Role of planar buckling on the electronic thermal and optical properties of Germagraphene nanosheets

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Role of planar buckling on the electronic, thermal, and optical properties of

Germagraphene nanosheets

Nzar Rauf Abdullaha,b, Yousif Hussein Azeezc, Botan Jawdat Abdullahd, Hunar Omar Rashida, Andrei Manolescue,

Vidar Gudmundssonf

aDivision of Computational Nanoscience, Physics Department, College of Science,

University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq.

bComputer Engineering Department, College of Engineering,

Komar University of Science and Technology, Sulaimani 46001, Kurdistan Region, Iraq.

cPhysics Department, College of Science, University of Halabja, Kurdistan Region, Iraq.

dPhysics Department, College of Science, Salahaddin University-Erbil, Erbil 44001, Kurdistan Region, Iraq.

eReykjavik University, School of Science and Engineering, Menntavegur 1, IS-101 Reykjavik, Iceland.

fScience Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland.

Abstract

We report the electronic, the thermal, and the optical properties of a Germagraphene (GeC) monolayer taking into

account buckling eﬀects. The relatively wide direct band gap of a ﬂat GeC nanosheet can be changed by tuning the

planar buckling. A GeC monolayer has an sp2hybridization in which the contribution of an s-orbital is half of the

contribution of a p-orbital leading to stronger σ-σbonds compared to the σ-πbonds. Increasing the planar buckling, the

contribution of an s-orbital is decreased while the contribution of a p-orbital is increased resulting in a sp3-hybridization

in which the σ-πbond becomes stronger than the σ-σbond. As a result, the band gap of a buckled GeC is reduced and

thus the thermal and the optical properties are signiﬁcantly modiﬁed. We ﬁnd that the heat capacity of the buckled

GeC is decreased at low values of planar buckling, which is caused by the anticrossing of the optical and the acoustic

phonon modes aﬀecting phonon scattering processes. The resulting optical properties, such as the dielectric function, the

refractive index, the electron energy loss spectra, the absorption, and the optical conductivity show that a buckled GeC

nanosheet has increased optical activities in the visible light region compared to a ﬂat GeC. The optical conductivity

is red shifted from the near ultraviolet to the visible light region, when the planar buckling is increased. We can thus

conﬁrm that the buckling can be seen as another parameter to improve GeC monolayers for optoelectronic devices.

Keywords: GeC monolayers, DFT, Electronic structure, Optical properties, Thermal properties

1. Introduction

Research on two-dimensional (2D) materials indicates

a great potential for next-generation electronic and op-

tical applications due to their rich physical characteris-

tics and outstanding electronic properties [1–5]. However,

some of the 2D materials such as graphene and silicene

have a vanishing gap and are thus called gapless materi-

als. The vanishing gap causes problems for applications

using graphene-based electronic devices. Thus, many in-

vestigations have tried to search for other 2D materials

[6,7]. In recent years, there a lot of attention has been

given to new 2D materials such as BN [8], MoS2[9], BeO

[10,11], and GeC [12], which have a wider band gap and

can be considered as semiconductor materials.

Theoretical investigations have reported that GeC

monolayers are semiconductors and structurally stable

[13,14]. This has led researchers to study them inten-

sively. In addition to computational analysis using density

Email address: nzar.r.abdullah@gmail.com (Nzar Rauf

Abdullah)

functional theory, experimental synthesis has been used to

investigate the production of GeC monolayer as a possi-

ble 2D material. Various synthesis techniques, including

plasma-enhanced chemical vapor deposition, activated re-

active evaporation, and chemical vapor deposition can all

be used to create germagraphene monolayers [15–17].

The band gap of a GeC monolayer is found to be 2.1

eV (GGA) and 4.06 eV using Heyd–Scuseria–Ernzerhof

(HSE) hybrid functional at zero value for the buckling

factor, i.e. a ﬂat structure [18]. The valuable band gap

of GeC indicating semiconducting properties can be fur-

ther improved using several techniques in order to enhance

its possible role in thermoelectric and optoelectronic ap-

plications. One may control the band gap of a fully hy-

drogenated GeC monolayer by biaxial strain or external

electric ﬁeld and a semiconductor-metal phase transition

takes place at certain elongation caused by biaxial strain.

The band gap has thus been enhanced to 3.49 eV dis-

playing photocatalytic characteristics for water splitting

[19]. Likewise, the mechanical, electronic, and magnetic

properties of a GeC monolayer can be modiﬁed through

Preprint submitted to Elsevier October 11, 2022

arXiv:2210.04247v1 [cond-mat.mtrl-sci] 9 Oct 2022

hydrogen or halogen passivation [20,21] Doping a GeC

monolayer could be considering as another technique to

modify the band gap. For instance, F and C dopant atoms

in a GeC monolayer disrupt the planar structure and a

surface-functionalized GeC monolayer with low-buckling

results [22]. With this type of doping the band gap is seen

to vary from 2.8 eV to 3.2 eV in calculations using HSE.

In this work, we perform DFT calculations based on

the Kohn-Sham formalism implemented in the Quantum

espresso software package [23,24]. In the calculations, we

tune the buckling parameter to study the electronic, the

thermal, and the optical properties of a GeC monolayer.

The results show that the buckling eﬀects can be consid-

ered as an alternative way for controlling it’s physical prop-

erties, such as the band gap, the thermal conductivity and

the heat capacity.

The structure of the paper is as follows: Sec. 2includes

details of the computational methods, and Sec. 3demon-

strates the calculated electrical, the thermal, and the op-

tical properties for a GeC monolayer with diﬀerent degree

of buckling. The last section, Sec. 4, is the conclusion.

2. Methodology

A 2×2 supercell of a GeC monolayer with equal number

of Ge and C atoms is considered. The GeC structure is

fully relaxed with high values of cutoﬀs for the plane-waves

kinetic energy and the charge densities ﬁxed at 1088.5 eV,

and 1.088 ×104eV, respectively [25]. In the relaxation

process, the forces on the atoms are less than 10−5eV/˚

where a dense Monkhorst-Pack grid with 18×18×1 is used.

The distance between GeC monolayers is assumed to be

20 ˚

A in the z-direction, which is long enough to cancel out

interlayer interactions. The generalized gradient approxi-

mation (GGA) is used with the Perdew-Burke-Ernzerhof

(PBE) functionals approximating the exchange and the

correlation terms implemented in QE software [26]. In

the calculations of the band structure and the density of

states (DOS), Self-Consistent Field (SCF) and non-self-

consistent ﬁeld (NSCF) calculations are performed, respec-

tively. In these calculations, we use a Monkhorst-Pack grid

of 18 ×18 ×1 for the SCF and 100 ×100 ×1 for the NSCF

[27]. The optical properties of a GeC monolayer are ob-

tained using QE with the optical broadening of 0.1 eV.

An ab initio molecular dynamics, AIMD, calculations

are utilized to check the thermodynamic stability. The

calculations, done in the NVT ensemble, are performed

for 10 ps with a time step of 1.0 fs using the heat bath

approach described by Nos´e-Hoover [28].

The optical characteristics of the GeC monolayer can

be calculated using a large number of empty bands which

is taken into account to evaluate the dielectric properties,

ε(ω) = ε1(ω) + iε2(ω), where ε1and ε2are the real and

the imaginary parts of the dielectric function. In the long

wavelength limit q→0, ε2(ω) is given in Refs. [29,30]

ε2(ω) = 2e2π

ωε0X

K,c,v |hΨv

K|~u·~r |Ψc

Ki|2δ(Ec

K−Ev

K−ω).(1)

Herein, ωindicates the frequency of the electromagnetic

waves, ε0refers to the free space permittivity. The labels

vand cindicate the valence and conduction bands, re-

spectively, and ~u and ~r demonstrate the polarization and

the position vectors of the electromagnetic ﬁeld, respec-

tively. The real part and the imaginary part of the com-

plex dielectric functions are connected to each other by the

Kramers-Kronig relation [31,32]. Both ε1(ω) and ε2(ω)

are obtained from the QE package. Once the dielectric

functions are obtained, the real part of the refractive in-

dex is calculated as [33]

n(ω) = 1

√2 hε2

1(ω) + ε2

2(ω)i

2+ε1(ω)!

.(2)

The optical conductivity is then computed from

σoptical =−i ω

4πhε(ω)−1i.(3)

3. Results

In this section, we show the obtained results for the

electronic, the thermal and the optical properties of a GeC

monolayer with diﬀerent values for the planar buckling

parameter, ∆. In addition, for the sake of comparison, we

recalculate the physical properties of a ﬂat GeC monolayer,

∆=0.0, and use them as reference points to compare to.

3.1. Electronic states

In a ﬂat, or planar, GeC monolayer (∆ = 0.0), all the

Ge and the C atoms are located in the same xy-plane as is

presented in Fig. 1for both a side view (I), and a top view

(II). If a ﬁnite planar buckling is considered (∆ 6= 0.0),

the Ge atoms are located in the same plane and all the C

atoms are situated in another plane. The planar buckling

indicates the vertical distance, ∆, between the Ge and

the C planes. There are several proposed techniques to

control the planar buckling in monolayers experimentally.

One of them is using an applied external electric ﬁeld on

the monolayer [34].

The degree of the hybridization of the s- and the p-

orbitals can be found using a simple equation, cos(θ) =

s/(s−1) = (p−1)/p, where θis the angle between the

equivalent orbitals, sand p[35]. The considered values

of planar buckling aﬀect the orbital hybridization. Most

ﬂat monolayers have an sp2hybridization, and the orbital

hybridization is approaching an sp3conﬁguration when the

planar buckling is increased [36,37]. A ﬂat GeC monolayer

(∆ = 0.0) has an sp2hybridization as is presented in Fig.

2(a), where the degree of the orbital hybridization is 2

indicating an sp2-hybridization at ∆ = 0.0, and the degree

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Roleofplanarbucklingontheelectronic,thermal,andopticalpropertiesofGermagraphenenanosheetsNzarRaufAbdullaha,b,YousifHusseinAzeezc,BotanJawdatAbdullahd,HunarOmarRashida,AndreiManolescue,VidarGudmundssonfaDivisionofComputationalNanoscience,PhysicsDepartment,CollegeofScience,UniversityofSulaimani,Sulaim...

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Role of planar buckling on the electronic thermal and optical properties of Germagraphene nanosheets

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