# Insights on the Excitation Spectrum of Graphene Contacted with a Pt Skin

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## Abstract

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## 1. Introduction

## 2. Experimental Methods

## 3. Theoretical Model

#### 3.1. Ground State Calculation

#### 3.2. Calculation of an Effective 2D Dielectric Function

#### 3.3. Electron Energy Loss Spectra

## 4. Results and Discussion

#### 4.1. Ab Initio Results

#### 4.1.1. Dirac Plasmon

#### 4.1.2. $\pi $ Plasmon

#### 4.2. Comparison with Experiments for $\pi $ Plasmon

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Pt-Skin Surface Response Function D_{Pt}

## References and Note

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**Figure 2.**The low-energy (IR) energy loss function (ELF) intensities, $-\U0001d574(1/\u03f5)$, in (

**a**) gr(${E}_{F}=$ 200 meV)/vacuum and (

**b**) gr(${E}_{F}=$ 200 meV)/Pt-skin interfaces, the intermediate-energy (VIS) ELF intensities in (

**c**) gr(${E}_{F}=1$ eV)/vacuum and (

**d**) gr(${E}_{F}=1$ eV)/Pt-skin interfaces and high-energy (UV) ELF intensities in (

**e**) gr(${E}_{F}=0$)/vacuum and (

**f**) gr(${E}_{F}=0$)/Pt-skin interfaces. The blue circles in the panels (

**b**,

**d**,

**f**) show the positions of the ELF intensities maxima in the unsupported graphene cases displayed in the panels (

**a**,

**c**,

**e**), respectively. The graphene Fermi energy ${E}_{F}$ is given relative to the Dirac point.

**Figure 3.**The experimental EELS spectra of the graphene/Pt-skin interface for various final (scattering) angles: (

**a**) ${\theta}_{f}={57}^{\circ}$–(

**h**) ${\theta}_{f}={71}^{\circ}$ (in steps of ${2}^{\circ}$). The incidence angle is ${\theta}_{i}={65}^{\circ}$ and the incident electron energy is ${E}_{i}=70$ eV. The experimental data are compared with theoretical results for the energy loss function, $-\U0001d574(1/\u03f5)$, obtained using two methods: ab initio calculations (red-solid) and an empirical model (magenta-dashed).The green dashed lines represent the EELS spectra of the self-standing graphene obtained using ab initio method, for comparison.

**Figure 4.**The ab initio (solid) and the empirical (dashed) Pt-skin surface response function, ${D}_{\mathrm{Pt}}\left(\omega \right)$, for $Q\approx 0$. The vertical dashed line shows the energy of the $\pi $ plasmon in unsupported graphene.

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**MDPI and ACS Style**

Despoja, V.; Radović, I.; Politano, A.; Mišković, Z.L.
Insights on the Excitation Spectrum of Graphene Contacted with a Pt Skin. *Nanomaterials* **2020**, *10*, 703.
https://doi.org/10.3390/nano10040703

**AMA Style**

Despoja V, Radović I, Politano A, Mišković ZL.
Insights on the Excitation Spectrum of Graphene Contacted with a Pt Skin. *Nanomaterials*. 2020; 10(4):703.
https://doi.org/10.3390/nano10040703

**Chicago/Turabian Style**

Despoja, Vito, Ivan Radović, Antonio Politano, and Zoran L. Mišković.
2020. "Insights on the Excitation Spectrum of Graphene Contacted with a Pt Skin" *Nanomaterials* 10, no. 4: 703.
https://doi.org/10.3390/nano10040703