There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

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Spintronics: Fundamentals and applications

It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.

Parity–time-symmetric whispering-gallery microcavities

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

The proximity effect at superconductor-ferromagnet interfaces produces damped oscillatory behavior of the Cooper pair wave function within the ferromagnetic medium. This is analogous to the inhomogeneous superconductivity, predicted long ago by Fulde and Ferrell (P. Fulde and R. A. Ferrell, 1964, ``Superconductivity in a strong spin-exchange field,'' Phys. Rev. 135, A550--A563), and by Larkin and Ovchinnikov (A. I. Larkin and Y. N. Ovchinnikov, 1964, ``Inhomogeneous state of superconductors,'' Zh. Eksp. Teor. Fiz. 47, 1136--1146 [Sov. Phys. JETP 20, 762--769 (1965)]), and sought by condensed-matter experimentalists ever since. This article offers a qualitative analysis of the proximity effect in the presence of an exchange field and then provides a description of the properties of superconductor-ferromagnet heterostructures. Special attention is paid to the striking nonmonotonic dependence of the critical temperature of multilayers and bilayers on the ferromagnetic layer thickness as well as to the conditions under which ``$\ensuremath{\pi}$'' Josephson junctions are realized. Recent progress in the preparation of high-quality hybrid systems has permitted the observation of many interesting experimental effects, which are also discussed. Finally, the author analyzes the phenomenon of domain-wall superconductivity and the influence of superconductivity on the magnetic structure in superconductor-ferromagnet bilayers.

Proximity effects in superconductor-ferromagnet heterostructures

Meissner effect in the diffusive normal metal/insulator/s-wave superconductor junctions is studied in the presence of the magnetic impurities for various situations, where we have used the Usadel equation with Nazarov’s generalized boundary condition. It is shown that the susceptibility of the diffusive normal metal for s-wave superconductor is almost independent of the height of the insulating barrier at the interface.

Meissner effect in diffusive normal metal/superconductor junctions

Low-temperature scanning electron microscopy was used to investigate the interaction of fluxons (Josephson vortices) with a superconducting (Abrikosov) vortex trapped in one of the electrodes of a long quasi-one-dimensional Josephson junction. The Abrikosov vortex penetrated a top superconducting film and spread out in the tunnel barrier area between the films. It was possible to move the Abrikosov vortex across the junction by the electron beam and to measure at the same time the value of the critical current of the junction. The bound states of a fluxon trapped by the Abrikosov vortex in the Josephson junction were also observed. >

Interaction of fluxons with Abrikosov vortices in long Josephson junctions

We study the effect of the Fermi surface anisotropy on Majorana modes along a superconductor/ ferromagnetic insulator (S/FI) boundary, formed on the surface of a three-dimensional topological insulator. In the previous works this problem was treated with a simplified Hamiltonian, describing an isotropic Dirac cone dispersion. This approximation is only valid near the Dirac point. However, in topological insulators the chemical potential often lies well above this point, where the Dirac cone is strongly anisotropic and its constant energy contour has a snowflake shape. Taking this shape into account we have found that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to get the Majorana bound state at the boundary. If the boundary is placed arbitrary, the Majorana bound state is absent. This provides an important selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.

Majorana modes in three-dimensional topological insulators with warped surface state

This paper discusses the Josephson effect in superconductor/diffusive half metal/superconductor junctions. The spin-flip scattering at the junction interfaces opens a Josephson channel between the two spin-singlet superconductors. The odd-frequency equal-spin-triplet Cooper pairs carry the Josephson current. As a consequence, the local density of states in a half metal has a large peak at the Fermi energy. We propose an experimental method to detect odd-frequency pairs by using the scanning tunneling spectroscopy.

Josephson current through a diffusive half metal

Ramp type Josephson junctions have been fabricated using DyBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// as electrode material and PrBa/sub 2/Cu/sub 3-x/Ga/sub x/O/sub 7-/spl delta// with x=0, 0.10 and 0.40 as junction barriers. Barrier thickness lie between 6-30 nm. Several junctions without barrier were made in order to find ways to minimize the damage of the ramp interface. In total about 40 chips were fabricated each containing several junctions and their I-V characteristics measured for various temperatures down to 4.2 K. Only those junctions showing clear RSJ-like curves were selected to be analyzed. In some cases we also measured I/sub c/ as a function of a small applied field and obtained a clear Fraunhofer pattern, but there is a tendency to flux trapping as evidenced by LTSEM. It was found at 4.2 K that the critical current density J/sub c/ scales with the specific resistance R/sub n/A as J/sub c/=C/sub bar/(R/sub n/A)/sup -m/ (m=1.8/spl plusmn/0.5). The barrier material dependent constant C/sub bar/ increases with x, whereas, for a given d, J/sub c/ is constant and R/sub n/A increases.<<ETX>>

Alexandre Avraamovitch Golubov

Papers

Meissner effect in diffusive normal metal/superconductor junctions

Interaction of fluxons with Abrikosov vortices in long Josephson junctions

Majorana modes in three-dimensional topological insulators with warped surface state

Josephson current through a diffusive half metal

Ramp type HTS Josephson junctions with PrBaCuO barriers