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

This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

We report measurements of the temperature dependence of the critical current, Ic, in Josephson junctions consisting of conventional superconducting banks of Nb and a weakly ferromagnetic interlayer of a CuxNi1-x alloy, with x around 0.5. With decreasing temperature Ic generally increases, but for specific thicknesses of the ferromagnetic interlayer, a maximum is found followed by a strong decrease down to zero, after which Ic rises again. Such a sharp cusp can be explained only by assuming that the junction changes from a 0-phase state at high temperatures to a I� phase state at low temperatures.

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Coupling of two superconductors through a ferromagnet: evidence for a pi junction.

Coupling of Two Superconductors through a Ferromagnet

In this Letter, we calculate the electron-phonon coupling of the newly discovered superconductor LaFeAsO1xFx using linear response. For pure LaFeAsO, the calculated electron-phonon coupling constant 0:21 and logarithmic-averaged frequency !ln 206 K give a maximum Tc of 0.8 K, using the standard Migdal-Eliashberg theory. For the F-doped compounds, we predict even smaller coupling constants. To reproduce the experimental Tc, a 5–6 times larger coupling constant would be needed. Our results indicate that electron-phonon coupling is not sufficient to explain superconductivity in the whole family of Fe-As-based superconductors, probably due to the importance of strong-correlation effects.

Is LaFeAsO1-xFx an electron-phonon superconductor?

A large number of experimental facts and theoretical arguments favor a two-gap model for superconductivity in MgB2 However, this model predicts strong suppression of the critical temperature by interband impurity scattering and, presumably, a strong correlation between the critical temperature and the residual resistivity No such correlation has been observed We argue that this fact can be understood if the band disparity of the electronic structure is taken into account, not only in the superconducting state, but also in normal transport

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Alexandre Avraamovitch Golubov

Papers

The current-phase relation in Josephson junctions

Coupling of two superconductors through a ferromagnet: evidence for a pi junction.

Coupling of Two Superconductors through a Ferromagnet

Is LaFeAsO1-xFx an electron-phonon superconductor?

Superconductivity in MgB2: clean or dirty?