgap states. Moreover, the odd ac components are strongly suppressed and even absent in some arrangements. This absence will lead to a doubling of the Josephson frequency. All these features are due to the d-wave order parameter changing sign when rotated $90^{\circ}$. Recently, there have been several theoretical reports on parallel current in the d-wave case for both the stationary Josephson junction and for the normal metal-superconductor junction. Also in our case there may appear current density parallel to the junction, and we present a few examples when this takes place. Finally, we give a fairly complete account of the method used and also discuss how numerical calculations should be performed in order to produce current-voltage curves

Theory of electron transport in superconducting heterostructures

This thesis deals theoretically with electron transport in superconducting heterostructures. Depending on the system I use different theoretical approaches. The thesis contains an introduction followed by four research papers (Papers I-IV). The introduction gives the background of the work in Papers I-IV. Also, I discuss the theoretical methods used and some concepts of importance concerning transport processes. In Paper I, the difference between point-contact and sandwich-type tunneling in high-Tc junctions is studied. This difference is related to a periodically extended Anderson model with negative-U centers. The theoretical analysis is based on the tunneling Hamiltonian formalism and a slave boson representation to deal with the electron correlation problem. Qualitative agreement with experiment is found. In Papers II-III, supercurrent through superconductor-normal metal-superconductor (SNS) structures is studied, using the Bogoliubov-de Gennes equation. In Paper II, attention is paid to normal reflection due to a finite ratio between the gap .DELTA. and the Fermi energy .mY.. The dispersion relation of the Andreev levels is calculated. A minigap of the order .DELTA.2/.my. is found. The critical current is reduced due to the normal reflection. In Paper III, a double SNS junction is studied. The Andreev levels associated with different normal regions interact, leading to splitting of the levels. In the double SNS junction there is a contribution from the continuous levels to the current, in addition to the contribution from the discrete subgap levels. In Paper IV, the critical current density is calculated for a heterostructure, using Ginzburg-Landau theory. The variable parameter in the heterostructure is the mean free path, which is small in some region and large far away from the contaminated region. The product between the critical current and the resistance is explored, and found to increase with resistance. The connection between the model considered and grain boundaries in high-Tc superconductors is discussed