Spin-Orbit Interaction and the Effective Masses of Holes in Germanium

Dresselhaus, G.; Kip, A. F.; Kittel, C.

doi:10.1103/physrev.95.568

Cited by 114 publications

(43 citation statements)

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“…The importance of spin-orbit (SO) coupling for the band structure of Bloch electrons was first noted by Elliott [1,2] and Dresselhaus et al [3]. Elliott [2] pointed out that we obtain (at least) a two-fold spin degeneracy of the energy bands k E ( ) n for each wave vector k throughout the Brillouin zone if space inversion is a good symmetry of the crystal structure.…”

mentioning

confidence: 81%

Focus on the Rashba effect

2015

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The Rashba effect, discovered in 1959, continues to supply fertile ground for fundamental research and applications. It provided the basis for the proposal of the spin transistor by Datta and Das in 1990, which has largely inspired the broad and dynamic field of spintronics. More recent developments include new materials for the Rashba effect such as metal surfaces, interfaces and bulk materials. It has also given rise to new phenomena such as spin currents and the spin Hall effect, including its quantized version, which has led to the very active field of topological insulators. The Rashba effect plays a crucial role in yet more exotic fields of physics such as the search for Majorana fermions at semiconductorsuperconductor interfaces and the interaction of ultracold atomic Bose and Fermi gases. Advances in our understanding of Rashba-type spin-orbit couplings, both qualitatively and quantitatively, can be obtained in many different ways. This focus issue brings together the wide range of research activities on Rashba physics to further promote the development of our physical pictures and concepts in this field. The present Editorial gives a brief account on the history of the Rashba effect including material that was previously not easily accessible before summarizing the key results of the present focus issue as a guidance to the reader.

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confidence: 81%

Focus on the Rashba effect

2015

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“…Figure 16 shows the shifts vs. T reported in [73] and a fit to a T 4 curve. Up to 20 K, the measured shifts follow well the T 4 dependence but fall a bit short of the T 4 prediction at 25 K and especially at 30 K, not surprisingly in view of the fact that for Cu 2 …”

Section: Other Materials: Cu 2 Omentioning

confidence: 91%

“…The most striking fact in this figure is the strong effect of the excitonic interaction: a strengthening of the 1 E structure seen around 3.5 eV (by nearly a factor of two) together with a weakening of the 2 E and ' 1 E structures (4.5 and 6 eV) so as to preserve the sum rule which applies to ω⋅ε 2 (ω). This effect is of a canonical nature: It is observed in most materials under consideration.…”

Section: Temperature and Isotope Effects On The Full ε 2 (ω) Spectra mentioning

confidence: 95%

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Electron–phonon interaction in tetrahedral semiconductors

Cardona

2005

Solid State Communications

163

141

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Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The oneelectron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T = 0).In this paper we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T 4 law (contrary to the Varshni T 2 result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g., CuCl) and possibly Ag (e.g., AgGaS 2 ). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.

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“…Consider a homogeneous non-degenerate semiconductor of the p-Ge type with constant carrier concentration placed in a weak electric field E along the (100) axis and magnetic field B along the (001) axis, with the dispersion law given by [3] where m, is the free electron mass; A , B, C are dimensionless constants describing the valence band parameters, i.e. the curvature and non-sphericity of constanbenergy surfaces.…”

Section: Theorymentioning

confidence: 99%

Study of the Hall Coefficient in p‐Type Germanium Taking into Account Anisotropic Charge Carrier Scattering

Gutsul

Kirnas

Litovchenko

et al. 1985

Physica Status Solidi (b)

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A quasi-momentum distribution function of light and heavy holes in p-type Ge is found by expanding the field and the collision terms of the kinetic equation in terms of the anisotropy parameter, indicating the degree of non-sphericity of constant energy surfaces, in the zeroth, first, and second order approximation. The above method for solving the kinetic equation enables one to calculate the magnetic field dependence of the Hall coefficient taking into account the complex structure of the valence band of p-Ge and the nature of carrier scattering. The calcuIated RHIRO = f ( B ) dependence is compared with the experimental values obtained on samples with p = 1.7 X x 1014 ~m -~ having an orientation E 11 (loo), B 11 (001) for T = 77 and 300 K.Durch Entwicklung der Feld-und StoBterme der kinetischen Gleichung nach dem Anisotropieparameter, der den Grad der Nicht-Sphirizitiit der Flachen konstanter Energie in nullter, erster und zweiter Niiherung angibt, wird eine Quasi-Impulsverteilungsfunktion der leichten und schweren Locher in p-leitendem Ge gefunden. Diese Methode zur Losung der kinetischen Gleichung ermoglicht die Berechnung der Abhangigkeit des Hallkoeffizienten vom Magnetfeld unter Berucksichtigung der komplexen Struktur des Valenzbandes von p-Ge und der Art der Tragerstreuung.Die berechnete RH/Ro = f(B)-Abhingigkeit wird mit experimentellen Werten an Proben mit p = 1,7 x 1014 und Orientierungen E I I (loo), B I I (001) bei T = 77 und 300 K verglichen.

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Spin-Orbit Interaction and the Effective Masses of Holes in Germanium

Cited by 114 publications

References 6 publications

Focus on the Rashba effect

Focus on the Rashba effect

Electron–phonon interaction in tetrahedral semiconductors

Study of the Hall Coefficient in p‐Type Germanium Taking into Account Anisotropic Charge Carrier Scattering

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