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We present a microscopic model for a singly charged quantum dot (QD) ensembleto reveal the origin of the long-range effective interaction between theelectron spins in the QDs. Wilson's numerical renormalization group (NRG) isused to calculate the magnitude and the spatial dependency of the effectivespin-spin interaction mediated by the growth induced wetting layer.Surprisingly, we found an antiferromagnetic Heisenberg coupling for very shortinter-QD distances that is caused by the significant particle-hole asymmetry ofthe wetting layer band at very low filling. Using the NRG results obtained fromrealistic parameters as input for a semiclassical simulation for a large QDensemble, we demonstrate that the experimentally reported phase shifts in thecoherent spin dynamics between single and two color laser pumping can bereproduced by our model, solving a longstanding mystery of the microscopicorigin of the inter QD electron spin-spin interaction.

Microscopic origin of the effective spin-spin interaction in a semiconductor quantum dot ensemble