Unraveling the Mesoscopic Character of Quantum Dots in Nanophotonics

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Unraveling the Mesoscopic Character of Quantum Dots in Nanophotonics

P. Tighineanu, A. S. Sørensen, S. Stobbe, and P. Lodahl

Phys. Rev. Lett. 114, 247401 – Published 19 June 2015

Abstract

We provide a microscopic theory for semiconductor quantum dots that explains the pronounced deviations from the prevalent point-dipole description that were recently observed in spectroscopic experiments on quantum dots in photonic nanostructures. The deviations originate from structural inhomogeneities generating a large circular quantum current density that flows inside the quantum dot over mesoscopic length scales. The model is supported by the experimental data, where a strong variation of the multipolar moments across the emission spectrum of quantum dots is observed. Our work enriches the physical understanding of quantum dots and is of significance for the fields of nanophotonics, quantum photonics, and quantum-information science, where quantum dots are actively employed.

Received 29 August 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.247401

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Authors & Affiliations

P. Tighineanu^*, A. S. Sørensen, S. Stobbe, and P. Lodahl^†

Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark

^*petru.tighineanu@nbi.ku.dk
^†lodahl@nbi.ku.dk; http://www.quantum-photonics.dk/

Article Text

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Supplemental Material

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References

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Issue

Vol. 114, Iss. 24 — 19 June 2015

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Images

Figure 1
Unraveling the mesoscopic character of QDs in the vicinity of a GaAs-air interface. The presence of the interface breaks the parity symmetry of the environment in the $z$ direction. Since reflections occur at the interface (the circular white arrow), the imaginary part of the electric field $E (r)$ generated by the electric-dipole component, which triggers spontaneous emission, inherits this lack of symmetry and is curved (indicated by the green arrow). (a) In the dipole approximation, the QD current $j (r)$ (brown arrow) perceives only the parallel component but not the out-of-plane component (the “curvature”) of the electromagnetic field at its position. (b) In In(Ga)As self-assembled QDs, the current density flows along a curved path that resembles the shape of the field environment, thereby exchanging energy more efficiently with it. As a consequence, the spontaneous-emission decay rate is enhanced and the photons (red arrows) are emitted at a faster rate compared to the case in (a).
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Figure 2
Observation of deviations from dipole theory for QDs near an interface. (a) Measured decay rates versus distance $z_{0}$ to the GaAs-air interface (data points) at an energy of 1.27 eV (wavelength $λ_{0} \sim 975 nm$ ). The dipole (multipolar) theory is indicated by the black dashed (blue solid) line. A refractive index $n = 3.5$ of GaAs was used. The inset is a schematic illustrating the sample geometry. (b) Extracted mesoscopic strength $Λ / μ$ over the emission spectrum of QDs (red squares) along with the prediction of the theoretical model (blue dashed line) assuming that the QDs have a fixed in-plane size and only the height varies, cf. the Supplemental Material [20].
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Figure 3
Sketch illustrating the microscopic model for mesoscopic QDs. (a) The atomic lattice inside the QD is assumed to change periodicity at the position $z = z_{T}$ . (b) Sketch of how the Bloch function $u_{g}^{2}$ of the atomic lattice varies spatially inside the QD. (c) Illustration of the matrix elements $⟨ p_{x} ⟩ \equiv ⟨ u_{g} | {\hat{p}}_{x} | u_{e} ⟩$ and $⟨ p_{z} ⟩ \equiv ⟨ u_{g} | {\hat{p}}_{z} | u_{e} ⟩$ for the three colored unit cells in (a). The symmetry of the integrand is broken in the transition region around $z = z_{T}$ , giving rise to pronounced mesoscopic effects.
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Figure 4
The mesoscopic strength and the associated current density running through the QD. (a) Spectral dependence of the QD height predicted by the theoretical model. (b) Mesoscopic strength as a function of the in-plane size of the QD for three fixed QD heights. (c)–(f) Plots of quantum current densities for various QD geometries. (c) Homogeneous crystal lattice where the current flow is uniform and points in the direction of the dipole moment. (d) Inhomogeneous lattice for a QD radius of 5 nm giving rise to a nonuniform current flow following a curved path. The QD height is 4 nm. (e),(f) Same as (d) but for QD radii of 10 and 20 nm, respectively. In (c)–(f), both the length of the arrows and the color scale indicate the magnitude of the flow and the direction of the arrows indicates the pointwise direction of the flow. The dashed white line sketches the position and orientation of the QD.
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