Insight Into Two-Dimensional Borophene: Five-Center Bond and Phonon-Mediated Superconductivity

Insight into Two-Dimensional Borophene: Five-Center Bond and Phonon-Mediated Superconductivity

Zhibin Gao,∗,† Mengyang Li,‡ and Jian-Sheng Wang†

†Department of Physics, National University of Singapore, Singapore 117551, Republic of Singapore ‡Institute for Chemical Physics & Department of Chemistry, Graduate Schoolof Science, Xi’anJiaotong University, Xi’an 710049, China

E-mail: [email protected]

Abstract Keywords

We report a previously unknown monolayer Ab initio calculations, Dirac cone, electronic borophene allotrope and we call it super-B with structure, charge doping, strain effect, su- a flat structure based on the ab initio calcu- perconductivity, electron-phonon coupling, 2D lations. It has good thermal, dynamical, and boron mechanical stability compared with many other typical borophenes. We find that super-B has a fascinating chemical bond environment consisting of standard sp, sp2 hybridizations and delo- Introduction calized five-center three-electron π bond, called Boron atom has five electrons with an electron π(5c-3e). This particular electronic structure configuration 1s22s22p1, which means that the plays a pivotal role in stabilizing the super-B number of valence electrons is less than the chemically. By extra doping, super-B can be available orbitals. Due to the small atomic transformed into a Dirac material from pristine radius, removal of valence electrons of boron metal. Like graphene, it can also sustain ten- requires a large amount of energy. Therefore, sile strain smaller than 24%, indicating superior boron likely forms covalent compounds, rather flexibility. Moreover, due to the small atomic than B3+ ions. However, owing to the smaller mass and large density of states at the Fermi electronegativity than hydrogen, boron atoms level, super-B has the highest critical temper- have a little positive charge in most covalent ature T of 25.3 K in single-element supercon- c compounds, except for special B-B bonds. ductors at ambient condition. We attribute this arXiv:1911.07464v1 [cond-mat.mtrl-sci] 18 Nov 2019 Matter always wants to be in the most stable high T of super-B to the giant anharmonicity c form. For most of non-metal atoms, stability of two linear acoustic phonon branches and an is achieved by following the octet rule. The- unusually low optic phonon mode. These pre- oretically, boron can accommodate five more dictions provide new insight into the chemical electrons according to the octet rule, but boron nature of low dimensional boron nanostructures commonly emerges three bonds, like BH , with and highlight the potential applications of de- 3 a total of six electrons in the outermost shell ex- signing flexible devices and high T supercon- c cepting for coordination compounds with four ductor. − − ligands like [BF4] and B[OH]4 . Hence, con-

1 ventional 2c-2e bond does not hold in the functional of Perdew-Burke-Ernzerhof (PBE)16 “electron-deficiency” boron compounds.1–3 Af- and HSE0617,18 with default mixing parame- terwards, many researchers find that localized ter value α = 0.25. The vacuum distance three-centered bonds, multi-centered bonds, over adjacent boron layer is set to be 20 A.˚ and delocalized σ and π bonds play very cru- The plane-wave cutoff is set to 500 eV. For cial roles in stabilizing the boron compounds.4,5 structure optimization, both lattice constants This particular electronic configuration also re- and atomic positions are relaxed with the cri- sults in many anomalous properties in boron terion for total energy of 1.0 × 10−8 eV and compounds.1,6,7 Hellmann-Feynman forces of 10−4 eV/ A.˚ The In 2012, for the first time, polymorphism of Brilliouin zone is sampled by 11 × 11. For 2D boron, called borophene, was proposed8 and the electron-phonon coupling (EPC), we used proper substrates were further explored theo- Quantum Espresso19 with 80 Ry energy cutoff. retically,9,10 which play pivotal roles in finally The self-consistent electron density in super-B synthesized borophene experimentally.11,12 was calculated by a 64 × 64 k-point grid. The In this study, we predict a previously un- dynamical matrices were calculated on a 10 × known 2D borophene allotrope, called super-B 10 grid after convergence test. The NBO analy- due to the large vacancy, based on the ab initio sis was carried out on B3LYP/6-311G(d,p) with calculations. Super-B is a hexagonal borophene Gaussian 1620 after optimization of B3LYP/6- with three atoms in each side, different from 31G(d,p). the hexagonal graphene. Besides, it has good thermal, dynamical, and mechanical stability. We find that the structure of super-B is formed Results by the standard sp, sp2 and delocalized π(5c- 3e) bonds in terms of the natural bond or- Structure bital (NBO) analysis. These particular type The optimized super-B is shown in Figure1a. of chemical bonds have never been reported The lattice constants are | ~a1| = | ~a2| = 5.45 A˚ in borophene before. Therefore, super-B sets with P6/mmm (space group no. 191). There a good example to break the stereotype that are two independent atoms based on the group triangular lattice with hexagonal vacancies is Wyckoff positions, whose fractional coordinates the only principle and concept of borophene. 1 2 1 1 are ( 3 , 3 ) and ( 2 , 2 ). In order to perform the Furthermore, by doping method, super-B can chemical bond analysis quantitatively, we use be transformed into a Dirac material from pris- hydrogen atoms to saturate boron atoms at the tine metal. It can also sustain 24% of biaxial border and explore the primitive cell located strain before fracture, indicating the same su- in the center region marked by a red box with perior flexibility as graphene. Due to the small negligible fringe effect. Each boron atom is la- atomic mass and large density of states at Fermi belled by a subscript number. We find that level, super-B has a phonon-mediated super- B3 is coordinated with three B (B1,B2 and conducting Tc of 25.3 K, which is derived from 2 B4) via sp hybridization, and B4 is linked to the giant anharmonicity of two linear acoustic the B3 and B5 with sp hybridization. The de- phonon branches and an unusually low optic Oz tailed NBO analysis is shown in Table1. It phonon mode. is clear that each boron atom has a p orbital which is perpendicular to the plane of super- Computational details B in Figure1b, and these p orbitals of boron, unhybridized and perpendicular to the plane of We studied the electronic structure, the equi- super-B, constitute an electron-deficiency π(5c- librium geometry, and structural stability of 3e) bond in the primitive cell, which is similar super-B using ab initio DFT as implemented in to the π(2c-2e) orbital in the primitive cell of VASP.13–15 We used the exchange-correlation graphene. Therefore, on the basis of period-

2 (a) (b)

H π (5c-3e) B a 1 1 3 2 5 4

Figure 1: (a) Crystal structure of super-borophene (super-B). The marginal boron atoms are sat- urated by hydrogens and the primitive cell is denoted by a red box. Each boronFigure atom is1 labelled by a cardinal number. (b) The hybridized orbital analysis in the primitive cell. Dotted and solid wedge shapes represent the boron atoms perpendicular to the plane of paper outside and inside respectively, which means seven boron atoms stand in same plane. One p orbital of each boron atom, totally seven, is perpendicular to plane of super-B (parallel to plane of paper), which is shown by two shaded dumbbells with one electron for sp and two white dumbbells without electron for sp2 hybridization. All delocalized orbitals perpendicular to the plane of super-B construct the large π(5c-3e) bond. The other p orbitals of sp boron atoms is parallel to the plane of super-B shown by two white dumbbells. Localized orbital locator (LOL) maps for (c) super-B and (d) graphene, showing strong π bonds (isovalue = 0.4 a.u.). icity rule, a large delocalized π(5nc-3ne) bond allotrope, like three-centered bond in triangular with electron-deficiency characteristic emerges lattice with/without vacancies.8,24 on the surface of super-B. In addition, the similarity of delocalized large In order to further verify the interesting π π bonds between graphene and super-B is also bond, localized orbital locator (LOL) maps reflected by the electronic configurations shown in Figure1c and Figure1d of super-B and in Figure2. The relationship between ben- graphene with isovalue 0.4 a.u. have been con- zene (C6H6) and graphene is the same as hy- 22,23 ducted by Multiwfn. All the π bonds are drogenated super-B (B12H6) and super-B. The well depicted in LOL picture. It is evident that electronic structure of benzene is well-known the π electrons from p orbitals of sp boron de- as three completely delocalized π orbitals, 6c- localized on the whole plane of super-B. All 2e π bonds,25 shown in Figure2b-2d based these delocalized large π bonds, analogous with on the adaptive nature density partitioning 21 graphene, significantly contribute to the stabil- (AdNDP). B12H6 is composed of three com- ity of super-B.Interestingly, the chemical bonds pletely delocalized 12c-2e π bonds with a lit- of super-B with π(5c-3e) bond have not been re- tle electron-deficiency characteristic. Here, the ported before in 2D materials and are quite dif- completely delocalized π bond in super-B is ver- ferent from the conventional bond in borophene ified again. Besides, we also find that there is no

3 (a) (b) (c) (d)

Graphene 3 6c-2e π bond

(e) (f) (g) (h)

Super-B 3 12c-2e π bond

Figure 2: (a)(e) Optimized structures of benzene (C6H6) and hydrogenated super-B (B12H6). Molec- ular orbitals of (b)(c)(d) 6c-2e π bonds of benzene and (f)(g)(h) 12c-2e π bonds of hydrogenated super-B based on the AdNDP method21 (white ball stands for hydrogen).

Figure 2 Jahn-Teller distortion in super-B by optimizing calculation. Therefore, our calculation confirms the atomic positions in a large supercell. that super-B is chemically, thermodynamically, The cohesive energy Ec is the amount of en- mechanically, and dynamically stable. ergy to break a material into isolated atoms. Intriguingly, we find a similar pattern, called Calculated Ec of super-B is 5.55 eV/atom, only α-graphyne, has been explored in the carbon 12 28 0.1 eV/atom higher than δ6-B, but more sta- counterpart but is not dynamically stable. 26 ble than the δ4-B shown in Table2. For any However, inserting two threefold-coordinated mechanically stable 2D materials, a necessary, carbon atoms into a 2D hexagonal lattice makes but not a sufficient condition must be satisfied: β-graphyne stable.29 We did a similar analy- 2 27 C11C22-C12>0 and C66>0. The calculated el- sis and found that the phonon dispersion of β- ements of super-B are C11=C22=146.0 GPa, borophyne has large imaginary frequency, re- C12=138.1 GPa, and C66=3.9 GPa, assuming flecting the significant distinction of electron or- an effective thickness of 0.384 nm (two van der bitals between carbon and boron. Considering Waals radius), which verifies the mechanical β-graphyne substructures and derivatives that stability of super-B. The phonon dispersion is have been experimentally synthesized in large- shown in the Supporting Information. Obvi- area nano-films,30,31 we are confident that the ously, there are two linear LA and TA acoustic same experimental technique can be extended phonon branches, and a parabolic ZA around to the super-B and boron nanostructures on the Γ-point. All frequencies are free from imagi- horizon. nary, confirming the lattice dynamical stability. Besides, we also implemented ab initio molec- Electronic structure and doping ular dynamics simulations using canonical en- semble and Nosé-Hoover thermostat at 600 K effect for 10 ps. The movie, shown in the Support- The projected electronic band structure and ing Information, indicates that the robustness density of states (DOS) of super-B are shown of our predicted super-B. Besides, we find that in Figure3a. Like graphene, pz orbital entirely super-B is non-magnetic, even having an odd dominates the electronic behavior around the number of electrons based on the first-principle Fermi level. We find that the intrinsic super-

4 Table 1: The natural bond orbital (NBO) analysis of atomic notation B3 and B4 in Figure1a including the number of occupancy with spin-up, spin-down electrons of boron and total of them, as well as contributions of s, p and d atomic orbitals.

Occupancy Hybridization of center borona Center atoms Bonding atoms Spin-up Spin-down total spλ s(%) p(%) d(%)

1.99 B3 B1 0.95 0.95 1.90 sp 33.37 66.53 0.10 1.99 B3 B2 0.95 0.95 1.90 sp 33.37 66.53 0.10 2.02 B3 B4 0.95 0.95 1.90 sp 33.06 66.84 0.10 1.00 B4 B3 0.95 0.95 1.90 sp 49.99 50.00 0.01 1.00 B4 B5 0.95 0.95 1.90 sp 49.99 50.00 0.01 aThe contribution of s, p and d orbitals of center boron is the average of spin-up, spin-down electrons of boron, and spλ of center boron is the almost same for both spin-up and spin-down.

Table 2: The calculated lattice constants, planer or buckling, coordination number, symmetry and cohesive energy for 2D borophene allotropes χ3, β12, δ4, δ6 and our proposed super-B.

Structures a1 (A)˚ a2 (A)˚ Planer Z Symmetry Ec (eV/atom) a χ3-B 4.45 4.45 Yes 4,5 C mmm 5.723 a β12-B 2.92 5.07 Yes 4,5,6 Pmmm 5.712 a δ4-B 2.93 3.28 Yes 4 Pmmm 5.384 a δ6-B 3.22 3.29 No 6 Pmmn 5.662 Super-Bb 5.45 5.45 Yes 2,3 P6/mmm 5.550

aRef. 12,26 bPresent work. All results are based on the PBE functionals.

5 This band is right!

(a) (b)

Px+ Py E D - E

EF F (eV)

Energy (eV) Energy ED Lattice constant a (Å)

Γ K M Γ DOS -0.4 -0.3 -0.2 -0.1 0.0 Injected charge e /B atom Figure 3: (a) Orbitally resolved band structure and total density of states for pristine super- borophene. (b) The lattice constant and the position of Dirac cone (ED) with respect to the Fermi level (EF ) asProjected a function undoped of injected band charge. The green dashed line is a parabolic ﬁtting of lattice constant with 0.999 R-Squared and the black dashed line is a linear ﬁtting of the relative gap between EF and ED with 0.992 R-Squared. Blue square denotes the situation of EF = ED. The dashed horizontal lines are guided for your eyes. Figure 2

B is metallic, which is analogous with α-B,24 of hole doping. Due to the special sp, sp2 and 12 1,8 β12-B, and other monolayer boron sheets. π(5c-3e) bond, the bond length increases from Below the EF around 0.52 eV, two pz bands 1.573 A˚ to 1.613 A˚ when injecting −0.2/B and cross each other, forming a standard Dirac cone further reaches to 1.731 A˚ at −0.4/B. This phe- (ED), which is verified by the total DOS in the nomenon is different from the previous orthog- right panel. onal -B allotrope33 in which doping has an Recently, honeycomb borophene by extra anisotropic effect on the lattice constants. Due doping of 1 e/B atom, identical with graphene’s to the P6/mmm symmetry of super-B, the net configuration, has been realized experimen- charge has the same effect on both a1 and a2 tally32 and theoretically.33 Here, we would like lengths. In this sense, doping is an effective to explore how large doping could make super- way to change the lattice constant of super-B 33,34 B a semimetal, like graphene. Since EF is larger and other 2D borophenes. than ED in the original state, one should pro- On the other hand, doping will change the vide a degree of hole doping to the super-B, electronic band structure, especially the posi- shifting up the bands. The results are shown tion of EF . The relative position of ED with in Figure3b. In the calculation, when adding respect to EF , in Figure3b, decreases when in- or removing an amount of electrons (holes), creasing the injected holes. We find that the the system will be compensated by the same ED-EF can be well fitted by a linear function amount uniform background charge of holes with 0.992 R-Squared, indicating a rigid band (electrons), retaining a continuous neutral con- shift in super-B. −0.4/B doping corresponds dition. This standard method has been verified to 1.44 × 1014 cm−2, which is an accessible by many previous works.33 and reachable value in the current experimen- In each doping concentration, we optimized tal technique, such as electrical gating and ionic both lattice constants and atomic positions. On liquid injection. Even though the rigid band the one hand, the lattice constant of super-B, shift is common in 2D transition metal dichalco- interestingly, can be well fitted by a quadratic genides,35 we have not found a similar behavior polynomial with 0.999 R-Squared as a function in 2D boron allotrope heretofore. The reason

6 (a) (b)

EF Energy (eV) Energy

Γ K M Γ DOS (c) (d)

Figure 4: (a) Electronic band structures from0.2 hole/B PBE (black doping solid line) and HSE06 (magentaFigure dashed 3 line) methods and projected density of states (PBE level) of super-B with injected electrons h∆Qi = −0.2 e/B, corresponding to a doping level of 7.7 × 1013 cm−2 that has been realized by electrical gatingand ionic liquid injection.(b) 3D Dirac cone formed by the valence and conduction bands in the vicinity of Dirac point. In the first Brillouin zone, the high symmetry k points are: Γ (0 0 0), K (-1/3 2/3 0), and M (0 0.5 0). (c,d) The isosurfaces of partial charge densities for the (c) VBM and (d) CBM of super-B with h∆Qi = −0.2e/B. The isosurface level value is 0.03 e A˚−3. behind it is that many 2D borophenes mainly the Supporting Information. They look simi- 8,24 possess three-centered bond characteristic, lar but they have different Fermi velocities υF . 2 rather than sp, sp , and delocalized π(5c-3e) Even though υF of super-B is smaller than α- bond in super-B. graphyne, we show the possibility to transform In order to further confirm the Dirac cone from metal to semimetal in 2D boron system of super-B at −0.2/B (7.7 × 1013 cm−2) dop- by extra doping. Furthermore, we calculate the ing concentration, we plot the electronic band partial charge densities of valence band max- and corresponding DOS in Figure4a using PBE imum (VBM) and conduction band minimum (black solid line) and standard HSE06 meth- (CBM) of super-B in Figure4c and 4d. VBM ods (pink dashed line). It shows that px+py stems from the delocalized orbitals, resulting in shift up or down using HSE06. However, the large π(5c-3e) bond that has mentioned in Fig- bands from pz orbital do not change its po- ure1c, whereas CBM shows localized in-plane sition, only having slightly different slopes of orbitals constituting the standard sp and sp2 two linear bands when hybrid functional is ap- bonds between boron atoms. This picture is plied. 3D band in the reciprocal space, in Fig- well consistent with the chemical NBO analysis ure4b, further proves the band crossing at the shown in Figure1. K-point. Besides, we compare the band structures of α-graphyne and hole-doped super-B in

7 (a) (b) 12 Uniaxial Biaxial

Poisson’s ratio ) 9 - 1 (cm 6

Stress (N/m) 3 Frequency Frequency

0 0 5 10 15 20 25 30 Strain ε (%) Γ K M Γ Figure 5: (a) Strain-stress curves of super-borophene while loaded along biaxial (green) and uniaxial (blue) directions, and Poisson’s ratio (pink) under biaxial strain. (b) phonon dispersion under 24% (solid black line) and 25% (red dashed line) biaxial strain. The critical points of both types of strain are marked by vertical dashed lines in (a). The blue arrows illustrates the “Kohn anomaly” related to lattice instability. Figure 4 1500 Mechanical property α2F ( ω) λ ω In practical applications, a large ideal strength ( ) 1200

of material is highly desired in ﬂexible electronic ) 1 devices.36–38 According to the deﬁnition, biaxial - m c

( 900 tensile strain can be expressed as ε = a/a0 − 1, y c in which a and a0 are the stretched and pris- n e tine lattice constant of materials. As biaxial u q 600 e strain ε increases, in Figure5a, the stress σ r F in green line first linearly increases, then grad- 300 ually saturates with a maximum value called ideal strength.27 The ideal strength of super-B is 9.50 N/m, which is the same order of many 0 other borophenes.36,39 In each strain, we calcu- Γ K M Γ 0 1 2 late the phonon dispersion to verify its stability. Figure 6: Phonon band structure and Smaller than ε ≤ 24%, all phonon frequencies electron-phonon coupling (EPC) of the super- are positive, shown in Figure5b (black line). borophene. The area of the pink circle is pro- When ε=25%, the system becomes unstable, portional to the EPC strength. The right panel which is a clear hint of the “Kohn anomaly” is Eliashberg spectral function α2F(ω) and the when reaching the ideal strength in super-B. ε total EPC constant λ(ω). = 25% strain is also called breaking point which means a material physically breaks at its breaking point. This phenomenon has been studied the slope of the strain-stress curve. A large E in graphene extensively.34,40,41 means a rigid material. The calculated E by For the uniaxial strain, the isotropically stress linear fitting equals 5.85 N/m, indicating a soft response of super-B is shown in Figure5a in mechanical property of super-B. We also verify blue line. The ideal strength is 1.66 N/m this value by using elastic tensor formula27,42,43 at ε=12%, relatively smaller than the biaxial E=(C11C22-C12C21)/C22. This ultrasoft elastic strain (phonon dispersion is shown in the Sup- property of super-B may have great potential porting Information). Young’s modulus E is for designing flexible electronic devices.36,39

8 Table 3: Single-element superconductivity of tion, having a very small DOS at EF . Metallic graphene, silicene, phosphorene, stanene, χ3-, β12- boron, also with very small M¯, is a promising , δ6- and super-borophene. candidate to satisfy all above criterion simultaneously. The famous bulk MgB2 in which mag- −1 µ∗=0.1 Materials λ ωlog (cm ) Tc (K) nesium is inserted into hexagonal boron, has an unprecedented high T of 39 K.6 a c Graphene 0.61 277.8 8.1 According to the BardeenCooperSchrieﬀer Siliceneb 0.44 236.9 1.7 (BCS) theory and Eliashberg equations, the spectral function can be expressed as51 Phosphorenec 0.54 176.3 4.2

d 2 1 X γqν Stanene 0.65 42.3 1.3 α F (ω) = δ(ω − ωqν) , (1) 2πN(EF ) ~ωqν e qν χ3-B 0.62 455.4 11.5

e where N, ωqν, and γqν are the electronic density β12-B 0.78 362.0 16.1 of states at EF , phonon frequency and linewidth e δ6-B 1.05 272.5 20.5 for phonon modes λ with the wave vector q. Super-Bf 1.95 102.1 20.8 The total EPC constant can be obtained when making a summation of spectral function over a Li doped graphene. 44 bSilicene under 0.44 e/atom the ﬁrst Brillouin zone doping. 45 cPhosphorene under 0.10 e/atom doping. 46 dLi doped stanene. 47 eThree experimental 2D X Z α2F (ω) 48 f λ = λ = 2 dω, (2) borophenes. Present work. qν ω qν

The Poisson’s ratio ν, defined as the nega- Finally, based on the AllenDynes formula,52 the 27,49 tive sign ratio of lateral to applied strain, critical temperature Tc of superconductor can is shown in Figure5a in a pink curve. The be estimated by equilibrium super-B has a very large ν of 0.95, ω −1.04(1 + λ) more than 5 times of borophene with vacancy T = log exp[ ], (3) =1/836 and also 5 times of graphene.50 This c 1.2 λ(1 − 0.62µ∗) − µ∗ ultrahigh of ν suggests that the response de- ∗ formation of super-B is almost with the same in which µ is the effective screened Coulomb amplitude when applied strain to the pristine repulsion constant (generally 0.10∼0.15) and structure. As strain increases, ν(ε) decreases ωlog reads significantly, indicating a gradual weakness of Z 2 dω 2 Poisson effect at large strain. The minimum ωlog = exp[ α F (ω)log(ω)]. (4) λ ω ν(ε) is 0.03 at ε=24%, reducing to a final satu- ration near the critical point.49,50 The calculated phonon dispersion, EPC, and spectral function of super-B are shown in Fig- Superconductivity ure6. The area of pink circle is proportional to the strength of EPC. The largest EPC strength As an accepted rule of thumb, a good phonon- stems from the ZA, TA and one special optical mediated superconductor may satisfy some of phonon mode. For the purely flat 2D materi- conditions: (i) a small average atomic mass M¯, als, such as graphene, ZA mode must satisfy a (ii) a large electronic density of states (DOS) at symmetry-based selection rule.53 Therefore, for EF , (iii) a large Debye temperature θD. As θD 2D materials, ZA modes generally dominant the is inversely proportional to M¯, a small M¯ gen- heat transport and show a giant anharmonicity erally means a large θD. In this sense, hydrogen (large Grüneisenparameter). is a good candidate for superconductor. How- As the vibrational direction of this optical ever, hydrogen is an insulator at normal condi- phonon is parallel to the z axis, we call it Oz

9 h phonon-mediated The Ta- in shown 3. are (1)-(4), ble Eq. the to according total The constant region. EPC phonon acoustic of frequency this nlsrtg osgicnl nacdthe enhanced LiC significantly of to strategy inal condition. ambient at ductors criti- temperature intrinsically cal highest higher the has little super-B edge, a even the and than comparable is in- which first-class temperature the critical has trinsically super-B Our borophene and allotropes. materials 2D related other some with K 20.8 is tion then and M again. and Γ K, approaching when to decreases Γ phonon-phonon from increases of firstly space phase large scattering. a to and ing energy lead- the simultaneously, satisfy conservation to momentum recent easier it with makes similar mode tellurene. spirit 2D in phonon discovered is acoustic which the regions into The simplicity. drops of anomalously, sake the for mode inset. an as rloi oe b oa nrya ucino ipaeetof displacement of function a as energy Total B (b) zone. Brillouin Grüneisen parameter (a) 7: Figure 2 utemr,Poeae al. et Profeta Furthermore, func- spectral Eliashberg corresponding The (a) n B and , O

α Grüneisen parameter γ 6 z 2 F( yisrigtemtlltimdet a to due lithium metal the inserting by oeehne h P ntelow- the in EPC the enhances mode Γ δ 4 ω 6 42 ,aesai u B but static are 1a, Figure in shown , B(05K.T h eto knowl- of best the To K). (20.5 -B ) lorvasthat reveals also 6, Figure in , h P tegho this of strength EPC The λ λ 19 (at =1.95 T n rtcltemperature critical and c nsnl-lmn supercon- single-element in TA ZA LA O z 42 K µ h o optical low The 01.W lolist also We =0.1). 44 rpsdasem- a proposed M T T c c γ fsuper-B of f2. K, 20.8 of ftreaosi n n pia hnnbace ntefirst the in branches phonon optical one and acoustic three of O O z z mode, mode T O T Γ c z c , 3 10 (b) n B and ,w banta hr s60% is there cm on that 300 based obtain low Besides, we (2), 6. Eq. Figure the in panel function right peak spectral the large Eliashberg the the about in brings finally, anhar- giant monicity, a This anharmonicity. to phonon lead large interactions phonon and phonon Specif- acoustic-optical acoustic-acoustic 5 b. strong Figure elimi- the in are ically, strain modes applied phonon by with soft nated evidenced the also that fact is the this electron-phonon Notably, as well scattering. as scattering, phonon- phonon the enhance would branch phonon tical of value average an is secondary The − ma- of terials. bonds chemical in anharmonicity large strong A phonon super-B. of in function vibration thermal a as large response volume finally shows and EPC, large T the to tributions TA anharmonicity.ZA, phonon and giant the from high the that find hope We level. Fermi at T state of density large iia ehd uha ea potassium. metal as such method, similar a c c 0 eogn oteZ oei lc line. black in mode ZA the to belonging 30, fe nlsso eaae hnnmds we modes, phonon separated of analysis After

h Grüneisen parameter The . Energy (meV/atom) fsprBcnas efrhrehne by enhanced further be also can super-B of 5 O aemvmnsi nopst direction opposite an in movements make z 42,5556 hnnmdsaetetremi con- main three the are modes phonon Displacement Displacement of along B z (Å) − 1 h ags au of value largest The First Quadratic Quadratic+cubic+quartic ntettlECcontributions, EPC total the in O z O -principles T − hnnmd,i hc B which in mode, phonon z c 0 hsuuulylwop- low unusually This 10. rnhi leln having line blue in branch fsprBmil stems mainly super-B of 5 3 z y γ 7a, Figure in , γ x Figure Figure α γ saround is 2 en a means F( ω λ ) 6 54 be- in 1 , which verifies that low frequency significantly is important result is that SWBNTs are always responsible for this unusually large λ. good metal. In order to further confirm the To further explore the phonon anharmonic metallic property, for example, we plot the DOS property in super-B, we calculate the total en- of zigzag (8,0) and armchair (8,8) tubes in the ergy as a function of displacement in phonon Supporting Information. At the EF , DOS is Oz mode, in which B1,B2, and B4 shown significantly enhanced when rolling into a cylin- in Figure1a are static but B 3 and B5 make der, which is irrelevant to the type of edge movements in an opposite direction, in Fig- shapes. This probably will, in turn, further am- ure7b. ZA and TA modes also have simi- plify the Tc of SWBNTs according to the rule lar behaviors. The first principle results can (ii) mentioned above. According to the previ- 59 be well fitted by a polynomial expression up ously seminal works, Tc will be unquestion- to quartic E(u)=225.56u2+1203.01u4 in the ably enhanced by rolling sheets into tubes as blue line. However, harmonic approximation a result of opening new electron-phonon scat- (green line) cannot produce a good agreement. tering channels. However, due to formidable The ratio between quartic and quadratic terms computing requirement, currently, one is quite is A4/A2≈5.33, indicating a quite large an- difficult to simulate the EPC in SWCNTs and harmonicity in super-B, which finally leads SWBNTs based on the accurate first-principle to a strong interaction between electrons and calculations. As one of the nearest neighbors of phonons. To the best of knowledge, supercon- carbon, super-B and SWBNTs are promising 57 ductor MgB2 binary alloy and 2D tellurene superconductors by using the similar method with high figure of merit zT 42,58 also exhibit of carbon.44 very large phonon anharmonicity. Compared with χ3-, β12-, and δ6−B, super-B For the band structure, we consider the dis- is a metastable phase of borophene. In retro- torted and undistorted super-B due to the Oz spect, the most stable phase of 2D silicon is phonon mode. The result is shown in the Sup- silicene with 18 atoms in the primitive cell,60 porting Information. The band splitting be- rather than the phase with 2 atoms.61 Even tween the undistorted and distorted structures though the latter is much less stable than the in super-B is around 0.07 eV. Although this previous, the latter, at present, could be easily 6 number is smaller than the MgB2 (Tc=39 K), grown with very accurate experimental tech- its impact is significantly large. We mark a nique.62,63 Similarly, blue phosphorus,64 as a special area with a blue circle which is close metastable of black phosphorus,65 has also been to the Fermi level and more importantly, and successfully grown on Au(111).66,67 The cohe- its DOS is quite large due to the relatively flat sive energy Ec of the experimentally attain- band. Hence, giant anharmonicity of this Oz able silicene with 2 atoms and phosphorene are phonon mode intensifies the DOS around the 3.71 eV/atom62,63 and 3.61 eV/atom,65,68 sep- Fermi level, then stimulates the EPC and fi- arately. A large Ec indicates a strong chem- nally leads to a high Tc. ical bond in materials. The Ec of super-B is 5.55 eV, indicating a strong and robust chemical bond to maintain stability. Furthermore, Discussion due to the complex chemical environment and variable substrate effect, a recently discovered Similar to carbon nanotube, boron can also be borophene has been synthesised.11 Notably, it rolled into a cylinder.24,26 We optimize singled- is a novel metastable borophene, also less stable walled borophene nanotubes (SWBNTs) with than the χ -, β -, and δ −B allotropes. different diameters and edge shapes (armchair 3 12 6 Very recently, a cutting-edge experimental or zigzag). We find that all SWBNTs are quite technique, called reactive molecular beam epi- stable remaining a good cylinder without any taxy method, has been successfully used to buckling or collapse. Results are shown in the attain the freestanding crystalline oxide per- table of the Supporting Information. The most ovskites.69 Borophene, like oxide perovskites,

11 has no counterpart in bulk material. Hence, ex- consisting of standard sp, sp2 hybridizations cept for the metal substrates, this recently de- and delocalized five-center three-electrons π(5c- veloped approach may shed light on the experi- 3e) bonds, based on the NBO analysis. This mental realization of super-B and other boron- exceptional electronic structure plays a cru- related nanostructures. cial role in stabilizing the super-B chemically. Furthermore, a 2D atomic layer with hexag- Meanwhile, By extra doping, super-B can be onal boron network has been bottom-up syn- transformed into a Dirac material from pris- thesized freshly. The main structure in their tine metal. Like graphene, it also has a supe- work54 is exactly our predicted super-B, which rior flexibility. Furthermore, due to the small further verifies the correctness of our theoretical atomic mass and large density of state at Fermi calculation and the importance of our work. level, super-B has the highest intrinsically crit- As a matter of fact, for strong coupling sys- ical temperature Tc of 25.3 K in single-element tems (λ > 1.5), superconducting temperature superconductors at ambient condition. We have T c should be calculated using a more general attributed this high Tc of super-B to the giant expression according to Allen and Dynes52 anharmonicity of two linear acoustic phonon branches and an unusually low optic Oz phonon f f ω 1.04(1 + λ) T = 1 2 log exp[− ], (5) mode. c 1.2 λ − µ∗(1 + 0.62λ) Author Information 3/2 1/3 f1 = [1 + (λ/Λ1) ] , (6) Corresponding Author ∗ (¯ω /ω − 1)λ2 E-mail: [email protected] f = 1 + 2 log , (7) 2 λ2 + Λ2 2 ORCID where f 1 and f 2 represent the strong-coupling Zhibin Gao: 0000-0002-6843-381X correction and shape correction, respectively. 52 The parameters Λ1 and Λ2 are given by Supporting Information The Supporting Information is available free of Λ = 2.46(1 + 3.8µ∗), (8) 1 charge on the ACS Publications website via the Internet at https://pubs.acs.org/journal/aamick. ∗ Phonon dispersion of super-B, electronic band Λ2 = 1.82(1 + 6.3µ )(¯ω2/ωlog), (9) structures of pristine α-graphyne and super-B 52 in which the general moment is defined as under −0.2 e/B doping, and movies of molec- 2 Z ular dynamics simulations at T=600 K at the < ωn >= dωα2F (ω)ωn−1, (10) end of 10 ps. λ

According to Eq. (5)-(10), the calculated T c Notes is 25.3 K when µ∗ = 0.1. Note that this re- The authors declare no competing financial in- sult is larger than 20.8 K based on Eq. (3), terest. further confirming our conclusion that super- Acknowledgement B has the highest critical temperature T c in We acknowledge David Tománek for many single-element superconductors at ambient con- fruitful discussions and good suggestions.We ditions. also thank Hanyu Liu for valuable discus- In summary, we have predicted a previously sions and kind help. M.L. acknowledges use- unknown monolayer borophene by first princi- ful discussions with Xiang Zhao. TheHPCplat- ples. It has good thermal, dynamical, and me- formofXi’anJiaotongUniversityis highlyappreci- chanical stability compared with many other ated. This work is supported by an MOE tier typical borophenes. We have found that super- 1 grant R-144-000-402-114. B has a fascinating chemical bond environment

12 References (10) Zhang, Z.; Yang, Y.; Gao, G.; Yakob- son, B. I. Two-Dimensional Boron Mono- (1) Li, W.-L.; Chen, X.; Jian, T.; Chen, T.- layers Mediated by Metal Substrates. T.; Li, J.; Wang, L.-S. From Planar Angew. Chem. Int. Ed. 2015, 54, 13022– Boron Clusters to Borophenes and Met- 13026. alloborophenes. Nature Rev. Chem. 2017, 1, 0071. (11) Mannix, A. J.; Zhou, X.-F.; Kiraly, B.; Wood, J. D.; Alducin, D.; Myers, B. D.; (2) Sergeeva, A. P.; Popov, I. A.; Pi- Liu, X.; Fisher, B. L.; Santiago, U.; azza, Z. A.; Li, W.-L.; Romanescu, C.; Guest, J. R. Synthesis of Borophenes: Wang, L.-S.; Boldyrev, A. I. Understand- Anisotropic, Two-Dimensional Boron ing Boron Through Size-Selected Clusters: Polymorphs. Science 2015, 350, 1513– Structure, Chemical Bonding, and Flux- 1516. ionality. Acc. Chem. Res. 2014, 47, 1349– 1358. (12) Feng, B.; Zhang, J.; Zhong, Q.; Li, W.; Li, S.; Li, H.; Cheng, P.; Meng, S.; (3) Wang, L.-S. Photoelectron Spectroscopy Chen, L.; Wu, K. Experimental Realiza- of Size-Selected Boron Clusters: From tion of Two-Dimensional Boron Sheets. Planar Structures to Borophenes and Nat. Chem. 2016, 8, 563. Borospherenes. Int. Rev. Phys. Chem. 2016, 35, 69–142. (13) Kresse, G.; Furthmüller,J. Efficient Iter- ative Schemes for ab initio Total-Energy (4) Eberhardt, W.; Crawford Jr, B.; Lip- Calculations Using A Plane-Wave Ba- scomb, W. N. The Valence Structure sis Set. Phys. Rev. B: Condens. Matter of the Boron Hydrides. J. Chem. Phys. Mater. Phys. 1996, 54, 11169–11186. 1954, 22, 989–1001. (14) Kresse, G.; Furthmüller, J. Efficiency (5) Lipscomb, W. N. The Boranes and Their of ab-initio Total Energy Calculations Relatives. Science 1977, 196, 1047–1055. for Metals and Semiconductors Using A Plane-Wave Basis Set. Comput. Mater. (6) Nagamatsu, J.; Nakagawa, N.; Mu- Sci. 1996, 6, 15–50. ranaka, T.; Zenitani, Y.; Akimitsu, J. Su- perconductivity at 39 K in Magnesium Di- (15) Kresse, G.; Hafner, J. Ab initio Molecular- boride. Nature 2001, 410, 63. Dynamics Simulation of The Liquid- Metal–Amorphous-Semiconductor Transi- (7) Feng, B.; Sugino, O.; Liu, R.-Y.; tion in Germanium. Phys. Rev. B: Con- Zhang, J.; Yukawa, R.; Kawamura, M.; dens. Matter Mater. Phys. 1994, 49, Iimori, T.; Kim, H.; Hasegawa, Y.; Li, H. 14251–14269. Dirac Fermions in Borophene. Phys. Rev. Lett. 2017, 118, 096401. (16) Perdew, J. P.; Burke, K.; Ernzer- hof, M. Generalized Gradient Approxima- (8) Penev, E. S.; Bhowmick, S.; tion Made Simple. Phys. Rev. Lett. 1996, Sadrzadeh, A.; Yakobson, B. I. Poly- 77, 3865–3868. morphism of Two-Dimensional Boron. Nano Lett. 2012, 12, 2441–2445. (17) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened (9) Liu, Y.; Penev, E. S.; Yakobson, B. I. Coulomb Potential. J. Chem. Phys. 2003, Probing The Synthesis of Two- 118, 8207–8215. Dimensional Boron by First-Principles Computations. Angew. Chem. Int. Ed. (18) Krukau, A. V.; Vydrov, O. A.; Iz- 2013, 52, 3156–3159. maylov, A. F.; Scuseria, G. E. Influence of The Exchange Screening Parameter

13 on The Performance of Screened Hybrid (27) Gao, Z.; Dong, X.; Li, N.; Ren, J. Novel Functionals. J. Chem. Phys. 2006, 125, Two-Dimensional Silicon Dioxide with In- 224106. Plane Negative Poissons Ratio. Nano Lett. 2017, 17, 772–777. (19) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; (28) Longuinhos, R.; Moujaes, E. A.; Alexan- Ceresoli, D.; Chiarotti, G. L.; Co- dre, S. S.; Nunes, R. Theoretical Chem- coccioni, M.; Dabo, I. QUANTUM istry of α-Graphyne: Functionalization, ESPRESSO: A Modular and Open-Source Symmetry Breaking, and Generation of Software Project for Quantum Simula- Dirac-Fermion Mass. Chem. Mater. 2014, tions of Materials. J. Phys.: Condens. 26, 3701–3708. Matter 2009, 21, 395502. (29) Malko, D.; Neiss, C.; Viñes, F.; (20) Frisch, M.; Trucks, G.; Schlegel, H.; Scuse- Görling, A. Competition for Graphene: ria, G.; Robb, M.; Cheeseman, J.; Scal- Graphynes with Direction-Dependent mani, G.; Barone, V.; Petersson, G.; Dirac Cones. Phys. Rev. Lett. 2012, 108, Nakatsuji, H. Gaussian 16. Gaussian 16, 086804. revision A.03; Gaussian, Inc.: Walling- ford, CT, 2016. (30) Li, G.; Li, Y.; Liu, H.; Guo, Y.; Li, Y.; Zhu, D. Architecture of Graphdiyne (21) Zubarev, D. Y.; Boldyrev, A. I. De- Nanoscale Films. Chem. Commun. 2010, veloping Paradigms of Chemical Bond- 46, 3256–3258. ing: Adaptive Natural Density Partition- ing. Phys. Chem. Chem. Phys. 2008, 10, (31) Inagaki, M.; Kang, F. Graphene Deriva- 5207–5217. tives: Graphane, Fluorographene, Graphene Oxide, Graphyne and (22) Schmider, H.; Becke, A. Chemical Content Graphdiyne. J. Mater. Chem. A 2014, 2, of The Kinetic Energy Density. J. Mol. 13193–13206. Struct.: THEOCHEM 2000, 527, 51–61. (32) Li, W.; Kong, L.; Chen, C.; Gou, J.; (23) Lu, T.; Chen, F. Multiwfn: A Multifunc- Sheng, S.; Zhang, W.; Li, H.; Chen, L.; tional Wavefunction Analyzer. J. Comput. Cheng, P.; Wu, K. Experimental Realiza- Chem. 2012, 33, 580–592. tion of Honeycomb Borophene. Sci. bull. 2018, 63, 282–286. (24) Tang, H.; Ismail-Beigi, S. Novel Precur- sors for Boron Nanotubes: The Compe- (33) Liu, D.; Tomnek, D. Effect of Net Charge tition of Two-Center and Three-Center on the Relative Stability of 2D Boron Al- Bonding in Boron Sheets. Phys. Rev. Lett. lotropes. Nano Lett. 2019, 19, 1359–1365. 2007, 99, 115501. (34) Si, C.; Duan, W.; Liu, Z.; Liu, F. (25) Popov, I. A.; Boldyrev, A. I. Chemi- Electronic Strengthening of Graphene by cal Bonding In Coronene, Isocoronene, Charge Doping. Phys. Rev. Lett. 2012, and Circumcoronene. Eur. J. Org. Chem. 109, 226802. 2012, 2012, 3485–3491. (35) Gao, Z.; Zhou, Z.; Tománek,D. Degen- (26) Wu, X.; Dai, J.; Zhao, Y.; Zhuo, Z.; erately Doped Transition Metal Dichalco- Yang, J.; Zeng, X. C. Two-Dimensional genides as Ohmic Homojunction Contacts Boron Monolayer Sheets. ACS Nano to Transition Metal Dichalcogenide Semi- 2012, 6, 7443–7453. conductors. ACS Nano 2019, 13, 5103– 5111.

14 (36) Zhang, Z.; Yang, Y.; Penev, E. S.; (46) Shao, D.; Lu, W.; Lv, H.; Sun, Y. Yakobson, B. I. Elasticity, Flexibility, and Electron-Doped Phosphorene: A Poten- Ideal Strength of Borophenes. Adv. Funct. tial Monolayer Superconductor. Europhys. Mater. 2017, 27, 1605059. Lett. 2014, 108, 67004.

(37) Liu, A. Y.; Cohen, M. L. Prediction of (47) Shaidu, Y.; Akin-Ojo, O. First Prin- New Low Compressibility Solids. Science ciples Predictions of Superconductivity 1989, 245, 841–842. in Doped Stanene. Comput. Mater. Sci. 2016, 118, 11–15. (38) Si, C.; Liu, Z.; Duan, W.; Liu, F. First- Principles Calculations on the Effect of (48) Penev, E. S.; Kutana, A.; Yakobson, B. I. Doping and Biaxial Tensile Strain on Can Two-Dimensional Boron Supercon- Electron-Phonon Coupling in Graphene. duct? Nano Lett. 2016, 16, 2522–2526. Phys. Rev. Lett. 2013, 111, 196802. (49) Gao, Z.; Liu, D.; Tománek, D. Two- (39) Wang, H.; Li, Q.; Gao, Y.; Miao, F.; Dimensional Mechanical Metamaterials Zhou, X.-F.; Wan, X. Strain Effects on with Unusual Poisson Ratio Behavior. Borophene: Ideal Strength, Negative Pos- Phys. Rev. Applied 2018, 10, 064039. sions Ratio and Phonon Instability. New J. Phys. 2016, 18, 073016. (50) Liu, F.; Ming, P.; Li, J. Ab initio Calcula- tion of Ideal Strength and Phonon Insta- (40) Yan, J.; Henriksen, E. A.; Kim, P.; bility of Graphene Under Tension. Phys. Pinczuk, A. Observation of Anomalous Rev. B: Condens. Matter Mater. Phys. Phonon Softening in Bilayer Graphene. 2007, 76, 064120. Phys. Rev. Lett. 2008, 101, 136804. (51) Bardeen, J.; Cooper, L. N.; Schrief- (41) Lazzeri, M.; Mauri, F. Nonadiabatic Kohn fer, J. R. Microscopic Theory of Supercon- Anomaly in a Doped Graphene Mono- ductivity. Phys. Rev. 1957, 106, 162–164. layer. Phys. Rev. Lett. 2006, 97, 266407. (52) Allen, P. B.; Dynes, R. C. Transition Tem- (42) Gao, Z.; Tao, F.; Ren, J. Unusually perature of Strong-Coupled Superconduc- Low Thermal Conductivity of Atomically tors Reanalyzed. Phys. Rev. B: Condens. Thin 2D Tellurium. Nanoscale 2018, 10, Matter Mater. Phys. 1975, 12, 905–922. 12997–13003. (53) Lindsay, L.; Broido, D. A.; Mingo, N. (43) Wang, Y.; Gao, Z.; Zhou, J. Ultralow Flexural Phonons and Thermal Trans- Lattice Thermal Conductivity and Elec- port in Graphene. Phys. Rev. B: Condens. tronic Properties of Monolayer 1T Phase Matter Mater. Phys. 2010, 82, 115427. Semimetal SiTe2 and SnTe2. Physica E 2019, 108, 53–59. (54) Kambe, T.; Hosono, R.; Imaoka, S.; Ya- mamoto, K. Solution Phase Mass Synthe- (44) Profeta, G.; Calandra, M.; Mauri, F. sis of 2D Atomic Layer With Hexagonal Phonon-Mediated Superconductivity in Boron Network. J. Am. Chem. Soc. 2019, Graphene by Lithium Deposition. Nat. 141, 12984–12988. Phys. 2012, 8, 131–134. (55) Gao, Z.; Li, N.; Li, B. Heat Conduc- (45) Wan, W.; Ge, Y.; Yang, F.; Yao, Y. tion and Energy Diffusion In Momentum- Phonon-Mediated Superconductivity in Conserving One-Dimensional Full-Lattice Silicene Predicted by First-Principles Ding-A-Ling Model. Phys. Rev. E 2016, Density Functional Calculations. Euro- 93, 022102. phys. Lett. 2013, 104, 36001.

15 (56) Gao, Z.; Li, N.; Li, B. Stretch Diffusion of Silicon on Ag (111). Nano Lett. 2012, and Heat Conduction In One-dimensional 12, 3507–3511. Nonlinear Lattices. Phys. Rev. E 2016, 93, 032130. (64) Zhu, Z.; Tománek, D. Semiconducting Layered Blue Phosphorus: A Computa- (57) Yildirim, T.; Gülseren,O.; Lynn, J. W.; tional Study. Phys. Rev. Lett. 2014, 112, Brown, C. M.; Udovic, T. J.; Huang, Q.; 176802. Rogado, N.; Regan, K. A.; Hay- ward, M. A.; Slusky, J. S.; He, T.; (65) Liu, H.; Neal, A. T.; Zhu, Z.; Luo, Z.; Haas, M. K.; Khalifah, P.; Inumaru, K.; Xu, X.; Tománek, D.; Ye, P. D. Phos- Cava, R. J. Giant Anharmonicity and phorene: An Unexplored 2D Semiconduc- Nonlinear Electron-Phonon Coupling in tor with A High Hole Mobility. ACS Nano 2014, 8, 4033–4041. MgB2: A Combined First-Principles Cal- culation and Neutron Scattering Study. (66) Gu, C.; Zhao, S.; Zhang, J. L.; Phys. Rev. Lett. 2001, 87, 037001. Sun, S.; Yuan, K.; Hu, Z.; Han, C.; (58) Gao, Z.; Liu, G.; Ren, J. High Thermo- Ma, Z.; Wang, L.; Huo, F.; Huang, W.; electric Performance in Two-Dimensional Li, Z.; Chen, W. Growth of Quasi-Free- Tellurium: An ab initio Study. ACS Appl. Standing Single-Layer Blue Phosphorus Mater. Interfaces 2018, 10, 40702–40709. on Tellurium Monolayer Functionalized Au (111). ACS Nano 2017, 11, 4943– (59) Benedict, L. X.; Crespi, V. H.; 4949. Louie, S. G.; Cohen, M. L. Static Conductivity and Superconductivity of (67) Zhang, J. L.; Zhao, S.; Han, C.; Wang, Z.; Carbon Nanotubes: Relations between Zhong, S.; Sun, S.; Guo, R.; Zhou, X.; Tubes and Sheets. Phys. Rev. B: Con- Gu, C. D.; Yuan, K. D. Epitaxial Growth dens. Matter Mater. Phys. 1995, 52, of Single Layer Blue Phosphorus: A New 14935–14940. Phase of Two-Dimensional Phosphorus. Nano Lett. 2016, 16, 4903–4908. (60) Vogt, P.; De Padova, P.; Quares- ima, C.; Avila, J.; Frantzeskakis, E.; Asen- (68) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; sio, M. C.; Resta, A.; Ealet, B.; Le Lay, G. Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Silicene: Compelling Experimental Evi- Black Phosphorus Field-Effect Transis- dence for Graphenelike Two-Dimensional tors. Nat. Nanotechnol. 2014, 9, 372. Silicon. Phys. Rev. Lett. 2012, 108, 155501. (69) Ji, D.; Cai, S.; Paudel, T. R.; Sun, H.; Zhang, C.; Han, L.; Wei, Y.; Zang, Y.; (61) Cahangirov, S.; Topsakal, M.; Aktürk, E.; Gu, M.; Zhang, Y. Freestanding Crys- S¸ahin, H.; Ciraci, S. Two- and One- talline Oxide Perovskites Down To the Dimensional Honeycomb Structures of Sil- Monolayer Limit. Nature 2019, 570, 87. icon and Germanium. Phys. Rev. Lett. 2009, 102, 236804. (62) Fleurence, A.; Friedlein, R.; Ozaki, T.; Kawai, H.; Wang, Y.; Yamada- Takamura, Y. Experimental Evidence for Epitaxial Silicene on Diboride Thin Films. Phys. Rev. Lett. 2012, 108, 245501. (63) Feng, B.; Ding, Z.; Meng, S.; Yao, Y.; He, X.; Cheng, P.; Chen, L.; Wu, K. Evi- dence of Silicene in Honeycomb Structures