Terahertz response of confined electron-hole pair: crossover between strong and weak confinement

We analyze theoretically THz response of an electron-hole pair confined in a semiconductor nanoparticle. We show that the interplay of particle confinement and electron-hole Coulomb interaction leads to significant renormalizations and energy shifts in THz linear conductivity of the nanocrystal. We develop and evaluate models in the strong and the weak confinement regime in order to correctly address the effect of Coulomb interaction. In the weak confinement regime, we find solutions of the problem in a form similar to the Wannier wavefunction whose spatial extent is reduced as a consequence of the confinement. The resulting states are scalable down to the strong confinement regime, enabling a theoretical description of the exciton response for arbitrarily sized nanoparticles.