On the interpretation of wave function overlaps in quantum dots

TL;DR

This paper clarifies that the common interpretation of wave function overlaps in quantum dots as a probability of electron-hole coincidence is incorrect, providing theoretical insights and experimental validation.

Contribution

It demonstrates that the envelope wave function overlap does not directly correspond to the probability of electron-hole coincidence, challenging a widespread assumption.

Findings

Theoretical analysis shows the mismatch between overlap integral and coincidence probability.

Predictions align well with recent experimental measurements.

Provides a new perspective on interpreting wave function overlaps in quantum dots.

Abstract

The spontaneous emission rate of excitons strongly confined in quantum dots is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability that the electron and the hole are located at the same point or region in space, i.e. they must coincide spatially to recombine. Here we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap integral, and the probability of electrons and holes coinciding and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We compare our qualitative predictions with recent measurements of the wave function overlap and find good agreement.