Exciton fine structure in CdSe nanoplatelets using a quasi-2D screened configuration-interaction framework

TL;DR

This paper tackles exciton binding energies and fine-structure splittings in CdSe nanoplatelets across ZnS crystal geometries by introducing a transferable quasi-2D screened configuration-interaction framework that combines DFT-derived single-particle states with a $\varepsilon_{2D}(q_{\|})$-based screening and a real-space Coulomb-cutoff to suppress spurious periodic interactions. The method computes Coulomb and exchange matrix elements via a screened interaction $W(\mathbf{q})$ built from a quasi-2D dielectric function and uses a Slater-determinant exciton basis to diagonalize the many-body Hamiltonian. Results across ZB(I), ZB(II), and WZ(I) show that the bright-bright splitting is largest in WZ due to intrinsic in-plane anisotropy, while ZB geometries display smaller but finite splittings from edge symmetry breaking; exciton binding energies decrease with increasing lateral size as confinement weakens. The framework delivers accurate, computationally efficient predictions and offers a transferable tool for studying excitons in other quasi-2D materials.

Abstract

We compute exciton binding energies and fine-structure splittings in CdSe nanoplatelets with two zincblende geometries and one wurtzite geometry, finding that the wurtzite structure exhibits the largest bright-bright splitting due to its intrinsic in-plane anisotropy, while the zincblende structures show smaller but finite splittings arising from atomistic symmetry breaking at edges and corners. These results are obtained using a theoretical framework that we developed, which combines DFT single-particle states with screened configuration interaction, a quasi-2D dielectric screening model, and an efficient Coulomb-cutoff scheme that eliminates periodic-image interactions and enables accurate Coulomb and exchange integrals at low computational cost. This methodology provides a transferable and practical route for studying excitons in CdSe nanoplatelets and other quasi-two-dimensional nanomaterials.

Figures (7)

• Figure 1: Quasi-2D dielectric function $\varepsilon_{2D}(q_{\parallel})$ of CdSe calculated using the Trolle et al.trolle2017model model along the 3D screening function of Resta resta1977thomas(blue line) used in the Trolle model. Results are shown for several effective layer thicknesses $d = L d_0$ ($L = 1, 2, 3, 4, 10, 20, 50$ ), where $d_0$ is 3.1 Å. As the layer thickness increases, the quasi-2D dielectric response gradually approaches the 3D limit.
• Figure 2: Cut-off function $f(x) = \frac{1}{1 + \exp[\beta(x - x_{\mathrm{cut}})]}$ shown for different values of the smoothness parameter $\beta$ and for a $x_{\mathrm{cut}} = 30 a.u.$. The same functional form applies to both in-plane and out-of-plane directions.
• Figure 3: CdSe nanoplatelet structure for three different configurations : (a) ZB(I) (b) ZB(II) and (c) WZ
• Figure 4: Four topmost valence band states (a) and bottom most conduction band states (b) for the zincblende (I) structure with a square lateral dimension of $31 \times 31\,\text{\AA}^2$
• Figure 5: Coulomb integrals $J_{\mathrm{vc}}$: (a) $J_{11}$, (b) $J_{12}$, (c) $J_{21}$, and (d) $J_{22}$ as a function of $n$, where the supercell has size $n \times n \times n$ and larger $n$ increases the vacuum separation between periodic images. Magenta dots show the raw data without the Coulomb cut-off. The green curve is a fit to $J(n) = a + b/n^{2}$, with $a$, the converged value at infinite vacuum separation, shown by the blue dashed line. Results from the Coulomb cut-off method are shown as red dashed lines.