Two-photon Indirect Optical Injection and Two-color Coherent Control in Bulk Silicon

TL;DR

This paper theoretically investigates two-photon indirect optical injection and two-color coherent control of carriers and spins in bulk silicon, revealing detailed selection rules, anisotropies, and temperature-dependent behaviors.

Contribution

It provides the first comprehensive theoretical analysis of two-photon indirect injection and coherent control in silicon, including phonon-assisted processes and polarization effects.

Findings

TA phonon-assisted transitions dominate at 4 K low energies

Carrier injection shows anisotropy and dichroism

Maximum spin polarization reaches 20% at 4 K

Abstract

Using an empirical pseudopotential description of electron states and an adiabatic bond charge model for phonon states in bulk silicon, we theoretically investigate two-photon indirect optical injection of carriers and spins and two-color coherent control of the motion of the injected carriers and spins. For two-photon indirect carrier and spin injection, we identify the selection rules of band edge transitions, the injection in each conduction band valley, and the injection from each phonon branch at 4 K and 300 K. At 4 K, the TA phonon-assisted transitions dominate the injection at low photon energies, and the TO phonon-assisted at high photon energies. At 300 K, the former dominates at all photon energies of interest. The carrier injection shows anisotropy and linear-circular dichroism with respect to light propagation direction. For light propagating along the $<001>$ direction, the carrier injection exhibits valley anisotropy, and the injection into the $Z$ conduction band valley is larger than that into the $X/Y$ valleys. For $\sigma^-$ light propagating along the $<001>$ ($<111>$) direction, the degree of spin polarization gives a maximum value about 20% (6%) at 4 K and -10% (20%) at 300 K, and at both temperature shows abundant structure near the injection edges due to contributions from different phonon branches. Forthe two-color coherent current injection with an incident optical field composed of a fundamental frequency and its second harmonic, the response tensors of the electron (hole) charge and spin currents are calculated at 4 K and 300 K. We show the current control for three different polarization scenarios. The spectral dependence of the maximum swarm velocity shows that the direction of charge current reverses under increase in photon energy.