Excitonic analysis of many-body effects on the1s-2pintraband transition in semiconductor systems

Abstract

We present a detailed study of many-body effects associated with the intraband 1s-2p transition in two-and three-dimensional photoexcited semiconductors. We employ a previously developed excitonic model to treat effects of exchange and phase space filling (PSF). In this work, we extend the model to include intraband transitions and static free-carrier screening. The exciton transition energies are renormalized by many-body interactions, and the excitonic dynamical equations provide simple expressions for the individual contributions of screening, PSF and exchange. The excitonic model correctly predicts the blue shift and bleaching of the 1s exciton resonance due to exchange and PSF. Free-carrier screening is found to enhance these effects by lowering the binding energy of the 1s exciton. In contrast, the effects of free-carrier screening on the 1s-2p transition energy are subtler. For a coherent exciton system, in the absence of free-carrier screening, exchange and PSF lead to a blue shift of the transition energy. However, screening decreases the 1s binding energy faster than the 2p binding energy, which in turn decreases the transition energy. Thus screening effects oppose exchange and PSF, and the overall magnitude and sign of the 1s-2p transition energy shift depends on the free-carrier density. Specifically, for low to moderate excitation densities, exchange and PSF can be dominated by screening, leading to a net redshift of the transition energy. The results for two-and three-dimensional systems are qualitatively similar, although the magnitude of the shift is much smaller in three dimensions. the formalism: the effects of screening, exchange, and PSF on the response to terahertz fields.We start from the familiar semiconductor Hamiltonian 13,25where H 0 represents the one-body energies of electrons and holes, V e−e , V h−h , and V e−h are electron-electron, holehole, and electron-hole Coulomb interactions, and H I is the interaction Hamiltonian between the carriers and the optical and terahertz electric fields. We project this Hamiltonian onto a basis of pair operators using the Usui transformation. 13,28,37,43 This transformation is not unitary, and must be augmented with a suitable electron-hole pairing operator. For optically excited direct-gap semiconductors, it is natural to employ a pairing scheme matching electrons and holes with opposite momenta, such that the total pair crystal momentum is zero. This transformation introduces the electron-hole-pair creation (annihilation) operator, B † k (B k ), which creates (destroys) an electron with crystal momentumhk and a hole with crystal momentum, −hk. The commutation relation for these operators is 13,37which is identical to the canonical bosonic commutation relation, [B k ,B † k ] = 0, when k = k but is given by a fermionic anticommutation relation, {B k ,B † k } = 1, when k = k . We thus refer to the electron-hole pairs as quasibosons (qbosons). We note that the fermionic nature of the qbosons is also reflected in the identity

Intraband and intersubband many-body effects in the nonlinear optical response of single-wall carbon nanotubes

“…This expression can be developed in the case of a contact interaction potential neglecting the dielectric screening effects 40 . We obtain :…”

“…We recall that the S 22 exciton is predominantly built from states belonging to the second conduction and valence subbands of the nanotubes and are therefore distinct from those used to build the S 11 exciton. In order to compute the spectral shift, we generalize the approach developed by Parks et al 39 in the case of two-dimensional structures. We again consider a contact interaction potential and we restrict our calculations to the 1s states of both the S 11 and the S 22 excitons.…”

Enhanced squeezing by absorption

“…The coherence is visible in the Rayleigh-peak at the laser frequency, and hence, it only scales with the absorption at ω L , as given in equation (21). The intensity of the quantum-well fluorescence, I q ∝  †Â q , was already discussed above.…”

Density dependence of the terahertz absorption spectra in optically excited semiconductors

“…Recently, the intraexciton 1s–2p transition energy and the 1s exciton creation energy in two‐ and three‐dimensional systems have theoretically been studied in Refs. , based on the exciton picture where the quasi‐Boson operator corresponding to excitons is introduced by the Usui transformation.…”

“…In contrast with Refs. , the present analysis is based on the e–h picture, and THz absorption spectra are calculated by solving the equation‐of‐motion for the transverse dielectric function.…”