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

Research in the use of organic polymers as the active semiconductors in light-emitting diodes has advanced rapidly, and prototype devices now meet realistic specifications for applications. These achievements have provided insight into many aspects of the background science, from design and synthesis of materials, through materials fabrication issues, to the semiconductor physics of these polymers.

Electroluminescence in conjugated polymers

Charge-Transfer and Energy-Transfer Processes in π-Conjugated Oligomers and Polymers: A Molecular Picture

The canonical example of a quantum-mechanical two-level system is spin. The simplest picture of spin is a magnetic moment pointing up or down. The full quantum properties of spin become apparent in phenomena such as superpositions of spin states, entanglement among spins, and quantum measurements. Many of these phenomena have been observed in experiments performed on ensembles of particles with spin. Only in recent years have systems been realized in which individual electrons can be trapped and their quantum properties can be studied, thus avoiding unnecessary ensemble averaging. This review describes experiments performed with quantum dots, which are nanometer-scale boxes defined in a semiconductor host material. Quantum dots can hold a precise but tunable number of electron spins starting with 0, 1, 2, etc. Electrical contacts can be made for charge transport measurements and electrostatic gates can be used for controlling the dot potential. This system provides virtually full control over individual electrons. This new, enabling technology is stimulating research on individual spins. This review describes the physics of spins in quantum dots containing one or two electrons, from an experimentalist’s viewpoint. Various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements. Furthermore, experimental techniques are discussed that allow for 1 the rotation of an electron spin into a superposition of up and down, 2 the measurement of the quantum state of an individual spin, and 3 the control of the interaction between two neighboring spins by the Heisenberg exchange interaction. Finally, the physics of the relevant relaxation and dephasing mechanisms is reviewed and experimental results are compared with theories for spin-orbit and hyperfine interactions. All these subjects are directly relevant for the fields of quantum information processing and spintronics with single spins i.e., single spintronics.

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Spins in few-electron quantum dots

Spin dynamics in semiconductors

This article reviews the current status of spin dynamics in semiconductors which has achieved a lot of progress in the past years due to the fast growing field of semiconductor spintronics. The primary focus is the theoretical and experimental developments of spin relaxation and dephasing in both spin precession in time domain and spin diffusion and transport in spacial domain. A fully microscopic many-body investigation on spin dynamics based on the kinetic spin Bloch equation approach is reviewed comprehensively.

A realistic pseudopotential model is introduced to investigate the phonon-induced spin relaxation of conduction electrons in bulk silicon. We find a surprisingly subtle interference of the Elliott and Yafet processes affecting the spin relaxation over a wide temperature range, suppressing the significance of the intravalley spin-flip scattering, previously considered dominant, above roughly 120 K. The calculated spin relaxation times T1 agree with the spin resonance and spin injection data, following a T-3 temperature dependence. The valley anisotropy of T1 and the spin relaxation rates for hot electrons are predicted.

Theory of the Spin Relaxation of Conduction Electrons in Silicon

Electron spin relaxation in bulk III-V semiconductors is investigated from a fully microscopic kinetic spin Bloch equation approach where all relevant scatterings, such as, the electron--nonmagnetic-impurity, electron-phonon, electron-electron, electron-hole, and electron-hole exchange (the Bir-Aronov-Pikus mechanism) scatterings are explicitly included. The Elliott-Yafet mechanism is also fully incorporated. This approach offers a way toward thorough understanding of electron spin relaxation both near and far away from the equilibrium in the metallic regime. The dependences of the spin relaxation time on electron density, temperature, initial spin polarization, photo-excitation density, and hole density are studied thoroughly with the underlying physics analyzed. We find that these dependences are usually qualitatively different in the nondegenerate and degenerate regimes. In contrast to the previous investigations in the literature, we find that: (i) In $n$-type materials, the Elliott-Yafet mechanism is less important than the D'yakonov-Perel' mechanism, even for the narrow band-gap semiconductors such as InSb and InAs. (ii) The density dependence of the spin relaxation time is nonmonotonic and we predict a peak in the metallic regime in both $n$-type and intrinsic materials. (iii) In intrinsic materials, the Bir-Aronov-Pikus mechanism is found to be negligible compared with the D'yakonov-Perel' mechanism. We also predict a peak in the temperature dependence of spin relaxation time which is due to the nonmonotonic temperature dependence of the electron-electron Coulomb scattering in intrinsic materials with small initial spin polarization. (iv) In $p$-type III-V semiconductors, the Bir-Aronov-Pikus mechanism dominates spin relaxation in the low-temperature regime only when the photoexcitation density is low. When the photoexcitation density is high, the Bir-Aronov-Pikus mechanism can be comparable with the D'yakonov-Perel' mechanism only in the moderate temperature regime roughly around the Fermi temperature of electrons, whereas for higher or lower temperature it is unimportant. The relative importance of the Bir-Aronov-Pikus mechanism decreases with the photoexcitation density and eventually becomes negligible at sufficiently high photoexcitation density. The effect of electric field on spin relaxation in $n$-type III-V semiconductors is also studied with behaviors very different from those in the two-dimensional case reported. Finally, we find good agreement of our calculation with the experimental results.

Electron-spin relaxation in bulk III-V semiconductors from a fully microscopic kinetic spin Bloch equation approach

Optical responses of graphene in the presence of intense circularly and linearly polarized terahertz fields are investigated based on the Floquet theory. We examine the energy spectrum and density of states. It is found that gaps open in the quasienergy spectrum due to the single-photon and multiphoton resonances. These quasienergy gaps are pronounced at small momentum, but decrease dramatically with the increase of momentum, and finally tend to be closed when the momentum is large enough. Due to the contribution from the states at large momentum, the gaps in the density of states are effectively closed, in contrast to the prediction in the previous work by Oka and Aoki [Phys. Rev. B 79, 081406(R) (2009)]. We also investigate the optical conductivity for different field strengths and Fermi energies, and show the main features of the dynamical Franz-Keldysh effect in graphene. It is discovered that the optical conductivity exhibits a multi-steplike structure due to the sideband-modulated optical transition. It is also shown that dips appear at frequencies being the integer numbers of the applied terahertz field frequency in the case of low Fermi energy, originating from the quasienergy gaps at small momentums. Moreover, under a circularly polarized terahertz field, we predict peaks in the middle of the ``steps'' and peaks induced by the contribution from the states around zero momentum in the optical conductivity.

M. W. Wu

Papers

Spin dynamics in semiconductors

Spin dynamics in semiconductors

Theory of the Spin Relaxation of Conduction Electrons in Silicon

Electron-spin relaxation in bulk III-V semiconductors from a fully microscopic kinetic spin Bloch equation approach

Optical response of graphene under intense terahertz fields