# Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

`BINIT`project was launched officially in 1997 [19].

## 2. Electronic Transport in Polycrystalline Graphene

`PEN`MX code [50,51,52], a software package based on norm-conserving pseudo-potentials and pseudo-atomic localized basis functions. Parametrized TB models are very effective to model the electronic properties of graphene at low energies, i.e., around the Fermi level. The good agreement between these two approaches was demonstrated in refs. [41,45].

## 3. Optical Absorption in Graphene and Borophene

## 4. Electronic Structure and Vibrational Properties of MXenes

## 5. Magnetoresistance in 2D Tunnel Junctions

`IESTA`electronic structure package [93,94]. Converged k-point grids and a basis set of double-$\zeta $ plus polarization quality were used.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Electronic transport through graphene grain boundaries (GBs). Atomic structures of (

**a**) the $(2,1)|(2,1)$ class-I GB, (

**b**) the $(5,0)|(3,3)$ class-II GB, (

**e**) the $(11,3)|(10,5)$ class-I GB and (

**f**) the $(24,0)|(16,12)$ class-II GB. The zero-bias conductances are given in (

**c**,

**d**) for class-I and class-II systems, respectively. Conductances through the smallest (blue lines) and largest (orange lines) GBs are compared to pristine graphene (black dashed lines). Reprinted and adapted with permission from reference [44].

**Figure 2.**Strain effects on the electronic transport through graphene grain boundaries. ($E-{k}_{\perp}$) maps of transmission obtained for the class-I GB in Figure 1a with different uniaxial strain magnitudes: 0% (

**left**), 3% (

**middle**) and 6% (

**right**), oriented with 45${}^{\xb0}$ with respect to BG axis. Reprinted and adapted with permission from reference [43].

**Figure 3.**Aharonov–Bohm interferences in polycrystalline graphene in the quantum Hall regime: (

**a**) Schematic of considered systems, (

**b**) computed conductance as a function of the magnetic field, and (

**c**,

**d**) images of the local density of left-injected electronic states at magnetic fields (

**c**) ${B}_{1}$ (conductance peak), marked in red in (

**b**,

**d**) ${B}_{2}$ (conductance valley) marked in blue in (

**b**). Reprinted and adapted with permission from reference [46].

**Figure 4.**Electronic and optical properties of borophene monolayers: (

**a**) Three 2D crystal polytype structures of borophene with increasing boron vacancies, i.e., buckled triangular, ${\beta}_{12}$, and ${\chi}_{3}$, with in (

**b**) the corresponding electronic band structures and in (

**c**) the corresponding longitudinal optical conductivities ${\sigma}_{xx}$, ${\sigma}_{yy}$, and their averaged $\frac{1}{2}({\sigma}_{xx}+{\sigma}_{yy})$ in dotted, dashed, and thick black line, respectively. Graphene optical conductivity is also given in red line.

**Figure 5.**Optical transmittance T of graphene and borophene monolayers (electric field in oblique direction) without Drude corrections (thick lines). To illustrate the effect of Drude corrections, two representative values of scattering time $\tau =1.2$ and 12 fs (dashed and dotted-dahsed black lines) are also displayed for the case of buckled triangular borophene.

**Figure 6.**Optical Hall conductivity ${\sigma}_{xy}$ of unstrained and 8% strained graphene along armchair ($\theta ={0}^{\xb0}$) and zigzag ($\theta ={90}^{\xb0}$) direction for incoming light polarized obliquely ($\varphi ={45}^{\xb0}$). Inset: Sketch illustrating the Faraday rotation mechanism of linearly polarized light (red and blue lines) in uniaxially strained graphene (green line). Visible (UV) light rotates (anti-)clockwise when strain is applied along the armchair direction.

**Figure 7.**Atomic structure of (

**a**) pristine V${}_{2}$C and (

**b**) terminated V${}_{2}$CT${}_{2}$ with MD2, and (

**c**) high-symmetry armchair and zigzag directions in both real and reciprocal space.

**Figure 8.**Electronic band structure of (

**a**) pristine V${}_{2}$C, and terminated (

**b**) V${}_{2}$CF${}_{2}$, (

**c**) V${}_{2}$C(OH)${}_{2}$, (

**d**) V${}_{2}$CF(OH). The Fermi level is fixed as the reference of zero energy.

**Figure 9.**Phonon spectra and projected density of states of (

**a**) pristine V${}_{2}$C, and terminated (

**b**) V${}_{2}$CF${}_{2}$, (

**c**) V${}_{2}$C(OH)${}_{2}$, (

**d**) V${}_{2}$CF(OH).

**Figure 10.**(

**a**,

**c**) Ball and stick representation of monolayer h-BN on Co (hcp $\langle 0001\rangle $) within the (

**a**) aligned and (

**c**) misaligned ($\alpha ={21.78}^{\xb0}$) configurations. Boron and nitrogen atoms are colored respectively in green and white. Cobalt atoms are depicted in red. (

**b**,

**d**) Spin polarization of the density of states projected on h-BN. The excess of majority spins is colored in blue, and the excess of minority spins is colored in red.

**Figure 11.**The spin dependent electronic transmission function of a (

**a**) symmetric and (

**b**) asymmetric Co${}_{1}$/h-BN/Co${}_{2}$ junction with both the parallel and anti-parallel relative orientation of FM magnetization. The transmission functions of the majority and minority spins are depicted in blue and red respectively. In the symmetric junction, Co${}_{1}$, h-BN and Co${}_{2}$ are exactly aligned hence giving rise to two epitaxial interfaces (see Figure 10b). In the asymmetric case, Co${}_{1}$ and h-BN are aligned but Co${}_{2}$ has been twisted by an angle of 21.78° hence corresponding to a less strongly bonded interface (see Figure 10d).

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## Share and Cite

**MDPI and ACS Style**

Champagne, A.; Dechamps, S.; Dubois, S.M.-M.; Lherbier, A.; Nguyen, V.-H.; Charlier, J.-C.
Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials. *Appl. Sci.* **2020**, *10*, 1724.
https://doi.org/10.3390/app10051724

**AMA Style**

Champagne A, Dechamps S, Dubois SM-M, Lherbier A, Nguyen V-H, Charlier J-C.
Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials. *Applied Sciences*. 2020; 10(5):1724.
https://doi.org/10.3390/app10051724

**Chicago/Turabian Style**

Champagne, Aurélie, Samuel Dechamps, Simon M.-M. Dubois, Aurélien Lherbier, Viet-Hung Nguyen, and Jean-Christophe Charlier.
2020. "Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials" *Applied Sciences* 10, no. 5: 1724.
https://doi.org/10.3390/app10051724