Computational study of dielectric function and optical properties of a graphane nano structure containing graphene quantum dot

Ab-Initio computational study of dielectric function and optical properties of a graphane nano structure containing graphene quantum dot has been undertaken within Density Functional Theory using SIESTA code. Band structure, PDOS, real and imaginary parts of dielectric function, reflectance and energy loss have been calculated and frequencies corresponding to peak positions have been tabulated for each case. A comparison has been made with the corresponding properties of pristine graphene.


Computational Details
In this work, we have used Troullier Martin, norm conserving, relativistic pseudopotentials in fully separable Kleinman and Bylander form for Carbon and Hydrogen. Our calculations have been performed in the framework of Density Functional Theory within the generalized gradient approximation (GGA) according to the Perdew, Burke, Ernzerhof (PBE) parameterization using SIESTA code and methods [20,21]. The graphane sheet is described within the supercell (5x5x1) approach, by a single layer of graphane with 50C atoms. Interaction between adjacent layers is hindered by a large spacing of ~20 Å. A 250 Ry mesh cutoff has been used for the reciprocal space expansion of the total charge density. Brillion zone has been sampled by using 11×11×1 Monkhorst-Pack of k points. Localized atomic orbitals basis set has been used with confinement energy of 0.02 Ry. Minimization of energy is carried out by giving sufficient number of SCF iterations using standard conjugate-gradients technique [20,21]. Optical calculations have been carried out using 33x33x3 optical mesh and 0.2 eV optical broadening.

Electronic Band Structure and Interband Transitions
The

Optical Properties 3.2.1 Real & Imaginary parts of dielectric function
The figure 3(a) shows the plot of real part of dielectric function spectrum for in-plane polarization (E⊥c) and out-of-plane polarization (E || c) for pristine graphene (red curve) and graphane containing graphene QD.
In the case of pristine graphene, for in-plane polarization (E⊥c), there is a dip in the amplitude of the real part of dielectric function and it attains a small negative value at 4.8 eV indicating that there is (a) (b) Figure 3 Plot of (a) Real part of dielectric function (ε 1 ), (b) Imaginary part of dielectric function for in-plane polarization (E⊥c) and out-of-plane polarization (E || c) for pristine graphene (red curve) and graphane containing graphene QD (black curve).

Reflectance spectrum & Electron Energy Loss (EEL)
The figure 4(a) shows the plot of reflectance spectrum for in-plane polarization (E⊥c) and out-ofplane polarization (E || c) for pristine graphene (red curve) and graphane containing graphene QD. For out-of-plane polarization in pristine graphene peaks appear at 14.58 eV and 17.29 eV, while for graphane containing graphene QD peaks appear at frequencies 8.1 eV and 13.96 eV. For in-plane polarization in pristine graphene peaks appear at 4.31 eV and 13.80 eV, while for graphane containing graphene QD peaks appear at frequencies 1.39 eV and 4.81 eV. The figure 4(a) shows the plot of electron energy loss (EEL) spectrum for in-plane polarization (E⊥c) and out-of-plane polarization (E || c) for pristine graphene (red curve) and graphane containing graphene QD.
Electron energy loss (EEL) function is proportional to the inverse of dielectric function and corresponds to the collective excitations of electrons of system. In the case of pristine graphene a sharp resonance peak at 5.12 eV and relatively broad peak around 15.16 eV have been found for in-(a) (b) Figure 4 Plot of (a) Reflectance spectrum, (b) Electron Energy Loss (EEL) Spectrum for in-plane polarization (E⊥c) and out-of-plane polarization (E || c) for pristine graphene (red curve) and graphane containing graphene QD(black curve). plane polarization (E⊥c) (see figure 4(b)), which are in very good agreement with recently calculated plane wave results 4.8 eV and 15.0 eV [7] and also with experimentally measured values of 4.7 eV and 14.5 eV respectively [8].
For out-of-plane polarization (E || c) resonance peaks have been found at 14.72 eV and 17.29 eV, while a plane wave calculation reveals resonance at 11.7 eV and 14.7 eV [7]. For graphane containing graphene QD, the sharp peaks are observed at frequencies 1.43 eV, 8.83 eV & 14.12 eV and a broad peak is observed around 10 eV for out-of-plane polarization. For in-plane polarization sharp peaks are observed at frequencies 1.47 eV, 3.50 eV, 4.97 eV, 6.27 eV & 10.09 eV.
Thus new sharp peaks appear in the frequency region of 0 eV to 5 eV for graphane containing graphene QD for in-plane polarization. Table 1 shows the peak positions in eV for imaginary part of dielectric function, reflectance and electron energy loss in case of out-of-plane polarization (E || c) and in-plane polarization (E⊥c) for pristine graphene and graphane containing graphene quantum dot (GQD).

Red Shift in Peak Frequencies
It is found that there is red shift in plasmonic resonance frequencies in the case of graphane nano structure containing graphene QD as compared to pristine graphene, although the shifts in the peaks are not uniform as can be seen in figure 4(b) and table 1. As compared to pristine graphene, the spectra of dielectric function show red shift of 0.56 eV for out-of-plane polarization (E || c) and 3.74 eV for in-plane polarization (E⊥c). In EEL spectrum the red shift of 0.60 eV has been found for E || c while red shift of 0.15 eV for E⊥c.

Conclusions
In conclusion, we have performed first principle calculations to study the dielectric function and change in optical response of graphane nanostructure containing graphene QD as compared to pristine graphene. In the band structure band gap appears near the Fermi energy which is found to be 5.23039 eV in pristine graphane (50C+50H) and 1.36846 eV in graphane containing graphene QD. In the plot of PDOS multiple peaks are observed near the Fermi energy which are due to C_2p z electrons. As compared to pristine graphene, the peak position in the spectra of dielectric function shows red shift of 0.56 eV for out-of-plane polarization (E || c) and 3.74 eV for in-plane polarization (E⊥c). The peak intensities are reduced as compared to pristine graphene. The graphane nano structure having graphene QD is optically more active in the visible region showing additional peaks between 0 eV to 5 eV as compared to pristine graphene. These electronic and dielectric properties of graphane nanostructure containing graphene QD can be useful for the applications in microelectronics and optoelectronic devices. .