# Interlayer Bound Wannier Excitons in Germanium Sulfide

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## Abstract

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## 1. Introduction

## 2. Experimental and Theoretical Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Optical image and (

**b**) AFM image of the hBN-coated GeS flake showing areas of different thickness. (

**c**) Typical angle-resolved Raman spectra of the GeS flake. The relative intensity of the GeS Raman peaks changes as a function of the angle (0–150 degree) between the incident polarized light and the flake.

**Figure 2.**(

**a**–

**c**) Cathodoluminescence (CL) spectra of the GeS flakes with thickness of 97 nm, 68 nm, and 45 nm; all these spectra can be deconvoluted with four Gaussian components with centers at 1.69, 1.91, 2.35, and 3.02 eV. (

**d**) The substrate CL spectrum can be fitted with only two Gaussian components centered at 1.91 and 2.35 eV.

**Figure 3.**GeS crystal structure (Ge yellow, S blue) on the left and its Brillouin Zone on the right.

**Figure 4.**

**Left panel**: Bulk GeS DFT bandstructure neglecting relativistic effects (green, solid) and taking them into account (black, dashed) and its quasiparticle bandstructure (red, solid).

**Right panel**: Imaginary part of the dielectric functions calculated at the GW+BSE method, with light polarized along X, Y, and Z directions.

**Figure 5.**Plot of the square modulus of the first bright excitonic wavefuction, fixing the hole position near an S atom, represented by the white dot at the center. Side view on the left, top view on the right. Numbers indicates the layers with respect to the one with the hole.

**Figure 7.**Plot of ${\left|\psi \right|}^{2}$ for ${\mathrm{\Gamma}}_{v}$ (

**left**) and ${\mathrm{\Gamma}}_{c}$ (

**right**). In green the isosurfaces at $1\%$ of maximum value. The represented atoms are: Ge (black), S (gray).

**Figure 8.**(

**a**) The calculated absorption coefficient of bulk GeS, obtained averaging over the three components of the dielectric tensor. (

**b**) The CL spectra reported in Figure 2 after normalization with respect to the maximum intensity of the broad peak at ~2 eV.

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**MDPI and ACS Style**

Postorino, S.; Sun, J.; Fiedler, S.; Lee Cheong Lem, L.O.; Palummo, M.; Camilli, L.
Interlayer Bound Wannier Excitons in Germanium Sulfide. *Materials* **2020**, *13*, 3568.
https://doi.org/10.3390/ma13163568

**AMA Style**

Postorino S, Sun J, Fiedler S, Lee Cheong Lem LO, Palummo M, Camilli L.
Interlayer Bound Wannier Excitons in Germanium Sulfide. *Materials*. 2020; 13(16):3568.
https://doi.org/10.3390/ma13163568

**Chicago/Turabian Style**

Postorino, Sara, Jianbo Sun, Saskia Fiedler, Laurent O. Lee Cheong Lem, Maurizia Palummo, and Luca Camilli.
2020. "Interlayer Bound Wannier Excitons in Germanium Sulfide" *Materials* 13, no. 16: 3568.
https://doi.org/10.3390/ma13163568