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We present a simple and pedagogical derivation of the spin current as the linear response to an external electric field for both Rashba and Luttinger spin–orbital coupling Hamiltonians. Except for the adiabatic approximation, our derivation is exact to the linear order of the electric field for both models. The spin current is a direct result of the difference in occupation levels between different bands. Moreover, we show a general topological spin current can be defined for a broad class of spin–orbit coupling systems.

In a biased two-dimensional electron gas, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to a Hall conductivity of charge carriers in the absence of an external magnetic field. We study the dynamical charge-Hall effect, the field-induced spin accumulation, and the magnetoelectric effect for a system with short-range elastic impurity scattering by analytically solving the kinetic equations for the spin-density matrix in the linear response regime. By tuning the strength of the Rashba and Dresselhaus spin-orbit coupling as well as the frequency and direction of the applied electric field, eigenmodes of the spin-coupled system are identified.

We investigate spin and charge current through a quantum dot pumped by a time-varying magnetic field. Using the density matrix method, quantum rate equations for the electronic occupation numbers in the quantum dot are obtained and solved in the stationary state limit for a wide set of parameters. Both charge and spin currents are expressed explicitly in terms of several relevant parameters and analyzed in detail. The results suggest a way of optimizing experimental parameters to obtain an maximal spin current without the charge current flow.

This article reviews steady-state spin densities and spin currents in materials with strong spin-orbit interactions. These phenomena are intimately related to spin precession due to spin-orbit coupling, which has no equivalent in the steady state of charge distributions. The focus will initially be on effects originating from the band structure. In this case, spin densities arise in an electric field because a component of each spin is conserved during precession. Spin currents arise because a component of each spin is continually precessing. These two phenomena are due to independent contributions to the steady-state density matrix, and scattering between the conserved and precessing spin distributions has important consequences for spin dynamics and spin-related effects in general. In the latter part of the article, extrinsic effects such as skew scattering and side jump will be discussed, and it will be shown that these effects are also modified considerably by spin precession. Theoretical and experimental progress in all areas will be reviewed.

In paper III of this series we proposed a scenario of superconductivity driven by hole "undressing" that involved a complete redistribution of the occupation of single particle energy levels: the holes near the top of the band were proposed to all condense to the bottom of the band. Here we consider a less drastic redistribution involving electrons with a definite spin chirality and show that it is in fact energetically favored by the Coulomb exchange matrix element J over the scenario proposed earlier. It is shown that spin splitting with chiral states reduces the Coulomb repulsion and hence that the Coulomb repulsion promotes spin splitting. Superconductors are proposed to possess a spin-split hole "core" at the bottom of the electronic conduction band in addition to a spin-split Fermi surface. The Dirac sea is proposed to play a key role. The new scenario leads naturally to the existence of a spin current in the superconducting state and is consistent with the Spin Meissner effect and negative charge expulsion discussed earlier within the theory of hole superconductivity.

Is superconductivity associated with a lowering or an increase of the kinetic energy of the charge carriers? Conventional BCS theory predicts that the kinetic energy of carriers increases in the transition from the normal to the superconducting state. However, substantial experimental evidence obtained in recent years indicates that in at least some superconductors the opposite occurs. Motivated in part by these experiments many novel mechanisms of superconductivity have recently been proposed where the transition to superconductivity is associated with a lowering of the kinetic energy of the carriers. However none of these proposed unconventional mechanisms explores the fundamental reason for kinetic energy lowering nor its wider implications. Here I propose that kinetic energy lowering is at the root of the Meissner effect, the most fundamental property of superconductors. The physics can be understood at the level of a single electron atom: kinetic energy lowering and enhanced diamagnetic susceptibility are intimately connected. We propose that this connection extends to superconductors because they are, in a very real sense, "giant atoms". According to the theory of hole superconductivity, superconductors expel negative charge from their interior driven by kinetic energy lowering and in the process expel any magnetic field lines present in their interior. Associated with this we predict the existence of a macroscopic electric field in the interior of superconductors and the existence of macroscopic quantum zero-point motion in the form of a spin current in the ground state of superconductors (spin Meissner effect). In turn, the understanding of the role of kinetic energy lowering in superconductivity suggests a new way to understand the fundamental origin of kinetic energy lowering in quantum mechanics quite generally. This provides a new understanding of "quantum pressure", the stability of matter and the origin of fermion anticommutation relations, it leads to the prediction that spin currents exist in the ground state of aromatic ring molecules, and that the electron wavefunction is double-valued, requiring a reformulation of conventional quantum mechanics.

Spin current is an important physical quantity in present day spintronics and it might be very useful in the physics of quantum plasmas of the spinning particles. Thus it is important to have an equation of the spin current evolution. This equation naturally appears as a part of the set of quantum hydrodynamic (QHD) equations. Consequently, we present the set of QHD equations derived from the many-particle microscopic Schrödinger equation, which consists of the continuity equation, the Euler equation, the Bloch equation and the equation of the spin current evolution. We use these equations to study the dispersion of the collective excitations in the three-dimensional samples of the magnetized dielectrics. We show that the dynamics of the spin current leads to the formation of new type of the collective excitations in the magnetized dielectrics, which we called the spin current waves. We focus our attention on the waves propagating perpendicular to the external magnetic field.

We investigate the ground state persistent spin current and the pair entanglement in one-dimensional antiferromagnetic anisotropic Heisenberg ring with twisted boundary conditions. By solving Bethe ansatz equations numerically, we calculate the dependence of the ground state energy on the total magnetic flux through the ring, and the resulting persistent current. Motivated by the recent development of the quantum entanglement theory, we study the properties of the ground state concurrence under the influence of the flux through the anisotropic Heisenberg ring. We also include an external magnetic field and discuss the properties of the persistent current and the concurrence in the presence of the magnetic field.

We investigate theoretically the spin current and spin current induced electric field in a weak Rashba spin-orbit coupling quantum wire (QW) using a definition for spin current by means of scattering matrix. It is found that there exists two non-zero linear spin current density elements which have oscillation peaks at the center of QW and their strengths can be changed by the number of propagation modes and Rashba constant, respectively. Moreover, the spin current induced electric field has also been calculated and its strength is measurable with present technology with which can be used to detect spin current.

We consider a lattice model in which phonons scatter with pairs of electrons carrying a net spin current. All the energy eigenvalues and eigenvectors of this model can be obtained analytically. For a suitable choice of parameters the ground state consists of a Fermi sea of non-interacting electrons, with a layer of paired electrons on top of it. The binding energy of one electron pair is partly canceled by increased kinetic energy of another pair of electrons. This results in a momentum-dependent gap in the spectrum of the electrons.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.

We propose a device that allows for magnetization switching in nanomagnets by means of a pure spin current induced by the spin Hall effect. For this purpose we combine the ideas of magnetization switching of a ferromagnet by a spin current produced via the spin accumulation at a ferromagnet/nonmagnet interface with the electronic measurement of the direct spin Hall effect, and the theoretical material design to identify systems with a large spin Hall angle and an appropriate spin diffusion length. We will discuss the device design with respect to the size of the charge and spin currents. Based on ab initio calculations, we predict dilute alloys ideally suited for this application. Noble metals with single-sheeted Fermi surfaces, doped with either heavy impurities like Bi and Pb in Cu or Bi in Ag and light impurities like C and N in Au, seem to be the best candidates for a spin Hall angle larger than 5%.

The mutual interaction between spin current and magnetization is a key phenomenon in spintronics. This interaction leads to a spinmotive force, a mechanism of energy-transfer from magnetization into conduction electrons. In this paper, the basic concepts and recent developments of the spinmotive force are introduced.

Pure spin currents carry information in quantum spintronics and could play an essential role in the next generation low-energy-consumption electronics. Here, we theoretically predict that the magnetic field can induce a quantum spin current without a concomitant charge current in metals without time reversal symmetry ${𝒯}$ and inversion symmetry ${𝒫}$ but respect the combined ${𝒫}{𝒯}$ symmetry. It is governed by the magnetic moment of the Bloch states on the Fermi surface, and can be regarded as a spinful generalization of the gyrotropic magnetic effect in ${𝒫}$-broken metals. The effect is explicitly studied for a minimal model of an antiferromagnetic Dirac semimetal, where the experimental signature is proposed. We further propose candidate materials, including topological antiferromagnetic Dirac semimetals, Weyl semimetals and tenary Heusler compounds.

We show that a charge current and a spin current are pumped from the spin dynamics in the presence of the spin-orbit interaction. We are particularly interested the inverse spin Hall effect which converts spin currents into charge ones. This conversion mechanism is demonstrated based on the conservation laws of charge and spin. The result is compared with the microscopic calculation.

Multiferroics, the materials in which both (anti)ferromagnetism and ferroelectricity can coexist, are the prospective host of the gigantic magnetoelectric (ME) effect. The multiferroics based on the spin-current (or inverse Dzyaloshinskiy-Moriya interaction) mechanism have recently been proved to realize in many cycloidal and conical spin states of frustrated magnets, in which the clamping between the magnetic and ferroelectric domains can show up. Recent advance in the research on the dynamical ME effects toward the electrical control of magnetism is presented.

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.

Spin transport in a magnetically nonuniform structure can lead to transfer of angular momentum from conduction electrons to local magnetization. This, in turn, gives rise to a spin-transfer torque, which can modify magnetic state of the system. Another mechanism of current-induced spin torque relies on spin-orbit interactions. However, the spin torque can be induced not only by electric field driving the current, but also by a temperature gradient which drives a thermocurrent due to the thermoelectric phenomena. Both current- and thermallyinduced spin torques allow to control and manipulate magnetic moments.