  Recent experiments on semiconductor quantum dots have demonstrated the
ability to utilize a large quantum dot to mediate superexchange interactions
and generate entanglement between distant spins. This opens up a possible
mechanism for selectively coupling pairs of remote spins in a larger network of
quantum dots. Taking advantage of this opportunity requires a deeper
understanding of how to control superexchange interactions in these systems.
Here, we consider a triple-dot system arranged in linear and triangular
geometries. We use configuration interaction calculations to investigate the
interplay of superexchange and nearest-neighbor exchange interactions as the
location, detuning, and electron number of the mediating dot are varied. We
show that superexchange processes strongly enhance and increase the range of
the net spin-spin exchange as the dots approach a linear configuration.
Furthermore, we show that the strength of the exchange interaction depends
sensitively on the number of electrons in the mediator. Our results can be used
as a guide to assist further experimental efforts towards scaling up to larger,
two-dimensional quantum dot arrays.
