Pure dephasing and phonon dynamics in GaAs- and GaN-based quantum dot structures: Interplay between material parameters and geometry

The pure dephasing of excitons in quantum dot structures due to their interaction with acoustic phonons as well as the spatiotemporal dynamics of the created nonequilibrium phonon population is studied theoretically. The theory is applied to GaAs- as well as GaN-based heterostructures. A detailed analysis of the interplay between different material parameters, different quantum dot geometries, and different electric fields is presented. The optical polarization induced by an ultrashort laser pulse exhibits a characteristic nonexponential behavior: it decays on a pico- or subpicosecond time scale to a value that strongly depends on temperature, structure, and material parameters and is then retained until, on a typically much longer time scale, it finally decays because of electron-hole recombination or transitions to other states. We find that, in general, the remnant optical polarization is much higher in the GaAs-based structures than in the GaN-based structure mainly because of the strongly enhanced piezoelectric coupling in GaN quantum dots. The optical excitation also leads to the buildup of a phonon population consisting of a polaron part that remains localized in the region of the quantum dot and a traveling part that leaves the dot region at the speed of sound. This traveling part exhibits characteristic anisotropies reflecting both the anisotropy of the quantum dot structure and of the coupling matrix elements.

Figure 1

Electron and hole charge distributions (thick lines) and confinement potentials (thin lines) in $z$ direction (left column) and in the in-plane direction (right column) showing the different quantum dot structures examined: (a) and (b) GaAs QD without field (QD A), (c) and (d) GaAs QD with applied field (QD B), (e) and (f) GaN QD with built-in field (QD C).

Figure 2

Effective coupling matrix elements [see Eq. (12)] of the different coupling mechanisms for the three structures examined in the paper: (a) QD A, (b) QD B, and (c) QD C. The thick lines refer to the coupling parameters of the respective material of the structures, i.e., GaAs in (a) and (b), GaN in (c). The thin lines indicate the calculations performed with the coupling parameters of the other material. Note that the thin solid line in (b) has been multiplied by a factor of 0.1.

Figure 3

Optical polarization induced by a $\delta$-like laser pulse for QD A induced by different coupling mechanisms for three different temperatures: (a) piezoelectric coupling, (b) coupling via deformation potential, and (c) both mechanisms included. The thick lines correspond to the calculations using the (correct) GaAs coupling parameters, whereas the thin lines show the calculations employing GaN coupling parameters.

Figure 4

Optical polarization induced by a $\delta$-like laser pulse for QD B (left column) and QD C (right column) for three different temperatures. (a) and (b) piezoelectric coupling, (c) and (d) coupling via deformation potential, (e) and (f) both mechanisms included. The thick lines correspond to the (correct) coupling parameters of the respective material of the structures, i.e., GaAs (left column) and GaN (right column). The thin lines indicate the behavior because of the coupling parameters of the other material.

Figure 5

Long-time values of the optical polarization due to coupling via both mechanisms for the three different structures (a) QD A, (b) QD B, and (c) QD C. The thick lines refer to the coupling parameters of the respective material of the structures, i.e., GaAs in (a) and (b), GaN in (c). The thin lines indicate the calculations performed with the coupling parameters of the other material.

Figure 6

Spatially resolved population of phonons created by the deformation potential interaction (i.e., only LA phonons) for the three different structures (a) QD A, (b) QD B, and (c) QD C. Plotted are the profiles in the [010] plane at time $t=9\mathrm{ps}$.

Figure 7

Spatially resolved population of phonons created by the piezoelectric interaction (i.e., LA and TA phonons) for the three different structures (a) QD A, (b) QD B, and (c) QD C. Plotted are the profiles at time $t=9\mathrm{ps}$, for the GaAs structures (a) and (b) in the $\left[1\overline{1}0\right]$ plane and for the GaN structure (c) in the [010] plane. Note that in (c) the LA phonon contribution has been multiplied by a factor of 10.