Hole spin relaxation during the tunneling between coupled quantum dots

We investigate theoretically the spin transport in an array of Ge/Si quantum dots. In the frame of the tight-binding approach we calculate the probability of hole spin-flip for resonant tunneling between localized states in neighboring quantum dots. The tunneling between hole ground states occurs mainly with conservation of the spin. For excited states the probability of the spin-flip is higher. We find that the main source of the spin-flip is the structure-inversion asymmetry (SIA) of the Ge quantum dot. Every tunneling event is accompanied by the small rotation of the angular momentum and this provokes the spin-flip. Simple estimations of the time of spin relaxation caused by the SIA-mechanism give ${\tau }_{\mathrm{SIA}}\sim {10}^{-5}\mathrm{s}$.

Figure 1

The schematic sketch of the tunneling process with spin-flip.

Figure 2

The probabilities of tunneling processes with spin-flip (▾) and without it (∎) for the ground and excited hole states in Ge QD. The height of the Ge nanocluster $h=1.5\mathrm{nm}$, lateral size $l=15\mathrm{nm}$.

Figure 3

Size dependence of probabilities $P_1$ and $P_2$ of the tunneling with spin-flip (▾) and without it (∎) correspondingly for the ground hole state in Ge QD ($h=1.5\mathrm{nm}$, $l$ is changed). Inset, size dependence of the $P_2∕P_1$ ratio.

Figure 4

The distribution of the angular momentum for the ground state. The arrows schematically show the direction and magnitude of the vector $⟨\psi \mid \widehat{\mathbf{J}}\mid \psi ⟩$ along the line passing through the center of the QD base. For better representation we multiply the deviation angle by 5.

Figure 5

Model structure of molecules. Upper molecules (a), (b) have a structure-inversion-asymmetry. Lower molecules (c), (d) are without it. The arrows schematically show the direction of the angular momentum.

Figure 6

The probability density profiles for light hole part ($J_z=1∕2$, dashed line) and heavy hole part ($J_z=3∕2$, solid line) for the ground state inside the Ge quantum dot ($h=1.5\mathrm{nm}$, $l=15\mathrm{nm}$). Each curve was normalized to full probability density.