Twisted-light-induced optical transitions in semiconductors: Free-carrier quantum kinetics

We theoretically investigate the interband transitions and quantum kinetics induced by light carrying orbital angular momentum, or twisted light, in bulk semiconductors. We pose the problem in terms of the Heisenberg equations of motion of the electron populations, and interband and intraband coherences. Our theory extends the free-carrier semiconductor Bloch equations to the case of photoexcitation by twisted light. The theory is formulated using cylindrical coordinates, which are better suited to describe the interaction with twisted light than the usual Cartesian coordinates used to study regular optical excitation. We solve the equations of motion in the low excitation regime, and obtain analytical expressions for the coherences and populations; with these, we calculate the orbital angular momentum transferred from the light to the electrons and the paramagnetic and diamagnetic electric current densities.

Figure 1

(Color online) First-order paramagnetic current for light with $l=1$ and polarization $\sigma -$. The center of the plot coincides with the beam axis. The factor $J_{m-l}\left(k_r^{\prime }r\right)J_m\left(k_{r}r\right)$ is drawn in dashed (red) line.

Figure 2

(Color online) First-order paramagnetic current for light with $l=1$. The center of each plot coincides with the beam axis. Each panel pictures a different slice along the $z$ axis, showing the wave nature and space variation of the pattern.

Figure 3

(Color online) First-order paramagnetic current for light with $l=2$. The center of the plot coincides with the beam axis. The space pattern is more complex than in the $l=1$ case and exhibits circulation around off-axis centers.