On the interpretation of wave function overlaps in quantum dots

TY - JOUR

T1 - On the interpretation of wave function overlaps in quantum dots

AU - Stobbe, Søren

AU - Hvam, Jorn M.

AU - Lodahl, Peter

PY - 2011/4/1

Y1 - 2011/4/1

N2 - The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) 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.

AB - The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) 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.

U2 - 10.1002/pssb.201000875

DO - 10.1002/pssb.201000875

M3 - Journal article

SN - 0370-1972

VL - 248

SP - 855

EP - 858

JO - Physica Status Solidi (B): Basic Research

JF - Physica Status Solidi (B): Basic Research

IS - 4

ER -