Confined1Sexcitons, Landau transitions, and cavity mode coupling in GaAs microcavities

Abstract

The reflection spectra of GaAs microcavities (MC) formed between ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ distributed Bragg reflectors were studied at $T=2\mathrm{K}$ and under a magnetic field applied perpendicularly to the layers (z direction). Several MC's were studied, whose length ${L}_{\mathrm{MC}}\ensuremath{\sim}{\ensuremath{\lambda}}_{\mathrm{exc}}=223\mathrm{nm}$ corresponds to the $1S$ exciton wavelength of bulk GaAs at $T=2\mathrm{K}$ $[E(1S)=1.515\mathrm{eV}].$ The spectra show a large number of sharp lines either within the broad MC-confined photon band, when the MC mode overlaps the continuum absorption, or within the upper Rabi split band when the MC mode is near resonance with the lowest $1S$ exciton states. The energy and intensity of these sharp lines vary with increasing magnetic field $(0lBl~4\mathrm{T}).$ For comparison, the reflection spectrum of a ${\ensuremath{\lambda}}_{\mathrm{exc}}$-wide GaAs layer (cladded by 100 nm-wide ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ layers) was similarly studied. It did not show the magnetic-field-dependent features observed in the MC samples. It is shown that the reflection spectra of the MC samples are determined by the resonant coupling between three types of excitations: (a) $1S$ excitons with ${k}_{z}g0$ that are spatially confined in the ${\ensuremath{\lambda}}_{\mathrm{exc}}$-wide MC, resulting in a quantization of their center of mass motion. (b) Landau transitions (magnetoexcitons) between electron and hole Landau levels with indices ranging up to $p=11.$ (c) MC-confined photons. The reflection spectra are calculated by constructing transfer matrices that describe light propagation along the z direction (in the MC and in each layer of the distributed Bragg reflectors) and introducing an energy-dependent dielectric function for the GaAs layer, in the form of a Lorentzian oscillator response function for the $1S$ exciton and for each one of the magnetoexcitons. The $1S$ exciton center of mass quantization is introduced by including its ${k}_{z}$ dispersion within the dielectric function and using Pekar's additional boundary condition. The calculated spectra fit reasonably well the experimental ones (in both energy and intensity). The fan diagrams show anticrossings between the spatially confined $1S$ exciton levels and the $pg~1$ magnetoexcitons, as they are tuned by the magnetic field. These anticrossings are observed experimentally only in the MC mode spectral range, as predicted by the model. Using the same model, the electronic excitations energy dependence on magnetic field is calculated for the ${\ensuremath{\lambda}}_{\mathrm{exc}}$-wide GaAs layer confined between the ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ layers (namely without the distributed Bragg reflectors). No anticrossings are obtained. It is thus concluded that the spatially confined $1S$ exciton levels and the $pg~1$ magnetoexcitons are coupled via their interaction with the MC-confined photons.