Spin polarization of photoelectrons in GaAs excited by twisted photons

Interband photoexcitation of electron states with the twisted photons in GaAs, a direct band-gap bulk semiconductor, is considered theoretically. Assuming linearity of the quantum transition amplitudes and applying Wigner-Eckart theorem, we derive a plane-wave expansion of twisted-photon amplitudes. We also obtain relative probabilities for magnetic sublevel population of the photoelectrons in conduction band. The approach for calculating the position-dependent electron polarization, resulting from photoabsorption of twisted light, is described for vertical transitions in the $\mathrm{\Gamma }$ point. Theoretical predictions for GaAs show modification of the magnitude and the sign of photoelectron polarization in the region near the photon's phase singularity.

Figure 1

Energy bands for GaAs, shown along with the transitions allowed for the twisted photons with right circular polarization. Numbers in the circles indicate squares of Clebsch-Gordan coefficients. In addition to transitions with $\mathrm{\Delta }m=1$ (solid vertical lines), c.f. Ref. [13], for the twisted photons the transitions with $\mathrm{\Delta }m=0$ (dash-dotted lines) and $\mathrm{\Delta }m=-1$ (dashed) are also allowed. For strained GaAs, only the transitions from $m=\pm 3/2$ sublevels can be selected by properly adjusting the laser's wavelength [14].

Figure 2

Photoexitation rate as a function of electron's distance to the optical vortex center for the vortex pitch angle ${\theta }_q=0.1$ rad; long-dashed blue is $m_{\gamma }=-2$, dot-dashed black is $m_{\gamma }=-1$, dashed red is $m_{\gamma }=0$, solid green is $m_{\gamma }=1$, dotted purple is $m_{\gamma }=2$. Incoming photon polarization is (a) left-circular, (b) right-circular.

Figure 3

Photoelectron polarization as a function of the electron's distance to the optical vortex center for the vortex pitch angle ${\theta }_q=0.1$ rad; long-dashed blue is $m_{\gamma }=-2$, dot-dashed black is $m_{\gamma }=-1$, dashed red is $m_{\gamma }=0$, solid green is $m_{\gamma }=1$, dotted purple is $m_{\gamma }=2$. GaAs sample and incoming photon polarization, are, respectively, (a) unstrained and left-circular, (b) unstrained and right-circular, (c) strained and left-circular polarization, and (d) strained and right-circular.

Figure 4

Photoelectron polarization averaged over the circular mesoscopic semiconducting target of radius $r$ centered at the beam axis with the pitch angle ${\theta }_q=0.1$ rad; long-dashed blue is $m_{\gamma }=-2$, dot-dashed black is $m_{\gamma }=-1$, dashed red is $m_{\gamma }=0$, solid green is $m_{\gamma }=1$, dotted purple is $m_{\gamma }=2$. GaAs sample and incoming photon polarization, are, respectively, (a) unstrained and left-circular, (b) unstrained and right-circular, (c) strained and left-circular polarization, and (d) strained and right-circular. Shadowed vertical regions indicate ten times lattice periods for GaAs $(r=5.65$ nm).