Temperature-dependent electron Landégfactor and the interband matrix element of GaAs

Abstract

Very high precision measurements of the electron Landé g factor in GaAs are presented using spin-quantum beat spectroscopy at low excitation densities and temperatures ranging from 2.6 to 300 K. In colligation with available data for the temperature-dependent effective mass temperature dependence of the interband matrix element within a common five-level k · p theory can model both parameters consistently. A strong decrease in the interband matrix element with increasing temperature consistently closes a long lasting gap between experiment and theory and substantially improves the modeling of both parameters. DOI: 10.1103/PhysRevB.79.193307 PACS number͑s͒: 78.55.Cr, 71.18.ϩy, 78.20.Ci, 78.47.Cd The semiempirical k · p theory is a universal tool to calculate the band structure in semiconductors and semiconductor heterostructures and is regularly employed in such different fields as the physics of semiconductor laser design, the quantum Hall effect and spintronics. The part of the theory describing magnetic field related phenomena has been extensively improved since its introduction by Kane 1 and Luttinger and Kohn 2 in the mid fifties. Nowadays, five and more band k · p models are state of the art and many lowtemperature experiments have confirmed the incredible accuracy of k · p calculations. [3][4][5][6][7][8] All these experiments support the validity of k · p theory whereas a single but central experiment, which measures the temperature dependence of the electron Landé g factor in GaAs, shows a strong discrepancy between experiment and k · p theory. 9In this Brief Report we present extremely high precision, temperature-dependent measurements of the electron Landé g factor and show that by introducing a temperaturedependent interband matrix element yields a consistent explanation for the temperature dependence of the electron Landé g factor and the effective mass within common k · p theory, while keeping full temperature dependence on the very well-known interband critical points. The k · p theory is a perturbation theory calculating the electronic band structure by expansion around a single point in the Brillouin zone. In direct semiconductors such as GaAs, the high symmetry ⌫ point is the natural expansion point. The only input parameters are in this case the measured band gaps at k = 0 and the interband matrix elements ͑P , PЈ , PЉ ,...͒. The change in the band-gap energies with the lattice temperature are very well known for GaAs and the only remaining relevant parameter which does not possess a direct experimental access is the interband matrix element P or the related Kane energy E P = ͑2m 0 / ប 2 ͒P 2 , respectively. 1 The temperature dependence of P has been assumed to be marginal since P is inversely proportional to the interatomic distance a ͑Ref. 10͒ and the well-known change in a with temperature T due to anharmonic lattice potential is small. According to the relation E P ϰ 1 / a 2 between 0 and 300 K E P should change about −0.4% or less.11,12 However, this procedure only considers the static...

Characterization of spin-orbit fields in InGaAs quantum wells

“…The negative sign is inferred from the theoretical model in which band-gap dependent corrections of the g-factor are subtracted from a positive value of 2 [14]. we observe a small increase of the negative g-factor towards zero, which is in agreement with observations in GaAs that were explained by a temperature dependence of the dipole matrix elements between the conduction and valence bands [16]. The spin decay time τ monotonically increases if T is lowered, reaching more than 1 ns at 10 K. Figure 2(c) shows the corresponding decay rate 1/τ .…”

Ultrahigh Bandwidth Spin Noise Spectroscopy: Detection of Largeg-Factor Fluctuations in Highly-n-Doped GaAs

“…The negative sign is assigned from the relation g à ¼ À0:48 þ E F . We determine the factor which reflects the energy dependence of the Landé g-factor to % 5:1 eV À1 for this doping concentration and attribute the deviation from the commonly known factor of 6:3 eV À1 for slightly doped samples [20,21] to bandgap renormalization arising from the high doping concentration. The deviation of g à being a constant is less than 10 À3 T À1 which is at least a factor of 5 lower than for low doped GaAs at low temperatures.…”

Semiconductor spintronics

“…The k · p theory can describe quite well a wide range of low-temperature experimental results. When increasing temperature, however, discrepancies between the measured effective masses and Landé g-factor in GaAs and the corresponding predictions of the temperature-independent k·p theory have been observed (Hopkins et al, 1987;Hazama et al, 1986;Oestreich and Rühle, 1995;Hübner et al, 2006).…”

“…For the case of GaAs C 1 = −0.02 (Hübner et al, 2006). In addition to the temperature dependence of the energy band-gaps one has to consider also the changes in the strength of the different momentum matrix elements.…”