magnetic optical transitions in quantum dots: part 2

Antiparallel beams of twisted light can produce new optical transitions between light hole and conduction band states in quantum dots.

In a previous post on light-hole transitions we showed that, according to theoretical studies, light-hole states in quantum dots (QD) could be excited at normal incidence, producing excitons with no band+spin angular momentum. Moreover, the envelope angular momentum (AM) of the electron was unchanged. The effect was induced by the $z$-component of the electric field. [1]

Here, we want to show that it may be possible to address other light-hole states, using the opto-magnetic interaction.

In Part 1 we proposed to analyze the opto-magnetic transition:
\begin{eqnarray*}
 \langle  {v, i \uparrow} \mid
  H_B
 \mid {c, j \uparrow} \rangle
&=&
   i \frac{q B_0}{2m}
   \sum_R \int_{{\text{cell}}} dr' \,
   {\cal E}_i^* u_{v}^* \left(  R_+ p'_z - z' P_+  \right) {\cal E}_j u_{c}
\end{eqnarray*}
connecting light-hole valence and conduction bands. The lower-case variables act at the level of the unit cell, and refer to the $z$-axis. Light-hole orbitals extend in the $z$ direction:
$$
|LH+\rangle = -1/\sqrt{6} [(|p_x\rangle + i |p_y\rangle)\downarrow - 2 |p_z\rangle)\uparrow]
$$
and so can be excited. On the other hand, upper-case coordinates act at the level of the whole semiconductor, and therefore they can affect the envelope function. This is in contrast to what happens for the excitation of light holes by an electric field $E_z$. This means that with $\sigma=-1$ and $\ell=2$ we can have an exciton with band+spin AM=0, but with envelope AM=1, see Fig. 1.

Figure 1: In red opto-magnetic transition producing an exciton with band+spin AM=0, but with envelope AM=1. In grey transitions induced by other beams, including TL with $E_z$. {note that the quantum numbers are named in a different way compared to Ref. [2]; here $J_z$ is the total angular momentum of the hole.}

Figure 1 makes clear that the use of single-pulse TL with different orientation and magnitude of OAM adds much versatility to the control of electronic states in quantum dots. [2]


REFERENCES

[1] GF Quinteiro, T Kuhn, Light-hole transitions in quantum dots: Realizing full control by highly focused optical-vortex beams, Phys. Rev. B 90, 115401 (2014).

[2]  G. F. Quinteiro, D. E. Reiter, T. Kuhn, Magnetic-optical transitions induced by twisted light in quantum dots, J. Phys.: Conf. Ser. 906 012014 (2017).