2DMater. 3 (2016) 045006 doi:10.1088/2053-1583/3/4/045006

PAPER

Electronic and optical properties of pristine and oxidized borophene

Aurélien Lherbier, Andrés Rafael Botello-Méndez and Jean-ChristopheCharlierUniversité catholique de Louvain, Institute of CondensedMatter andNanosciences, Chemin des étoiles 8, B-1348 Louvain-la-Neuve,Belgium

E-mail: aurellien.lherbier@uclouvain.be

Keywords: borophene, electronic structure, optical properties, ab initio, oxidation

Supplementarymaterial for this article is available online

AbstractBorophene, a two-dimensionalmonolayer of boron atoms, was recently synthesized experimentallyandwas shown to exhibit polymorphism. In its closed-packed triangular form, borophene is expectedto exhibit anisotropicmetallic character with relatively high electron velocities. At the same time, verylow optical conductivities in the infrared-visible light regionwere predicted. Based on its promisingelectronic transport properties and its high transparency, borophene could become a genuine legopiece in the 2Dmaterials assembling game known as the van derWaals heterocrystal approach.However, borophene is naturally degraded in ambient conditions and it is therefore important toassess themechanisms and the effects of oxidation on borophenemonolayers. Optical and electronicproperties of pristine and oxidized borophene are here investigated byfirst-principles approaches.The transparent and conductive properties of borophene are elucidated by analyzing the electronicstructure and its interplay with light. Optical response of borophene is found to be strongly affected byoxidation, suggesting that opticalmeasurements can serve as an efficient probe for borophene surfacecontamination.

1. Introduction

Borophene is known to be polymorphic [1], thus thewordborophenedenotes generically various two-dimen-sional (2D) monolayers of boron (B) that have beendiscussedpreviously in the literature [2–6].Manyof theseB monolayers contain hexagonal holes stabilizing theplanar structure. The fundamental ground state accord-ing to [2] is obtained for hexagonal hole concentrationx= 0.1–0.15 in is thus the densestboron limit, which corresponds to the closed-packedtriangular borophene. In dense B monolayers cases, thebuckling and the coupling between sublattices has beenshown to enhance their energetic stability and possiblyrise to the emergence of distorted Dirac cone [3].Magnetic properties have also been predicted for one oftheseBmonolayers [7].

At least two experimental works reported recentlythe synthesis of borophene monolayers via controlledatomic deposition of boron atoms on a silver (Ag) sur-face [8, 9]. Various phases were observed, dependingmainly on the deposition rate and the temperature,attesting the predicted large polymorphism of

borophene. In the following, we focus on one of thesephases and thus refer to borophene solely as the densebuckled monolayer of B atoms arranged in two inter-penetrating rectangular sublattices (or equivalently thebuckled triangular lattice), i.e. , which was pre-sumably one of the phases recently synthesized [8].

The reported phonon band structure of thefree standing borophene attests small instabilities[6, 8, 10, 11]. Such instabilities seem to be furtherwashed out when borophene is fully hydrogenated, i.e.forming borophane, for which the emergence of aDirac cone was recently predicted [12]. Applyingstrain to borophene can also wash out the phononinstability. These results suggest that the underlyingAg surface could stabilize borophene in the experi-ments. When decoupled from the substrate, such bor-ophene flakes may either stay trapped in its localmetastable minimum or undergo a phase transition toa lower energy phase.

Free-standing borophene displays attractive prop-erties. It is metallic while its bulk phases are semi-conducting. It exhibits a highly anisotropic metalliccharacter due to its anisotropic atomic structure

RECEIVED

19 July 2016

REVISED

16 September 2016

ACCEPTED FOR PUBLICATION

20 September 2016

PUBLISHED

6October 2016

© 2016 IOPPublishing Ltd

[8, 10], similarly to phosphorene [13], although phos-phorene is a ∼2 eV band gap semiconductor. In con-trast to graphene, high optical transparency (nearly100% transmission) is predicted up to roughly 3 eV.Combining the goodmetallicity with such a high opti-cal transparency could make borophene a good candi-date as a transparent conductive 2D material withpossible applications in photovoltaics and touchscreens. Borophene is also predicted to have interest-ing mechanical properties. It is found to be a hard andbrittle 2Dmaterial with anisotropic critical strains andnegative out-of-plane Poisson’s ratio [14, 15]. Finally,combining its promising properties with the ones ofother 2D materials such as graphene or transitionmetal dichalcogenides, might lead to new van derWaals heterostructures with superior properties.

However, chemical stability of borophene withrespect to ambient conditions, and in particular withrespect to oxygen (O) has not been discussed so far.This is an important issue to consider since signatureof oxidation was already reported in the pioneerexperiment of Mannix et al [8]. How the electronicand optical properties of pristine borophene change asa consequence of such a surface degradation? In thepresent paper, one answers this question using a first-principles approach. Different adsorption sites foroxygen atoms are considered and the calculatedadsorption energies demonstrate indeed that bor-ophene is prone to chemically adsorption. The elec-tronic structure remains metallic upon oxygenationbut the decrease of electronic dispersion and the defectinduced-disorder is expected to lower the con-ductivity. Furthermore, optical conductivities arefound to increase with oxidation which lower the opti-cal transparency, suggesting a high optical sensitivityof borophene with respect to any surface modifica-tions, especially in the infrared region.

2.Methods

First-principles simulations were conducted to relaxstresses, optimize atomic positions, to compute elec-tronic band structures, density of states (DOSs),optical conductivity, transmittance and reflectance ofpristine and oxidized 2D borophene sheets. Calcula-tions were performed using the self-consistent densityfunctional theory (DFT) method as implemented inthe SIESTA [16] package. The exchange-correlationenergy and electron–ion interaction are describedusing GGA-PBE [17] functional and norm-conservingpseudopotentials [18] in the fully non-local form. Adouble-ζ polarized basis set of numerical atomicorbitals is used and the energy cutoff for real-spacemesh is set to 500 Ry. The energy levels were populatedfollowing a Fermi–Dirac distribution function with anelectronic temperature of 300 K. The geometries wererelaxed until the forces on each atom and the stress onthe unit cell were less than 0.01 eVÅ−1and

0.001 GPa, respectively. An inter-layer vacuum dis-tance ≈ 30Åwas used in order to avoid any spuriousimage interaction. Spin polarization has beenaccounted for in all calculations but none of themexhibited a net magnetic moment. A fine k-point gridof 100× 100× 1 for the unit cell and an equivalentone for the n× n supercell was employed using theMonkhorst–Pack scheme [19]. A denser k-point gridof 900× 900× 1was used to evaluate theDOS and theaverage velocity was computed using central numer-ical derivative as

( )( )

( )

( )åå

d

d

d

=-

=-

-

+ -v

E E

k

v Ev E E

E E

2,

,

1

x yb

b k b k

x y

x yb x y

b

b

k

kk b k

kb k

,,

, 1 , 1

,

,, ,

, ,

,,

x y x y, ,

where k are the k-points sampling the Brillouin zone,b is the band index, and ( )d -E Eb k, is a delta-Diracfunction centered on each of the eigenvalues andapproximated by a Lorentzian in the numericalcomputation. Beyond DFT calculations were per-formed on pristine borophene to include self-energycorrections to the eigenvalues through a G0W0

approach on top of a LDA starting point as implemen-ted in the ABINIT package [20–22].

The optical properties were computed from theimaginary part (e2) and real part (e1) of the complexdielectric function (ε). The Kramers–Kronig relationwas employed to obtain e1 from e2 and since bor-ophene is a metal, a Drude term was added to bothpart of ε as

( ) ( ) ( )e e= -+ G

E EE

E, 21 1

p2

2 2

( ) ( ) ( )e e= +G

+ GE E

E

E

E32 2

p2

2 2

with w=Ep p where w =e

n e

mp2

0is the plasmon

frequency and G =twhere τ is a relaxation time in

the Drude model. The parameter Γ was varied from20 Ha (≈ 544 eV) to 0.2 mHa (≈ 5.44 meV) whichcorresponds to τ varying from 1.21× 10−18 s to1.21× 10−13 s, respectively. For optical properties, theintegration over the Brillouin zone was performed ona dense k-point grid of 1100× 1100× 1 in case of theunit cell (an equivalent grid was used for the case ofsupercells), taking into account all the availableelectronic bands for interband transitions, and abroadening factor of 25 meV was applied. To accountfor the 2D nature of the system, the imaginary part ofthe dielectric function ε was renormalized [23](including both interband transition and Drudeterms), as

( ) ( ) ( )e e=E EH

h, 42D 3D

whereH is the total height of the 3D periodic simulationcell (in our case 30Å), and h is the polarizable electronicthickness which was estimated using the buckling height

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2DMater. 3 (2016) 045006 ALherbier et al

and the van der Waals atomic radius [24] ( =hborophene

+h r2buckling boronvdW = 4.73Åand =h r2graphene carbon

vdW =3.40Å).

3. Electronic structure

3.1. Pristine boropheneThe lattice parameters of the optimized rectangularunit cell of borophene are displayed in figures 1(a)–(c),i.e. (a= 1.6212; b= 2.8699) Åwith a buckling heightof 0.89Åbetween bottom and top atoms (B1 and B2respectively). The calculated cohesive energy (Ec) is−6.707 eV/atom (see equation (5)) while the cohesiveenergy of the bulk crystal of boron (α-rhombohedralwith 12 B atoms per unit cell) is−7.262 eV/atom, i.e.borophene is metastable by 0.555 eV/atom withrespect to bulk phase.

( )= -E E N E , 5c borophene B B

where EB and Eborophene are the total energies of anisolated B atom and of the borophene layer containingNB boron atoms. Other boron monolayer structureshave been reported with differences in total energieswith respect to bulk phase being in the order0.32–0.40 eV/atom [2, 3]. This means that the presentborophene structure (buckled closed-packed triangu-lar) is not themost stable 2D phase butmay be favoredby the underlying Ag surface onwhich it is grown.

The electronic band structure (figure 1(d)) exhi-bits a priori a strongly anisotropic metallic character asthe bands are found to be highly dispersive in the kxdirection (Γ–X and Y–S) with relatively high groupvelocity of 6.6 105 m s−1, while it appears that nobands cross the Fermi level in the ky direction (Γ–Yand X–S) as reported previously [8, 10]. Notwith-standing, one also notes that dispersion occurs alongthe obliqueΓ–S path. This reveals that bands can actu-ally cross the Fermi level parallel to the ky direction in

Figure 1. (a) and (b) side views, (c) top view, of a 3 × 3 borophene supercell. The central 1 × 1 unit cell contains two boron atoms (B1andB2 depicted as green and blue spheres, respectively) and is delimited by red filled lineswhile the repeated cells are delimited by reddashed lines. (d)Electronic band structure and density of states (DOS)with zero energy aligned to the Fermi level (EF). The Brillouinzone is shown in the inset. The highest group velocity (6.63 105m s−1) for a band crossing the Fermi level is highlighted by a red dashedline. (e) 3Dplot of the two electronic bands (only for positive ky) crossing the Fermi level (symbolized by the semi-transparent plane)in an energy window∼ [−1;+1] eV. (f)Comparison betweenKhon–Sham (KS) band structures with Siesta (GGA-PBE) andAbinit(LDA)with theG0W0 corrected one.

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2DMater. 3 (2016) 045006 ALherbier et al

some region of the 2D Brillouin zone. In order to havebetter insight on the exact anisotropy of the electronicstructure it is thus important to plot the electronicband structure in the whole 2D Brillouin zone andidentify the Fermi surface (which in 2D actually redu-ces into a Fermi line) (see figure 1(e)).While electronicbands always cross the Fermi level for any line parallelto kx, this is not the case for lines parallel to ky. There-fore, it is expected that transport will occur only forselective wave vectors k whose kx component belongsto the allowed region (figure 1(e)). This sets a maximalangle (k q

max ) for the wave vectors k=(kx, ky) ≡ (kr,k q). One also notes, that the two bands crossing theFermi level become exactly degenerate at the edge ofthe Brillouin zone along the S–Y path.

Then, theDOS around the Fermi level (figure 1(d))exhibits an almost planar shape, typical of 2D free elec-tron gas, except when approaching an energy equal toEF−1 eV, where a van Hove singularity is observed.This energy point corresponds to a saddle point of anelectronic band at the Γ point (figures 1(d) and (e)).The presence of this peak generates a native asym-metry between electrons and holes which will add tothe above mentioned asymmetry between transportdirections. Finally, the band structure of borophenewas recalculated within a LDA approach using ABI-NIT package and then corrected by applying a oneshot G0W0 approximation to the quasi particle pro-blem. No significant changes were observed betweenthe Kohn–Sham structure and theG0W0 one. One canonly notice an increase of the local band gap at the Γpoint, and generally speaking an increase of the Fermivelocity.

3.2.Oxidized boropheneExperimental measurements indicate that bare bor-ophene on a Ag substrate is partially oxidized withinseveral hours unless it is capped with amorphoussilicon/silicon oxide [8]. Even after encapsulation and

after several weeks, residual oxygen bound to boro-phene has been found [8]. Therefore, the effect ofoxygen on the electronic and optical properties ofborophene cannot be ignored and should beaddressed. Due to computational limitations, how-ever, one-side oxidation of the free standing boro-phene is considered rather than the surface oxidationof the full borophene-substrate system. It is worthnoting that the detached free standing borophene canexperience strong structural changes before the oxida-tion takes place, due to the aforementioned smallphonon instabilities. Nevertheless, our simulationsaim to describe the properties of oxidation of thesupported borophene albeit with the assumption of alimited impact of the underneath substrate.

A 3× 3 borophene supercell is first considered withfour adsorption sites which correspond to a position ontop of a boron atom (B1 or B2), a bridge position eitherin between first nearest-neighbor atoms (along the x-direction) or in between third nearest neighbor atoms(along the y-direction) of the top layer (B2–B2) (see sup-plementaryfigure 7). The last case is found tobe themoststable adsorption site with a relatively high adsorptionenergy of−4.548 eV. The adsorption energy of the otherconfigurations can be in found in supplementary table 1.The adsorption energy (Ead) has been computed withrespect to total energies of isolated borophene andmole-cular oxygen (O2) as

( )= - ++ ⎜ ⎟⎛⎝

⎞⎠E E E

E

2. 6ad borophene O borophene

O2

A negative value of Ead means that the adsorption isfavorable.

During the adsorption, the two B2 atoms bound tothe O atom are slightly displaced out of the top layerand get closer to each other as depicted in figures 2(a)–(c). The corresponding folded electronic band struc-ture (compared to the band structure of pristine bor-ophene), as well as the DOS and the average velocities

Figure 2. (a) and (b) side views, (c) top view, of a 3 × 3 supercell of oxidized borophene. Boron atomsB1 andB2 are depicted as greenand blue spheres respectively while the oxygen adatomO is represented by a red sphere. (d)Electronic band structure and density ofstates (DOS)with zero energy aligned to the Fermi level (EF).

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2DMater. 3 (2016) 045006 ALherbier et al

(vx and vy), are plotted in figure 2(d). From the bandstructure, one notes that many band crossings andband degeneracies are avoided and lifted up, respec-tively, but it remains difficult to clearly assess theimpact of oxygen adatombecause of the folding. How-ever, the impact on the DOS is more obvious. Severalnew peaks appear and are well distributed in energywhich makes the DOS curve much more noisy than inpristine case but still non-zero at the Fermi level (nogap opening). The band structures and DOS for theother adsorption sites are displayed in supplementaryfigure 8. Even more obvious than the impact on theDOS is the impact on velocities. Indeed, as it can beseen in figure 2(d), right to the DOS, the computedaverage velocity along the x- and y-direction largelydecreases when the O adatom is incorporated com-pared to the pristine case. One also notes that theanisotropy has almost disappeared. Finally, chargetransfer between borophene and O adatom has beeninvestigated using Voronoi and Hirshfeld methods.The O adatom is found to loose 0.15–0.17 ∣ ∣e in bridgepositions while it looses 0.23–0.25 ∣ ∣e in top positions.The electronic charge gained by borophene is spreadover the system.

To provide a better understanding of the mod-ifications induced by O adatoms, it is also essential toinvestigate its dependence as a function of the con-centration. For this purpose, in addition to the pre-vious 3× 3 supercell, larger supercells have beenconsidered i.e. a 4× 4, a 5× 5, and a 6× 6 (supple-mentary figure 9). The corresponding oxygen surfacedensity are nO = 2.34 1014, 1.31 1014, 8.41 1013, and5.84 1013 cm−2. The dependence on the DOS is illu-strated in figure 3. As it can be seen, the DOS remainsalways non-zero and thus the oxidation preservesa priori the metallic character. However, due to thepresence of numerous DOS peaks and the velocitydecreasing one can anticipate the presence of localizedstates around the defects and thus strong scatteringmechanisms which should largely degrade the electro-nic conductivity andmobility in oxidized borophene.

4.Optical properties

4.1. Pristine boropheneBeside its potentially interesting anisotropic conduc-tion properties, pristine borophene is expected to behighly transparent owing to its extremely small thick-ness. This could make the material interesting forphotovoltaic applications and touch screens. A trans-parent conductor is a priori a counter-intuitive prop-erty since common bulk metals are usually nottransparent but instead looks gray and shiny to humaneyes. It is because a large part of light is reflected at theinterface. It is however well known that beyond theplasmon frequency, i.e. for photon energy larger than

w=Ep p, the reflectance can strongly decrease andpossibly render the metal transparent. For most ofmetals the plasmon frequency is in the ultra-violet(UV) which means they indeed reflect light in thevisible region. However, when the thickness is reducedto few (or even one) atomic layers (the so-called thinfilm limit; TFL), the reflectance drops to nearly zeroand the transmission increases to almost 100% andtheir variations are actually mostly related to theoptical conductivity. In the following one assessescarefully the optical properties of borophene account-ing correctly for the 2D nature, in contrast to a recentwork [10] where the 3D bulk formula was considered,showing relatively high reflectance. We first discussthe optical conductivity and second the transmittance(the reflectance plots can be found in supplementarymaterial).

The real part of optical conductivity ( ( )s =E1

( ) e eE E0 2 , where e0 is the vacuum dielectric con-stant) of borophene is first investigated and is dis-played in figures 4(a)–(d). Different polarizations oflight are considered, i.e. an electric field along the xdirection, along the y direction, and average of bothdirections (i.e. a light propagating along the z direc-tion). In figure 4(a), the scattering time parameter ori-ginating from the Drude model is fixed to τ= 1.2110−18 s (Γ= 20 Ha) which is a very small valuedescribing thus a ‘bad’metal (actually amean free path

Figure 3.Electronic density of states for different concentrations of oxygen adatoms (nO).

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2DMater. 3 (2016) 045006 ALherbier et al

in the order of a picometer). At the same time one cansee, from equations (2) and (3), that for such a largevalue of Γ, the Drude contributions (µ G1 2) becomesnegligible, just as if one was using only the usual inter-band transitions to describe the optical properties. Insuch a situation, the optical conductivity is found to bealmost zero for low energy radiation up to 3 eV (i.e.violet, close to the end of visible light). Then in the UVpart, the optical conductivity increases slowly up to6.5 eV before exhibiting an enhanced signal composedof a series of four peaks at 6.5, 8.2, 8.5 and 9.6 eV. Thelow optical absorption of borophene is even betterhighlighted by comparing it with the one ofmonolayergraphene (gray dashed lines in figure 4) whose opticalconductivity is between 1 and 2 s0 (with s p= e h20

2 )up to 3 eV. The fact that borophene appears to betransparent in the infrared-visible region is relatedhere to the fact that it has been considered as a badmetal (and acts thus as an insulator) and that inter-band transitions occur only above 3 eV.One also notesthe anisotropy of the optical absorption between x andy directions. In particular, the optical conductivityremains very small up to 6.5 eV for polarization alongthe x direction.

When going now to the case of a ‘good’metal, thatis increasing τ up to 1.21 10−13 s (mean free path in theorder of 102 nm) (figures 4(b)–(d)), one observes first

an almost constant increase of the optical conductivityforming a plateau, and then a divergence at low energygoing towards a delta-Dirac function at zero energywhich finally restores a very low optical conductivity inthe visible region, i.e. similar to the one observed infigure 4(a) except for the zero energy limit. This is theexpected behavior for s1 of a perfect metal in theDrude model, i.e. a delta-Dirac function at zeroenergy. This reflects the fact that in the static limit, i.e.for a constant electric field, the dc conductivity tendsto infinity ( ( )s ¥01 ) as the scattering vanishes andhence does not damp the acceleration of electronscaused by the electric field. For an alternating field thereal part of the ac conductivity is zero ( ( )s w = 01 ),and the ac conductivity becomes actually purely ima-

ginary ( ( )s w =w

n e

m22

). Hence, in both limits of a bad

and good metal, borophene would exhibit nearly zeroconductivity in the visible region. As mentioned pre-viously, the fact that the optical conductivity is zero inthe visible region implies, following the TFL, that thetransmittance goes to 100% and that the materialshould be fully transparent.

The actual transmittance and reflectance havebeen computed following both rigorous Fresnelequations, and TFL equations (that are obtained fromthe former ones by taking the limit of small thickness).In contrast to the bulk case where reflectance accounts

Figure 4. (a)Comparison of the optical conductivity of pristine borophenewith pristine graphene. Different electric field orientationsare considered, i.e. (1,0,0) (x), (0,1,0) (y), and (1,1,0) (x + y)/2. (optical conductivity of graphene being isotropic only the (1,1,0) case isplotted) (scattering time parameter of theDrudemodel τ = 1.21 × 10−18 s). (b)–(d)Zoom in the low energy energy region ofborophene optical conductivity for different values of the scattering time parameter of theDrudemodel. (b)–(d) correspond to (1,1,0),(1,0,0), and (0,1,0) electricfields respectively.

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2DMater. 3 (2016) 045006 ALherbier et al

only for one interface (typically between vacuum andthe material), the reflectance in thin films accounts forthe presence of a back side interface which producessecondary reflections. As most ab initio codes do not

have this particular treatment for 2D thin systems, it isimportant to carefully compute optical propertiesusing general Fresnel equations or at least TFLequations. Although small differences are observed in

Figure 5. (a)Comparison of the transmittance of pristine borophenewith pristine graphene. Different electric field orientations areconsidered, i.e. (1,0,0) (x), (0,1,0) (y), and (1,1,0) (x + y)/2. (Optical conductivity of graphene being isotropic only the (1,1,0) case isplotted.) (Scattering time parameter of theDrudemodel τ = 1.21 10−18 s.) (b)–(d)Zoom in the low energy energy region ofborophene optical transmittance for different values of the scattering time parameter of theDrudemodel. (b)–(d)Correspond to(1,1,0), (1,0,0), and (0,1,0) electricfields respectively.

Figure 6.Optical conductivity of pristine and oxidized borophene aswell as pristine graphene for comparison.

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2DMater. 3 (2016) 045006 ALherbier et al

reflectance curves, both approaches yield very similarresults for transmittance validating therefore the TFLin case of graphene and borophene. The reflectance(R), the transmittance (T), and the absorbance (A), inTFL are given by [25, 26]

( ) ( )( )

( )bb

=- -+ +

R En n n

n n n7TFL

above below2film 2

above below2film 2

( )( )

( )=+

b

b1, 8

n

n

2

2

2

2

2film

2film

( )( )

( )b

=+ +

T En n

n n n

49TFL

above below

above below2film 2

( )( )=

+ b

1

1, 10

n

2

22film

( )( )

( )bb

=+ +

A En n

n n n

411TFL

above2film

above below2film 2

( )( )b

=+ b

n

1, 12

n

2film

2

22film

where e= + =n n ni1 2 is the complex refractiveindex for a non-magnetic material. The superindexindicates which medium it refers to, i.e. the mediumabove the film from where light comes, the mediumbelow the film into which light is transmitted, and thefilm itself. Equations (8), (10) and (12) give the reducedexpression of equations (7), (9) and (11) respectively,when above and below media are vacuum.

b = =p

ln d n dE

c

4 film film 2 film film, where d film is thefilm thickness (or equivalently the polarizable electronicthickness defined as h in method section). (The fullyrigorous Fresnel equations are also given in supple-mentary material, but as mentioned both sets ofequations gives similar results.) The transmittance ofborophene is displayed in figure 5. The scattering timeparameter is first fixed to τ= 1.21 10−18 s (bad metalcase) in figure 5(a) for which one observes hightransparency up to 6 eV, and a complete transparency(100% transmission) up to 3 eV. High anisotropy isalso found between light polarization with respect tocrystal orientation. Then in figures 5(b)–(d) corresp-onding to these different polarization of the electricfield, one varies τ up to 1.21× 10−13 s (good metalcase). In the visible range, T starts to decrease forminga plateau at 96%–98%, and then increase again to100%. In the infrared range, T is first strongly reducedespecially close to zero energy where T eventuallydrops to zero in a very goodmetal case. The reflectancecurves can be found in supplementary figure 10 andcorroborate results found for optical conductivitiesand transmittance. The reflectance is nearly zero in theinfrared-visible range except when considering Drudemodel with long scattering time (τ= 1.21× 10−13 s)especially in the infrared region.

4.2.Oxidized boropheneThe optical conductivities of oxidized borophenesystems are presented in figure 6 and correspond tothe 3× 3, 4× 4, 5× 5, and 6× 6 supercells (depictedin supplementary figure 9). At low energy, prominentpeaks are clearly observed in the infrared (IR) spec-trum part. Optical conductivity is also significantlyincreased in the visible light region. Except for the3× 3 supercell, the optical conductivity curves of thelarger oxidized borophene supercells are nicely repro-duced using pristine borophene and a Drude termwith τ= 1.21× 10−15 s. Such a large increase in theinfrared suggests that optical conductivity is highlysensitive to probably any surface modification, whichmakes optical conductivity/absorption measurementan interesting tool to investigate the cleanness ofborophene surface. This result also implies thattransparency of borophene will be slightly limited bysurface chemical functionalization, although the abso-lute values in figure 6 indicate that even for reasonablyhigh degree of oxygenation (1013 cm <-2 n < 10O

14

cm−2), the optical conductivity in the visible range islower than in pristine graphene.

5. Conclusion

Electronic and optical properties of pristine andoxidized borophene have been extensively studiedusing a first-principles approach. Pristine boropheneis found to be metallic with a relatively high electronicvelocity (6.6 105 m s−1). The full anisotropy of itselectronic structure has been revealed by inspectingcarefully the Fermi surface (line) in the 2D firstBrillouin zone showing that the permitted wavevectors at the Fermi energy have a maximal angle.Pristine borophene has also been found to exhibitextremely low optical conductivities due to theabsence of interband transitions up to 3 eV. Aniso-tropy was also reported for the computed opticalconductivity showing that for an electric field orientedalong the main conductive direction (x-axis, that isalong non-buckled B lines), thematerial stays opticallyinactive up to 6.5 eV. Although the exact valuedepends on disorder (through the scattering time τ),the calculated transmittances have been shown topossibly reach 100% in the visible range makingborophene more transparent than graphene. Then, ithas been predicted that oxidation of borophene ishighly probable due to the reported high adsorptionenergies (E ~ad 4.0–4.5 eV). Different adsorption siteswere considered and the preferred one was found to bein between adjacent B lines. Upon oxidation, boro-phene remainsmetallic. However, from the computedelectronic structure one anticipates dc conductivitydegradation due to the disorder which increases theeffective masses and decreases velocities. Finally,optical properties of oxidized borophene display alarge increase of the optical conductivity and

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2DMater. 3 (2016) 045006 ALherbier et al

reflectance in the infrared region while it remainsrelatively low (smaller than in pristine graphene) in thevisible region for reasonable degree of oxygenation,letting the opportunity to investigate borophene as acandidate for transparent conductivematerial.

Acknowledgments

AL, ARBM and J-CC acknowledge financial supportfrom the Fédération Wallonie-Bruxelles through theAction de Recherche Concertée (ARC) on 3Dnanoarchitecturing of 2D crystals (no. 16/21-077),and from the Belgium FNRS. This project has receivedfunding from the European Union’s Horizon 2020research and innovation programme under grantagreement No 696656. Computational resources havebeen provided by the supercomputing facilities of theUniversité catholique de Louvain (CISM/UCL) andthe Consortium des Équipements de Calcul Intensifen Fédération Wallonie Bruxelles (CÉCI) funded bythe Fonds de la Recherche Scientifique de Belgiqueunder the conventionN° 2.5020.11.

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