Inverse spin-Hall effect and spin-swapping in spin-split superconductors

When a spin-splitting field is introduced to a thin film superconductor, the spin currents polarized along the field couples to energy currents that can only decay via inelastic scattering. We study spin and energy injection into such a superconductor where spin-orbit impurity scattering yields inverse spin-Hall and spin-swapping currents. We show that the combined presence of a spin-splitting field, superconductivity, and inelastic scattering gives rise to a renormalization of the spin-Hall and spin-swap angles. In addition to an enhancement of the ordinary inverse spin-Hall effect, spin-splitting gives rise to unique inverse spin-Hall and spin-swapping signals five orders of magnitude stronger than the ordinary inverse spin-Hall signal. These can be completely controlled by the orientation of the spin-splitting field, resulting in a long-range charge and spin accumulations detectable much further from the injector than in the normal-state. Our results demonstrate that superconductors provide tunable inverse spin-Hall and spin-swapping signals with high detection sensitivity.Comment: 6 + 9 pages, 3 figure

Magnetization reorientation due to the superconducting transition in heavy-metal heterostructures

Recent theoretical and experimental work has demonstrated how the superconducting critical temperature ($T_c$) can be modified by rotating the magnetization of a single homogeneous ferromagnet proximity-coupled to the superconducting layer. This occurs when the superconductor and ferromagnet are separated by a thin heavy normal metal that provides an enhanced interfacial Rashba spin-orbit interaction. We consider the reciprocal effect: magnetization reorientation driven by the superconducting phase transition. We solve the tight-binding Bogoliubov-de Gennes equations on a lattice self-consistently and find that the relative angle between the spin-orbit field and the magnetization gives rise to a contribution in the free energy even in the normal state due to band-structure effects. For temperatures below $T_c$, superconductivity gives rise to a competing contribution. By lowering the temperature, in addition to reorientation of the favored magnetization direction from in-plane to out-of-plane, a $\pi/4$ in-plane rotation for thicker ferromagnetic layers is possible. Furthermore, computation of $T_c$ of the structure in the ballistic limit shows a dependence on the in-plane orientation of the magnetization, in contrast to our previous result on the diffusive limit. This finding is relevant with respect to thin-film heterostructures since these are likely to be in the ballistic regime of transport. Finally, we discuss the experimental feasibility of observing the magnetic anisotropy induced by the superconducting transition when other magnetic anisotropies, such as the shape anisotropy for a ferromagnetic film, are taken into account. Our work suggests that the superconducting condensation energy in principle can trigger a reorientation of the magnetization of a thin-film ferromagnet upon lowering the temperature below $T_c$, in particular for ferromagnets with weak magnetic anisotropies.Comment: 11 pages, 10 figure

Controlling the Superconducting Transition by Rotation of an Inversion Symmetry-Breaking Axis

We consider a hybrid structure where a material with Rashba-like spin-orbit coupling is proximity coupled to a conventional superconductor. We find that the superconducting critical temperature $T_c$ can be tuned by rotating the vector $\boldsymbol{n}$ characterizing the axis of broken inversion symmetry. This is explained by a leakage of $s$-wave singlet Cooper pairs out of the superconducting region, and by conversion of $s$-wave singlets into other types of correlations, among these $s$-wave odd-frequency pairs robust to impurity scattering. These results demonstrate a conceptually different way of tuning $T_c$ compared to the previously studied variation of $T_c$ in magnetic hybrids.Comment: 4 pages, (11 pages including Supplemental Material), 3 figure

Magnetization reorientation due to the superconducting transition in heavy-metal heterostructures

© 2019 American Physical Society. UK. Recent theoretical and experimental work has demonstrated how the superconducting critical temperature (Tc) can be modified by rotating the magnetization of a single homogeneous ferromagnet proximity-coupled to the superconducting layer. This occurs when the superconductor and ferromagnet are separated by a thin heavy normal metal that provides an enhanced interfacial Rashba spin-orbit interaction. In the present work, we consider the reciprocal effect: magnetization reorientation driven by the superconducting phase transition. We solve the tight-binding Bogoliubov-de Gennes equations on a lattice self-consistently and compute the free energy of the system. We find that the relative angle between the spin-orbit field and the magnetization gives rise to a contribution in the free energy even in the normal state, T>Tc, due to band-structure effects. For temperatures below Tc, superconductivity gives rise to a competing contribution. We demonstrate that by lowering the temperature, in addition to reorientation of the favored magnetization direction from in-plane to out-of-plane, a π/4 in-plane rotation for thicker ferromagnetic layers is possible. Furthermore, computation of Tc of the structure in the ballistic limit shows a dependence on the in-plane orientation of the magnetization, in contrast to our previous result on the diffusive limit. This finding is relevant with respect to thin-film heterostructures since these are likely to be in the ballistic regime of transport rather than in the diffusive regime. Finally, we discuss the experimental feasibility of observing the magnetic anisotropy induced by the superconducting transition when other magnetic anisotropies, such as the shape anisotropy for a ferromagnetic film, are taken into account. Our work suggests that the superconducting condensation energy in principle can trigger a reorientation of the magnetization of a thin-film ferromagnet upon lowering the temperature below Tc, in particular for ferromagnets with weak magnetic anisotropies

A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

A Formalization of Linkage Analysis

In this report a formalization of genetic linkage analysis is introduced. Linkage analysis is a computationally hard biomathematical method, which purpose is to locate genes on the human genome. It is rooted in the new area of bioinformatics and no formalization of the method has previously been established. Initially, the biological model is presented. On the basis of this biological model we establish a formalization that enables reasoning about algorithms used in linkage analysis. The formalization applies both for single and multi point linkage analysis. We illustrate the usage of the formalization in correctness proofs of central algorithms and optimisations for linkage analysis. A further use of the formalization is to reason about alternative methods for linkage analysis. We discuss the use of MTBDDs and PDGs in linkage analysis, since they have proven efficient for other computationally hard problems involving large state spaces. We conclude that none of the techniques discussed are directly applicable to linkage analysis, however further research is needed in order to investigated whether a modified version of one or more of these are applicable

Checking Consistency of Pedigree Information is NP-complete (Preliminary Report)

Consistency checking is a fundamental computational problem in genetics. Given a pedigree and information on the genotypes of some of the individuals in it, the aim of consistency checking is to determine whether these data are consistent with the classic Mendelian laws of inheritance. This problem arose originally from the geneticists' need to filter their input data from erroneous information, and is well motivated from both a biological and a sociological viewpoint. This paper shows that consistency checking is NP-complete, even in the presence of three alleles. Several other results on the computational complexity of problems from genetics that are related to consistency checking are also offered. In particular, it is shown that checking the consistency of pedigrees over two alleles can be done in polynomial time