Insensitivity of spin dynamics to the orbital angular momentum transferred from twisted light to extended semiconductors

We study the spin dynamics of carriers due to the Rashba interaction in semiconductor quantum disks and wells after excitation with light with orbital angular momentum. We find that although twisted light transfers orbital angular momentum to the excited carriers and the Rashba interaction conserves their total angular momentum, the resulting electronic spin dynamics is essentially the same for excitation with light with orbital angular momentum $l=+\left|l\right|$ and $l=-\left|l\right|$. The differences between cases with different values of $\left|l\right|$ are due to the excitation of states with slightly different energies and not to the different angular momenta per se and vanish for samples with large radii where a $k$-space quasicontinuum limit can be established. These findings apply not only to the Rashba interaction but also to all other envelope-function-approximation spin-orbit Hamiltonians like the Dresselhaus coupling.

Figure 1

Diagonal elements of the density matrix ${\rho }_{cm\nu cm\nu }$ after an excitation of a cylindrical quantum disk with radius $R$ with a box-shaped pulse of length $t=5$ ps and orbital angular momentum $l$ of the light. (a) and (b) show the occupations of an $R=1.2\mu \text{m}$ quantum disk with $l=0$ and $l=5$, respectively. (c) and (d) display the occupations for a larger $R=5\mu \text{m}$ disk with $l=0$ and $l=5$. For a better comparison, the matrix elements are plotted against the energies ${\epsilon }_{cm\nu }$ instead of the indices $\nu$, and the absolute values of the occupations are rescaled.

Figure 2

Spin dynamics after excitation with twisted light with orbital angular momentum $l=\{-5,0,5\}$ and quantum-disk radius $R=1.2\mu \text{m}$ and with $l=\{0,5\}$ and $R=\{5\mu \text{m},10\mu \text{m}\}$.