# Unpaired hole-particles probe quantum dot asymmetry

**In short: We demonstrate that two unpaired holes trapped within a nanometer sized quantum dot act as an efficient probe of the dot symmetry. Our finding enables highly accurate characterization of dot asymmetry, and it may therefore be used to locate quantum dots with the high symmetry needed to generate polarization-entangled photons required for applications within quantum cryptography and quantum computing.**

Perfectly symmetric semiconductor quantum dots are potential building blocks of future optical quantum information systems, including quantum cryptography for secure data sharing as well as quantum computing. High symmetry is needed to generate the, for these systems, crucial polarization-entangled photons. It is however a huge challenge to fabricate quantum dots with such high symmetry. Part of the problem lies in the size of a typical quantum dot – an extremely small three-dimensional crystalline object with a typical radius of 10 nanometers – making it very hard to monitor and control its size and shape. Therefore, there is a need for efficient and accurate characterization of quantum dot asymmetry.

Quantum dots are often referred to as artificial atoms since they have many properties in common with single atoms. In particular, they both exhibit a set of fully quantized energy levels. Each energy level in a quantum dot can hold up to two paired particles. According to the Pauli exclusion principle, two unparied particles must go into different energy levels. In this case a pure quantum mechanical effect - the exchange interaction - comes into play. This effect originates from the indistinguishability of the two particles. In atom physics, such exchange interactions are known to modify the electron energy levels and form so-called singlet and triplet states. In a quantum dot the effect of exchange is different, due to its crystalline nature and the existence of two types of charge carrying particles - in addition to electrons we have holes, which is the absence of electrons acting as positive particles.

Unpaired electrons in quantum dots have been studied for long and it is known that two electrons to a very good approximation form singlet and triplet states analogous to atom physics. These states are virtually unaffected by any quantum dot shape asymmetry. However, the effect of hole exchange is much less explored.

In our work, we demonstrate theoretically that two unpaired holes either form singlet and triplet-like states, as for electrons, or two doublet states. Which of the two cases that occurs depends on the nature of the involved energy levels. Moreover, one of the doublets is strongly affected by dot asymmetry, with a significant energy splitting upon symmetry breaking.

An experimental approach consisting of optical characterization, via the well known photoluminescence technique, was used to experimentally measure the energy spectrum of unpaired holes in a quantum dot. Ideally the holes should form doublets which then could be detected using this experimental approach. In photoluminescence measurements, a laser beam shines monochromatic light onto a quantum dot, causing the dot itself to emit light with a rather complex spectrum. This spectrum carries detailed information about the particles remaining in the dot after photon emission. In particular, the spectral features of two remaining holes can be identified and analyzed. A perfectly symmetric quantum dot is theoretically expected to exhibit precisely two peaks in a spectrum, corresponding to the two doublets, while symmetry breaking is manifested by three peaks, since one of the doublets in asymmetric quantum dots splits into two peaks. Experimentally we observe three peaks with various degree of splitting of this doublet for all the studied quantum dots, indicating that all the investigated dots are, to some degree, asymmetric.

Our findings suggest an efficient and uninvasive characterization method probing quantum dot asymmetry. The energy splitting of the doublet is an important feedback parameter in the quantum dot fabrication process for a symmetry optimization loop. It can also be used for locating highly symmetric dots suitable for quantum information applications.

Details of this research are described in *Physical Reiview B* **88** 045321 (2013)

doi:10.1103/PhysRevB.88.045321

**Authors**

D. Dufåker, K. F. Karlsson, L. O. Mereni, V. Dimastrodonato, G. Juska, E. Pelucchi, and P. O. Holtz

**Contact**

Fredrik Karlsson, associate professor

Phone: +46 (0)13 28 25 33

E-mail: freka@ifm.liu.se

**Funding
**

- Swedish Research Council (VR).
- Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University.

Responsible for this page:
Fredrik Karlsson

Last updated:
02/11/14