Exciton-exciton interactions in quantum wells: Optical properties and energy and spin relaxation

Abstract

The gas of interacting excitons in quantum wells is studied. We obtain the Hamiltonian of this gas by the projection of the electron-hole plasma Hamiltonian to exciton states and an expansion in a small density. Matrix elements of the exciton Hamiltonian are rather sensitive to the geometry of the heterostructure. The mean field approximation of the exciton Hamiltonian gives the blue shift and spin splitting of the exciton luminescence lines. We also write down the Boltzmann equation for excitons and estimate the energy and spin relaxation time resulting from the exciton-exciton scattering. Making use of these calculations we succeeded to explain some recent experimental results which have not been explained so far.

Pattern formation in the exciton inner ring

“…The repulsive interaction between indirect excitons in the CQW results in the exciton energy enhancement with density. 7,9,10,17,18,20,41,[47][48][49][50][51][52][53] The observed energy enhancement (Fig. 3) indicates that the exciton density increases with increasing P probe .…”

Superfluidity and collective properties of excitonic polaritons in gapped graphene in a microcavity

“…Therefore, we conclude that the superfluid density n s and Kosterlitz-Thouless temperature T c are decreasing functions of the gap δ in graphene and increasing functions of the exciton density n. Besides, it follows from Eq. (28), that Rabi splitting is decreasing function of the gap as Ω R ∼ δ −1/2 . The advantage of observing the superfluidity and BEC of polaritons formed by gapped graphene excitons and microcavity photons in comparison with these formed by quantum well excitons and microcavity photons is based on the fact that the superfluidity and BEC of polaritons formed by gapped graphene excitons can be controlled by the gap which depends on doping.…”

Scattering Rates and Lifetime of Exact and Boson Excitons

“…We then find that the first lines of eqs. (13)(14) are still valid with mnḠijmn ξ eff mn00 now equal to 2ξ eff ij00 . (Note that the similar sum for exact excitons gives 4ξ ij00 : This is actually the mathematical reason for the factor 2 change between the α's of eq.…”

“…Many works have been devoted to exciton-exciton (X-X) interactions [3][4][5][6][7][8][9][10][11][12][13][14]. They however [15] accept or end with an effective bosonic Hamiltonian, so that they do not tackle the consequences of transforming exact excitons into bosons.…”