# Plasmon Resonance in a System of Bi Nanoparticles Embedded into (Al,Ga)As Matrix

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## Abstract

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## 1. Introduction

## 2. Calculation Methods and Computational Details

`FermiSurfer`[57].

## 3. Calculation Results and Discussion

#### 3.1. Electronic Structure and Dielectric Function of Bismuth

#### 3.2. Electronic Structure and Dielectric Function of Al${}_{x}$Ga${}_{1-x}$As

#### 3.3. Localized Surface Plasmons

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

LSPR | Localized surface plasmon resonance. |

NP | Nanoparticle. |

MBE | Molecular-beam epitaxy. |

VPE | Vapor-phase epitaxy. |

LT | Low temperature. |

PAW | Projector-augmented wave. |

GGA-PBE | Perdew–Burke–Ernzerhof generalized gradient approximation. |

vdW | van der Waals. |

BL | Bilayer. |

DFT-D3 | vdW functional with Becke–Johnson damping. |

mBJ | modified Becke–Johnson semilocal exchange potential. |

HSE06 | Heyd–Scuseria–Ernzerhof screened hybrid functional. |

QS$GW$ | Quasiparticle self-consistent $GW$. |

TRIM | Time reversal-invariant momentum. |

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**Figure 1.**(

**a**) Crystal structure of the bulk Bi. (

**b**) Bulk electronic spectra calculated within three approximations: GGA-PBE, metaGGA-mBJ, and HSE06 along high symmetry lines of the bulk Brillouin zone (see panel (

**d**)). (

**c**) Magnified view of the spectra near the Fermi level at the L point. (

**d**) Bulk Fermi surface calculated according to the GGA-PBE approach. (

**e**) Imaginary and real parts of the dielectric function $\epsilon \left(\omega \right)$ calculated within mBJ and PBE approaches in comparison with fitted experimental data from Ref. [40] (see keys for the meaning of line styles and colors). Insets show the changes in $\epsilon \left(\omega \right)$ calculated within mBJ approach within the energy range of interest (≈1–2.5 eV) under hydrostatic (left) and uniaxial (right) strain (dashed lines) in comparison with that for equilibrium lattice (solid lines).

**Figure 2.**Maps of the optical extinction spectra for systems of spherical Bi NPs embedded into Al${}_{x}$Ga${}_{1-x}$As semiconductor matrices of different chemical composition x. Solid lines mark the edges of the direct (${E}_{g}^{\Gamma}$) and indirect (${E}_{g}^{X}$, ${E}_{g}^{L}$) band gaps. The diameter of NPs is 10 nm. The filling factor is 1%. The Bi NPs are (

**a**) mechanically relaxed, (

**b**) stretched by 1% along trigonal axes and compressed by 0.5% in the perpendicular plane, and (

**c**) compressed by 0.5% in all the directions.

**Figure 3.**Maps of the differential optical extinction spectra for systems of spherical Bi NPs embedded into Al${}_{x}$Ga${}_{1-x}$As semiconductor matrices of different chemical composition x. The diameter of NPs is 10 nm. The filling factor is 1%. (

**a**) multipole contributions, (

**b**) volume-conserving uniaxial deformation, (

**c**) hydrostatic deformation.

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**MDPI and ACS Style**

Ushanov, V.I.; Eremeev, S.V.; Silkin, V.M.; Chaldyshev, V.V.
Plasmon Resonance in a System of Bi Nanoparticles Embedded into (Al,Ga)As Matrix. *Nanomaterials* **2024**, *14*, 109.
https://doi.org/10.3390/nano14010109

**AMA Style**

Ushanov VI, Eremeev SV, Silkin VM, Chaldyshev VV.
Plasmon Resonance in a System of Bi Nanoparticles Embedded into (Al,Ga)As Matrix. *Nanomaterials*. 2024; 14(1):109.
https://doi.org/10.3390/nano14010109

**Chicago/Turabian Style**

Ushanov, Vitalii I., Sergey V. Eremeev, Vyacheslav M. Silkin, and Vladimir V. Chaldyshev.
2024. "Plasmon Resonance in a System of Bi Nanoparticles Embedded into (Al,Ga)As Matrix" *Nanomaterials* 14, no. 1: 109.
https://doi.org/10.3390/nano14010109