Anomalous diamagnetic shift for negative trions in single semiconductor quantum dots

Abstract

We report on the magnetic response of negative trions X − in single self-assembled InAs/GaAs quantum dots. Unlike the conventional quadratic diamagnetic shift for neutral excitons, the observed X − diamagnetic shifts are small and nonquadratic. In particular, we also observed a reversal in sign of the conventional diamagnetic shift. A theoretical analysis indicates that such anomalous behaviors for X − arise from an apparent change in the electron wave function extent after photon emission due to the strong Coulomb attraction induced by the hole in its initial state. This effect can be very pronounced in small quantum dots, where the electron wave function becomes weakly confined and extended much into the barrier region. When the electrons gradually lose confinement, the magnetic response of X − will transit gradually from the usual quadratic diamagnetic shift to a quartic dependence, and finally into a special paramagnetic regime with an overall negative energy shift.The diamagnetic shift of confined excitons has long been used as a measure of the spatial extent of the excitonic wave functions in various semiconductor nanostructures such as quantum wires, 1-4 quantum dots ͑QDs͒, 4-6 as well as quantum rings. 7 In a weak magnetic field B, the exciton diamagnetic shift is expected to exhibit a quadratic B dependence, i.e., ⌬E = ␥B 2 , with a diamagnetic coefficient ␥ proportional to the area of the excitonic wave function, which reflects both the spatial confinements and interparticle Coulomb interactions. 8 For excitons ͑X͒ strongly confined in QDs, where the single-particle energies dominate over the Coulomb energies, ␥ is a measure of the spatial confinement of the QDs, while the magnetic responses of interparticle Coulomb energies only appear as correction terms to the overall diamagnetism. This simple picture is also true for biexcitons ͑XX͒ and trions ͑X + or X − ͒ strongly confined in QDs, except for a slight but systematic difference in ␥ due to the different magnetic responses of interparticle Coulomb energies. 6 On the other hand, when excitons are weakly confined in QDs such that Coulomb energies dominate over the single-particle energies, ␥ becomes a measure of the magnetic response of Coulomb energies. For exciton complexes weakly confined in QDs, the diamagnetic behaviors are expected to be more complicated because of the more elaborate Coulomb interactions. In particular, it has been theoretically predicted that a weakly confined negative trion ͑X − ͒ in large-size QDs would exhibit a negative magnetic dispersion, 5 based on the interpretation of the reported weak negative magnetic dispersion for X − in two-dimensional systems. 9,10 However, such an unusual behavior of X − has not yet been observed in past works focused on charged trions in QD system, 11,12 probably because the condition to observe this anomalous behavior is critical as we shall explain in this Brief Report.In this Brief Report, we report on the magnetic response of negative trions ͑X − ͒ in single InAs/GaAs self-assembled QDs. We ...

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