# Interband, Surface Plasmon and Fano Resonances in Titanium Carbide (MXene) Nanoparticles in the Visible to Infrared Range

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## Abstract

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## 1. Introduction

## 2. Analysis of Experimental Data of EELS and Optical Absorption Spectroscopy of Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$

## 3. Calculation of Optical Spectra of Single Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ Nanoparticles

^{®}package, modeling the shapes and sizes of sheets as close as possible to the synthesized samples in the above-mentioned experiments with a known dielectric function [13,26]. It is important that scanning electron microscope (SEM) and atomic force microscope (AFM) images show a continuous coverage of Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ flakes predominantly oriented parallel to the substrate. MXenes flakes parallel to Si-SiO2 substrates, as shown in [13], take place even for thicknesses of less than 10 nm, corresponding to just a few MXene layers. A more detailed description of the modeling method is provided in Section S2 of the SI. The resulting plots are accompanied with corresponding intensity maps (spatial distribution of electric field normalized to the amplitude of the incident field). Throughout the paper the scale bars on the right side of each inset correspond to the absolute value of the ratio between the amplitude of the total electric field and the amplitude of the incident field. The direction of wave incidence coincides with the Z-axis in the figures, and the electric field oscillates along the Y-axis. In all of the calculations, MXene particles are embedded in air, i.e., the effect of the substrate that could be important in certain experiments is not considered here. We also compare our results with experiments performed with MXene films on substrates. This approach is justified by the very small difference of the reflectance between common substrates and MXene [13]. On the other hand, neglecting the role of the substrate of MXene films is also justified by the fact that our results, which are based on experimental values of the dielectric function from [26], match well with measured absorption data.

## 4. Calculation of Optical Spectra of Coupled Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ Nanoparticles

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Simulated absorption cross-section (CS) of Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ disk of diameter 500 nm with 14 nm height. Inset: electric field intensity map at IBT resonance—640 nm.

**Figure 2.**Simulated absorption CS of Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ cylinder of diameter 500 nm with heights 200 nm (blue) and 300 nm (red). Inset: electric field intensity map of cylinder of diameter 500 nm with height 300 nm at the wavelength of TSP resonance—1200 nm.

**Figure 3.**Simulated absorption CS of Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ cylinder of diameter 1000 nm with height 300 nm. Inset: electric field intensity map at the wavelength of QSP resonance—980 nm.

**Figure 4.**Simulated absorption CS of large spheroidal particle with semiaxes of 500, 200 and 200 nm. Inset: electric field intensity map at quadrupole resonance wavelength, 960 nm.

**Figure 5.**Simulated absorption CS of 7.5 nm thick triangular Ti${}_{3}$C${}_{2}$T${}_{\mathrm{x}}$ sheet with side lengths 300, 400 and 500 nm. For the ease of modeling, the triangles are capped at corners by arcs of 2 nm curvature radius. Incident electric field is: perpendicular (TM polarization, red curve) and parallel (TE polarization, blue curve) to the plane of sheet being perpendicular to the hypotenuse. Insets: electric field intensity maps placed above each curve, at the excitation wavelengths of 680 nm for the red one, and 780 nm for the blue.

**Figure 6.**Simulated absorption CS of coupled MXene nanospheroids in end-to-end configuration with equal short semiaxes ($a=b=5$ nm) and varying long semiaxis ($c=20$, 25 or 30 nm). Inset: electric field intensity map in the case of coupled spheroids with semiaxis $c=25$ nm and $a=b=5$ nm, irradiated by parallel electric field at 760 nm.

**Figure 7.**Simulated absorption CS of coupled identical MXene ellipsoids with semiaxes $c=100$ nm, $a=40$ nm and $b=10$ nm. Insets: electric field intensity maps at IBT maxima—800 nm and LSP resonance at 2030 nm.

**Figure 8.**(

**A**) Coupled spheroids with semiaxes of 500, 200 and 200 nm in end-to-end configuration. Electric field intensity maps at TSP maximum—1780 nm in the XY-plane (

**B**) and YZ-plane (

**C**) are presented.

**Figure 10.**Electric field intensity maps at Fano resonance—1440 nm in the XY-plane (

**A**) and YZ-plane (

**B**).

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**MDPI and ACS Style**

Gonçalves, M.; Melikyan, A.; Minassian, H.; Makaryan, T.; Petrosyan, P.; Sargsian, T.
Interband, Surface Plasmon and Fano Resonances in Titanium Carbide (MXene) Nanoparticles in the Visible to Infrared Range. *Photonics* **2021**, *8*, 36.
https://doi.org/10.3390/photonics8020036

**AMA Style**

Gonçalves M, Melikyan A, Minassian H, Makaryan T, Petrosyan P, Sargsian T.
Interband, Surface Plasmon and Fano Resonances in Titanium Carbide (MXene) Nanoparticles in the Visible to Infrared Range. *Photonics*. 2021; 8(2):36.
https://doi.org/10.3390/photonics8020036

**Chicago/Turabian Style**

Gonçalves, Manuel, Armen Melikyan, Hayk Minassian, Taron Makaryan, Petros Petrosyan, and Tigran Sargsian.
2021. "Interband, Surface Plasmon and Fano Resonances in Titanium Carbide (MXene) Nanoparticles in the Visible to Infrared Range" *Photonics* 8, no. 2: 36.
https://doi.org/10.3390/photonics8020036