Josephson effect in SF_{\rm F}XSF_{\rm F} junctions

We investigate the Josephson effect in S$_{\rm F}$XS$_{\rm F}$ junctions, where S$_{\rm F}$ is a superconducting material with a ferromagnetic exchange field, and X a weak link. The critical current $I_c$ increases with the (antiparallel) exchange fields if the distribution of transmission eigenvalues of the X-layer has its maximum weight at small values. This exchange field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S$_{\rm F}$IS$_{\rm F}$ junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference of the exchange fields $h_1-h_2$ in an S$_{\rm F}$IS$_{\rm F}$ junction corresponds to the potential difference $V_1-V_2$ in an SIS junction; i.e., the singularity in $I_c$ [in an S$_{\rm F}$IS$_{\rm F}$ junction] at $|h_1-h_2|=\Delta_1+\Delta_2$ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S$_{\rm F}$IS$_{\rm F}$ junctions.Comment: 5 pages, 5 figure

Proximity effect in atomic-scaled hybrid superconductor/ferromagnet structures: crucial role of electron spectra

We study the influence of the configuration of the majority and minority spin subbands of electron spectra on the properties of atomic-scaled superconductor-ferromagnet S-F-S and F-S-F hybrid structures. At low temperatures, the S/F/S junction is either a 0 or junction depending on the energy shift between S and F materials and the anisotropy of the Fermi surfaces. We found that the spin switch effect in F/S/F system can be reversed if the minority spin electron spectra in F metal is of the hole-like type

Invariant Peano curves of expanding Thurston maps

We consider Thurston maps, i.e., branched covering maps $f\colon S^2\to S^2$ that are postcritically finite. In addition, we assume that $f$ is expanding in a suitable sense. It is shown that each sufficiently high iterate $F=f^n$ of $f$ is semi-conjugate to $z^d\colon S^1\to S^1$, where $d$ is equal to the degree of $F$. More precisely, for such an $F$ we construct a Peano curve $\gamma\colon S^1\to S^2$ (onto), such that $F\circ \gamma(z) = \gamma(z^d)$ (for all $z\in S^1$).Comment: 63 pages, 12 figure