Biexcitons in highly excited CdSe nanoplatelets

F. García Flórez, Laurens D. A. Siebbeles, and H. T. C. Stoof

Phys. Rev. B 102, 115302 – Published 8 September 2020

Abstract

We present the phase diagram of free charges (electrons and holes), excitons, and biexcitons in highly excited CdSe nanoplatelets that predicts a crossover to a biexciton-dominated region at easily attainable low temperatures or high photoexcitation densities. Our findings extend previous work describing only free charges and excitons by introducing biexcitons into the equation of state, while keeping the exciton and biexciton binding energies constant in view of the relatively low density of free charges in this material. Our predictions are experimentally testable in the near future and offer the prospect of creating a quantum degenerate, and possibly even superfluid, biexciton gas. Furthermore, we also provide simple expressions giving analytical insight into the regimes of photoexcitation densities and temperatures in which excitons and biexcitons dominate the response of the nanoplatelets.

Received 1 April 2020
Revised 20 July 2020
Accepted 3 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.115302

Physics Subject Headings (PhySH)

Biexcitons Excitons

Core-shell nanoparticles II-VI semiconductors Multilayer thin films

Random phase approximation Statistical methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. García Flórez ^1,*, Laurens D. A. Siebbeles^2,†, and H. T. C. Stoof ^1,‡

¹Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princentonplein 5, 3584 CC Utrecht, The Netherlands
²Optoelectronic Materials Section, Department of Chemical Engineering, Delft University of Technology, Van der Maasweg 9, 2629 HZ, Delft, The Netherlands

^*f.garciaflorez@uu.nl
^†l.d.a.siebbeles@tudelft.nl
^‡h.t.c.stoof@uu.nl

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Vol. 102, Iss. 11 — 15 September 2020

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Images

Figure 1
Fraction of free charges (red, top left, label $q$ ), excitons (green, middle, label $X$ ), and biexcitons (blue, bottom right, label $X_{2}$ ), as a function of temperature $T$ and photoexcitation density scaled by the (three-dimensional) exciton Bohr radius squared $n_{γ} a_{0}^{2}$ . The white horizontal solid line corresponds to the region experimentally explored in Ref. [51], at the constant temperature $T = 294 K$ . The white dashed line marks the points for which the density of excitons and biexcitons is equal. The squares ( $⧫$ , from bottom to right) dotted line represents the photoexcitation density above which biexcitons become quantum degenerate. The circles ( $•$ , from right to top) dotted line represents the photoexcitation density above which excitons are expected to show signs of quantum degeneracy.
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Figure 2
Fraction of free charges $X_{q}$ as a function of temperature $T$ and photoexciation density scaled by the exciton Bohr area $n_{γ} a_{0}^{2}$ . The maximum number of free charges per Bohr area is $n_{q} a_{0}^{2} ≃ 0.1$ , with $a_{0}^{2} = 4.68 {nm}^{2}$ , obtained in the upper right corner.
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Figure 3
Fraction of excitons $X_{X}$ as a function of temperature $T$ and photoexciation density scaled by the exciton Bohr area $n_{γ} a_{0}^{2}$ . The dashed line is computed using Eqs. (8) and (9). The maximum number of excitons per Bohr area is $n_{X} a_{0}^{2} ≃ 1$ , with $a_{0}^{2} = 4.68 {nm}^{2}$ , obtained in the upper right corner.
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Figure 4
Fraction of biexcitons $X_{X_{2}}$ as a function of temperature $T$ and photoexciation density scaled by the exciton Bohr area $n_{γ} a_{0}^{2}$ . The dashed line is computed using Eq. (8). The maximum number of biexcitons per Bohr area is $n_{X_{2}} a_{0}^{2} ≃ 1$ , with $a_{0}^{2} = 4.68 {nm}^{2}$ , obtained in the lower right corner.
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Figure 5
Degeneracy parameter for excitons $η_{X} \equiv n_{X} λ_{X}^{2} / g_{s}^{2}$ as a function of temperature $T$ and photoexciation density scaled by the exciton Bohr area $n_{γ} a_{0}^{2}$ . The circles ( $•$ ) dotted line represents the photoexcitation density for which $η_{X} = 1 / 2$ , that is, when excitons are expected to show signs of quantum degeneracy. It is obtained from $n_{γ}^{•} (η_{X} = 1 / 2)$ , using Eq. (12). The minimum degeneracy temperature $T^{*}$ , computed using Eq. (13), is $T^{*} ≃ 569 K$ .
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Figure 6
Degeneracy parameter for biexcitons $η_{X_{2}} \equiv n_{X_{2}} λ_{X_{2}}^{2}$ as a function of temperature $T$ and photoexciation density scaled by the exciton Bohr area $n_{γ} a_{0}^{2}$ . The squares ( $⧫$ ) dotted line represents the photoexcitation density for which $η_{X_{2}} = 1$ , computed using Eq. (14). The maximum value of the degeneracy parameter is $η_{X_{2}} ≃ 9$ , however, points for which $η_{X_{2}} \geq 2$ are represented with the same color.
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