Response properties of III-V dilute magnetic semiconductors including disorder, dynamical electron-electron interactions, and band structure effects

A theory of the electronic response in spin and charge disordered media is developed with the particular aim to describe III-V dilute magnetic semiconductors like Ga${}_{1-x}$Mn${}_x$As. The theory combines a detailed $\mathbf{k}·\mathbf{p}$ description of the valence-band, in which the itinerant carriers are assumed to reside, with first-principles calculations of disorder contributions using an equation-of-motion approach for the current response function. A fully dynamic treatment of electron-electron interaction is achieved by means of time-dependent density-functional theory. It is found that collective excitations within the valence-band significantly increase the carrier relaxation rate by providing effective channels for momentum relaxation. This modification of the relaxation rate, however, has only a minor impact on the infrared optical conductivity in Ga${}_{1-x}$Mn${}_x$As, which is mostly determined by the details of the valence-band structure and found to be in agreement with experiment.

Figure 1

Schematic diagram of the possible single-particle excitations in the valence band of a $p$-type semiconductor. Dashed lines indicate intravalence-band excitations within the heavy-hole band (hh), within the light-hole band (lh), and intervalence-band excitations between heavey-hole and light-hole bands (hh-lh) and between split-off and heavy hole and light hole bands (so).

Figure 2

Imaginary part of the noninteracting density and longitudinal spin response functions in $p$-doped GaAs for different wave vectors (a) $q=0.003\hspace{0.5em}{\AA }^{-1}$ and (b) $q=0.05\hspace{0.5em}{\AA }^{-1}$. The hole concentration is $p=3.5\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$.

Figure 3

Schematic diagram of the excitation spectrum within the semiconductor valence band. Labels indicate the edges of single-particle excitation regions within the heavy-hole band (hh), within the light-hole band (lh), between heavy-hole and light hole bands (hh-lh), and between the split-off band and heavy- and light-hole bands (so); see Fig. 1. As a result, the plasmon mode in the valence band lies entirely within the single-particle excitation spectrum and is effectively suppressed due to Landau damping.

Figure 4

Dispersion (dashed black) and lifetime broadening (solid red) of the valence band plasmon calculated for the $p$-doped GaAs with the hole concentration of $p=3.5\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$. Dotted lines correspond to the onset of the intraband single-particle excitations within the light-hole and heavy-hole bands.

Figure 5

Total (charge and spin) carrier relaxation rate for Ga${}_{0.948}$Mn${}_{0.052}$As with hole concentration $p=3\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$. Dashed line: static screening model. Solid line: evaluation of Eq. (10) with full dynamic TDDFT treatment of electron interaction. See discussion in text.

Figure 6

Infrared conductivity of ferromagnetic Ga${}_{0.948}$Mn${}_{0.052}$As with hole concentration $p=3\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$. Calculations are performed according to Eq. (12), and using a relaxation rate obtained through Eq. (10) (solid line) or a fixed $\tau {}^{-1}=230\hspace{0.5em}{\mathrm{ps}}^{-1}$ (dashed line). Symbols are the experimental data of Ref. 40.

Figure 7

Band structure of ferromagnetic Ga${}_{0.95}$Mn${}_{0.05}$As with hole concentration $p=3.5\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$. Alignment of localized spins results in strongly anisotropic valence band spin splitting. Inset shows a cut of the Fermi surface by the plane $k_y=0$.

Figure 8

Temperature dependence of infrared conductivity of Ga${}_{0.948}$Mn${}_{0.052}$As with hole concentration $p=3\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$ and $T_c=70$ K calculated with weak-disorder, lifetime broadening of $\Gamma =5$ meV.

Figure 9

Temperature dependence of the infrared conductivity of Ga${}_{0.948}$Mn${}_{0.052}$As with hole concentration $p=3\times {10}^{20}\hspace{0.5em}{\mathrm{cm}}^{-3}$ and $T_c=70$ K. Upper panel: experimental data of Ref. 40. Lower panel: results from Eq. (12).