Spin-Orbit Coupling Effects in Zinc Blende Structures
TL;DR: In this article, a character table for the group of the wave vector at certain points of symmetry in the Brillouin zone is given, and a possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure is presented.
Abstract: Character tables for the "group of the wave vector" at certain points of symmetry in the Brillouin zone are given. The additional degeneracies due to time reversal symmetry are indicated. The form of energy vs wave vector at these points of symmetry is derived. A possible reason for the complications which may make a simple effective mass concept invalid for some crystals of this type structure will be presented.
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TL;DR: Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems as discussed by the authors, where the primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport.
Abstract: 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.
9,158 citations
Cites background from "Spin-Orbit Coupling Effects in Zinc..."
...(71) is proportional to the cube of the lattice momentum, as was first found by Dresselhaus (1955)....
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...(71) is proportional to the cube of the lattice momentum, as was first found by Dresselhaus (1955). For GaAs a'0....
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TL;DR: The band structure of InSb is calculated using the k ·. p perturbation approach and assuming that the conduction and valence band extrema are at k = 0 as mentioned in this paper.
2,905 citations
TL;DR: In this article, the physics of spins in quantum dots containing one or two electrons, from an experimentalist's viewpoint, are described, and various methods for extracting spin properties from experiment are presented, restricted exclusively to electrical measurements.
Abstract: 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.
2,389 citations
Cites background from "Spin-Orbit Coupling Effects in Zinc..."
...We then retain Dresselhaus, 1955 HD2D, 001 = − px x + py y , 13 where depends on material properties and on pz 2 ....
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...This effect is known as the Dresselhaus contribution to the spin-orbit interaction Dresselhaus, 1955; Dyakonov and Kachorovskii, 1986; Wrinkler, 2003 ....
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TL;DR: In this article, a review of recent advances in the condensed matter search for Majorana fermions is presented, which has led many in the field to believe that this quest may soon bear fruit.
Abstract: The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.
2,156 citations
TL;DR: In this paper, the authors provide numerical and graphical information about many physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material, including properties of the material itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage.
Abstract: This review provides numerical and graphical information about many (but by no means all) of the physical and electronic properties of GaAs that are useful to those engaged in experimental research and development on this material. The emphasis is on properties of GaAs itself, and the host of effects associated with the presence of specific impurities and defects is excluded from coverage. The geometry of the sphalerite lattice and of the first Brillouin zone of reciprocal space are used to pave the way for material concerning elastic moduli, speeds of sound, and phonon dispersion curves. A section on thermal properties includes material on the phase diagram and liquidus curve, thermal expansion coefficient as a function of temperature, specific heat and equivalent Debye temperature behavior, and thermal conduction. The discussion of optical properties focusses on dispersion of the dielectric constant from low frequencies [κ0(300)=12.85] through the reststrahlen range to the intrinsic edge, and on the ass...
2,115 citations
References
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TL;DR: In this paper, the results of cyclotron resonance experiments on charge carriers in silicon and germanium single crystals near 4\ifmmode^\circ\else\textdegree\fi{}K were given.
Abstract: An experimental and theoretical discussion is given of the results of cyclotron resonance experiments on charge carriers in silicon and germanium single crystals near 4\ifmmode^\circ\else\textdegree\fi{}K. A description is given of the light-modulation technique which gives good signal-to-noise ratios. Experiments with circularly polarized microwave radiation are described. A complete study of anisotropy effects is reported. The electron energy surfaces in germanium near the band edge are prolate spheroids oriented along $〈111〉$ axes with longitudinal mass parameter ${m}_{l}=(1.58\ifmmode\pm\else\textpm\fi{}0.04)m$ and transverse mass parameter ${m}_{t}=(0.082\ifmmode\pm\else\textpm\fi{}0.001)m$. The electron energy surfaces in silicon are prolate spheroids oriented along $〈100〉$ axes with ${m}_{l}=(0.97\ifmmode\pm\else\textpm\fi{}0.02)m$; ${m}_{t}=(0.19\ifmmode\pm\else\textpm\fi{}0.01)m$. The energy surfaces for holes in both germanium and silicon have the form $E(k)=A{k}^{2}\ifmmode\pm\else\textpm\fi{}{[{B}^{2}{k}^{4}+{C}^{2}({{k}_{x}}^{2}{{k}_{y}}^{2}+{{k}_{y}}^{2}{{k}_{z}}^{2}+{{k}_{z}}^{2}{{k}_{x}}^{2})]}^{\frac{1}{2}}.$ We find, for germanium, $A=\ensuremath{-}(13.0\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(8.9\ifmmode\pm\else\textpm\fi{}0.1)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(10.3\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$; and for silicon, $A=\ensuremath{-}(4.1\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|B|=(1.6\ifmmode\pm\else\textpm\fi{}0.2)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$, $|C|=(3.3\ifmmode\pm\else\textpm\fi{}0.5)(\frac{{\ensuremath{\hbar}}^{2}}{2m})$. A discussion of possible systematic errors in these constants is given in the paper.
792 citations
TL;DR: In this article, the problem of finding the Brillouin zones is studied from the point of view of group theory, where a representation of the symmetry group is associated with the underlying problem.
Abstract: It is well known that if the interaction between electrons 1 a metal is neglected, the energy spectrum has a zonal ructure. The problem of these “Brillouin zones” is eated here from the point of view of group theory. In is theory, a representation of the symmetry group ol ie underlying problem is associated with every energy slue.
589 citations
TL;DR: In this paper, the authors investigated the circumstances under which two wave functions occurring in the Hartree or Fock solution for a crystal can have the same reduced wave vector and the same energy.
Abstract: The circumstances are investigated under which two wave functions occurring in the Hartree or Fock solution for a crystal can have the same reduced wave vector and the same energy. It is found that coincidence of the energies of wave functions with the same symmetry properties, as well as those with different symmetries, is often to be expected. Some qualitative features are derived of the way in which energy varies with wave vector near wave vectors for which degeneracy occurs. All these results, like those of the preceding paper, should be applicable also to the frequency spectrum of the normal modes of vibration of a crystal.
423 citations
351 citations
TL;DR: In this paper, a criterion is developed to facilitate calculation of when and how such additional degeneracy will occur, and the consequences of the reality of the Hamiltonian are tabulated for a number of cases.
Abstract: In the Hartree and Fock approximations the description of the electronic state of a crystal can be made in terms of one-electron wave functions and one-electron energies, which have a band structure. It is known that in addition to the "sticking together" of these energy bands caused by the spatial symmetry of the crystal, additional "sticking" may be necessitated by the fact that the Hamiltonian of the problem is real. In this paper a criterion is developed to facilitate calculation of when and how such additional degeneracy will occur. The consequences of the reality of the Hamiltonian are tabulated for a number of cases. It is pointed out that the same "sticking together" of bands occurs in the theory of the frequency spectrum of the normal modes of vibration of a crystal.
192 citations