Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots

We theoretically consider the effect of strain on the spin dynamics of a single heavy hole (HH) confined to a self-assembled quantum dot and interacting with the surrounding nuclei via hyperfine interaction. Confinement and strain hybridize the HH states, which show an exponential decay for a narrowed nuclear spin bath. For different strain configurations within the dot, the dependence of the spin decoherence time $T_2$ on external parameters is shifted and the nonmonotonic dependence of the peak is altered. Application of external strain yields considerable shifts in the dependence of $T_2$ on external parameters. We find that external strain affects mostly the effective hyperfine coupling strength of the conduction band (CB), indicating that the CB admixture of the hybridized HH states plays a crucial role in the sensitivity of $T_2$ on strain.

Figure 1

The decoherence rate $1/T_2$ for different internal strain configurations as a function of the Zeeman energy ${\omega }_n$. (a) For most configurations the maximum is shifted to the left with respect to the unstrained case except if $\mathrm{Tr}\mathit{\varepsilon }\gtrsim \xi$. (b) Large ${\omega }_n$, i.e., magnetic fields $B$ or polarizations $p$, cause a power-law decay of $1/T_2$. The legend in the lower panel is valid for both plots and denotes the strain configurations.

Figure 2

Shift of the peak of the decoherence rate located at ${\omega }_{n,\text{max}}$ when external strain ${\varepsilon }_{\parallel }$ up to the breaking limit is applied. In both panels the change is roughly linear. For the asymmetric lateral strain configuration (b) the relative change of ${\omega }_{n,\text{max}}$ is considerably larger than for the symmetric configuration (a). The legends display the internal strain configurations of the dots, ${\varepsilon }_{xx}^0$ and ${\varepsilon }_{yy}^0$, at ${\varepsilon }_{\parallel }=0$. For all configurations we keep ${\varepsilon }_{zz}=0.06$ constant.

Figure 3

The largest contributions to the hyperfine coupling as a function of applied external strain ${\varepsilon }_{\parallel }$. The relative change of the CB coupling (a) is much larger than the change of the LH coupling (b). In the legend the internal strain configurations of the dots, ${\varepsilon }_{xx}^0$ and ${\varepsilon }_{yy}^0$, at ${\varepsilon }_{\parallel }=0$ are displayed. Again we keep ${\varepsilon }_{zz}=0.06$ constant for all configurations.