Two-dimensional Boron Monosulfides: Semiconducting and Metallic Polymorphs

TL;DR

This study predicts four stable two-dimensional boron monosulfide sheets with diverse electronic properties, including the first intrinsic superconducting 2D material, highlighting their potential for nanoelectronic applications.

Contribution

It introduces four novel 2D BS structures with detailed stability, electronic, and superconducting properties, expanding the family of 2D materials beyond traditional chalcogenides.

Findings

All four BS sheets are thermally and dynamically stable.

Alpha-BS is a feasible exfoliation from bulk material.

Delta-BS exhibits intrinsic superconductivity with a critical temperature of about 21.56 K.

Abstract

The typical two-dimensional semiconductors, group \uppercase\expandafter{\romannumeral3A} chalcogenides, have garnered tremendous interest for their outstanding electronic, mechanical, and chemical properties. However, so far, there have been almost no reports on boron monosulfides (BS) binary material. Here, four two-dimensional BS sheets, namely the $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-BS sheets, are proposed and discussed from $\emph{ab initio}$ calculations. State-of-the-art first-principles calculations reveal all these structures are thermally and dynamically stable, indicating the potential for successful experimental synthesis. Especially, for $\alpha$-BS, it has a calculated exfoliation energy of 0.96 J m$^{-2}$, suggesting the preparation of $\alpha$-BS is feasible by the exfoliation of bulk rhombohedral-BS. Our results show that $\alpha$-, $\beta$-, $\gamma$-BS are semiconductors, whereas $\delta$-BS is a metallic system. Remarkably, our calculations indicate that $\delta$-BS is a superconductor with a large electron-phonon coupling ($\lambda$ = 1.51) leading a high superconducting critical temperature ($T_c$ $\approx $ 21.56 K), which is the first report of intrinsic superconducting property among all two-dimensional group \uppercase\expandafter{\romannumeral3A} chalcogenides. The desired mechanical and electronic properties render the BS sheets as the promising two-dimensional materials for future applications in nanoelectronics.

Equations

$$T_c=\frac{\omega {}_{log}}{1.2}exp(-\frac{1.04[1+\lambda ]}{\lambda -{\mu }^{\ast }[1+0.62\lambda ]})$$

Full text

I INTRODUCTION

In recent years, there has been a rapidly increasing research interest in two-dimensional (2D) layered materials, since the physical properties of 2D crystals often remarkably change from those of their bulk counterparts, providing a new alternative for applications in nanodevices. The most representative sample is graphene, because of its excellent electronic, mechanical, and thermal properties.novoselov2004electric ; neto2009electronic Inspired by pioneering work of Novoselov and Geim et al.,novoselov2004electric the subject of discovering new 2D materials other than graphene is one of the most significant fields of current scientific research. Beyond graphene, there is a very wide spectrum of 2D crystals that range from insulators to semiconductors and metals.butler2013progress ; bhimanapati2015recent i.e., hexagonal boron nitride ($h$-BN),pakdel2014nano transition metal chalcogenides (TMCs),heine2014transition , metal carbides and nitrides (MXenes),anasori20172d and mono-elemental 2D materials.mannix2017synthesis However, compared to bulk materials, there is still a lack of variety and assortment of 2D materials.

Another new family of 2D crystals, 2D group IIIA chalcogenides, are promising materials for photoelectronics,hu2013highly gas sensing,yang2014high and Li-ion Battery anodeszhang2017enabling . Until now, various layered group IIIA chalcogenides, i.e., GaS,hu2013highly GaSe,lei2013synthesis ; jie2015layer GaTe,wang2014role ; wang2015high and InSe,mudd2013tuning have been synthesized experimentally. Following by these achievements, the great endeavors have also been done to investigate the intriguing physical and chemical properties of these materials for potential applications in many fields.hu2013highly ; yang2014high ; zhang2017enabling ; xu2016synthesis In fact, bulk boron-sulfur binary material, is also a light-element member of group IIIA chalcogenides family. Experimentally, boron-sulfur binary compounds have been known since 1977,diercks1977crystal ; krebs1980b8s16 and its monosulfides structure were reported in 2001,sasaki2001high bulk rhombohedral boron monosulfide ($r$-BS), namely. However, unlike other common group IIIA chalcogenides semiconductors, little research has been done toward preparation of the 2D binary BS compounds due to the lack of knowledge of their physical properties.demirci2017structural To date, only several structural and electronic properties of bulk binary BS compounds have been reported, showing that the bulk $r$-BS is a semiconductor with an estimated band gap of 3.4 eV.sasaki2001high ; demirci2017structural

In this letter, we present four new BS monolayer structures, named $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-BS, predicted via combined ab initio calculations and structure search method. Both dynamical and thermal stability of these sheets is investigated by phonon spectrum calculation and ab initio molecular dynamics (AIMD) simulation. The electronic structure calculations show that the $\alpha$-, $\beta$-, and $\gamma$-BS are semiconductors with the band gaps of 4.03, 3.89, and 2.94 eV, respectively; whereas $\delta$-BS is a metallic sheet. More importantly, electron-phonon coupling calculations show that $\delta$-BS is superconducting with a high superconducting critical temperature ($T_{c}$) of 21.56 K.

II COMPUTATIONAL METHODOLOGY

The search of stable BS systems is performed using the structure particle swarm optimization (PSO) algorithms as implemented in the CALYPSO package.wang2014perspective ; wang2010crystal All the calculations were carried out with the Vienna Ab initio Simulation Package (VASP).kresse1993ab The density functional theory (DFT) with the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional were employed.blochl1994projector ; perdew1996generalized The kinetic cutoff of the plane wave was set to 650 eV and the precision of energy convergence was 10*-5* eV. The atomic positions were relaxed until the maximum force on each atom was less than 10*-3* eV$/$Å. All 2D structures were simulated with a periodic boundary condition, and the vacuum region between adjacent layers was fixed to at least 20 Å in order to eliminate possible interaction. Electronic band structures were obtained by he Heyd-Scuseria-Ernzerhof (HSE06) screened hybrid functionalpaier2006screened and compared with those with conventional PBE functional. Phonon dispersions and frequency densities of states (DOS) were performed in Phonopy codetogo2015first interfaced with the density functional perturbation theory (DFPT)baroni2001phonons as carried out in VASP code. AIMD simulations are performed to determine the thermal stability of sheets. The uniaxial strain was applied along the x and y directions to simulate the stress-strain relationship of sheets, defined as ${\epsilon}$ = (a - a0)/a0, where a and a0 are the lattice constants with and without strain, respectively. The van der Waals (vdW) interaction is incorporated by the vdW-DF method proposed by Dion et al.dion2004van to estimate the exfoliation energy. The Quantum-ESPRESSO 6.1 packagegiannozzi2009quantum is used to study the electron-phonon coupling (EPC) in $\delta$-BS. The norm-conserving pseudopotentials (FHI) with a cutoff energy of 120 Ry were used. The Gaussian smearing method with a smearing parameter of $\sigma$ = 0.02 Ry was used.

III RESULTS AND DISCUSSION

Crystal structures. Optimized structures of all predicated BS sheets are shown in Figure 1, and the calculated lattice parameters are summarized in Table S1. We identify four different phases, denoted by $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-BS, as shown in Figures 1a-1d, respectively. Evidently, $\alpha$- and $\beta$-BS sheets share similar structural features with the previously fabricated 2D hexagonal GaS and GaSe.late2012gas ; hu2012synthesis They adopt the hexagonal lattices with two B and two S atoms in each unit cell. The optimized lattice constants for $\alpha$- and $\beta$-BS are $a$ = $b$ = 3.06, and $a$ = $b$ = 3.04 Å, respectively. Also, the obtained results for $\beta$-BS is very well in good agreement with previous theoretical work.demirci2017structural However, the $\gamma$-BS and $\delta$-BS crystallize in the orthorhombic lattice with space group C2/m and Pmma, showing the C2h and D2h symmetry, respectively. As shown in Figures 1c-1d, 1 unit cell of $\gamma$-BS ($\delta$-BS) monolayer consists of 4 (2) B atoms and 4 (2) S atoms with the optimized lattice parameters being $a$ = 7.38 (3.07) Å and $b$ = 3.06 (2.59) Å, respectively.

Stabilities. To examine the relative stability of these different allotropes, the cohesive energy (Ec) per atom with respect to the energy of an isolated B and S atoms is calculated, as defined as Ecoh = (nEB + mES - EBS)/${n+m}$, in which EB, ES, andEBS are the calculated total energies of a single B atom, a single S atom, and the BS sheet, respectively; $n$ ($m$) is the number of B(S) atoms in the unit cell. According to our calculations, these monolayers have the cohesive energies of 5.23, 5.22, 5.11 and 4.92 eV per atom for $\alpha$-, $\beta$-, $\gamma$-, and $\delta$-BS, respectively. Thus, $\alpha$-BS is a energetically most stable phase, while $\beta$-, $\gamma$-, and $\delta$-BS are the metastable phases. As a reference, the cohesive energies of the experimentally realized 2D silicene, and phosphorene, are 3.71 and 3.61 eV per atom, respectively.wang2016semi Therefore, the even higher cohesive energies can ensure that the proposed monolayers are strongly bonded with the unique networks.

The dynamical stability of these monolayers can be further checked by phonon dispersion curves, as shown in Figure 2. No imaginary phonon frequencies were observed in the whole Brillioun zone, suggesting their dynamical stability. The highest frequency of $\gamma$-BS reaches up to 1073 cm*-1* , higher than that of 473 cm*-1* in MoS2,molina2011phonons t-SiC (735 cm*-1*),fan2017novel and silicene (580 cm*-1*),cahangirov2009two indicating the strong B-S and B-B bonds in the structures. Additionally, their thermal stability is also confirmed by performing the AIMD simulations, as shown in the Figures S1-S2. Therefore, the above-mentioned results demonstrate that all these monolayers have satisfactory energetic, dynamical, and thermal stability.

Mechanical Properties. The mechanical properties are indispensable for new materials applications in the real world. Conventionally, for a mechanically stable 2D free-standing configuration, the calculated elastic constants should satisfy C11C22-C12C21 $>$ 0 and C66 $>$ 0.wei2014superior As listed in Table S1, all the calculated elastic constants of the proposed new structures satisfy the this criteria, indicating that these 2D compounds have favorable mechanical stability. As listed in Table S1, the in-plane Young’s modulus (or in-plane stiffness) is calculated to be 212 GPa$\cdot$nm for $\beta$-BS, which is distinctly higher than that of experimentally synthesized 2D GaS (73 GPa$\cdot$nm) and silicene (61 GPa$\cdot$nm).demirci2017structural ; zhang2011stability However, for $\gamma$- and $\delta$-BS sheets, as elastic constant C11 is not equal to C22, indicating they are mechanically anisotropic.

Besides in-plane Young’s modulus, ideal strength is also an important mechanical property for 2D material. The ideal tensile stress versus strain for the BS sheets is shown in Figure 3. With small strains deformations, the sheets exhibit linear stress-strain relationship (with distinguished elastic anisotropy for $\gamma$- and $\delta$-BS). As the applied strains increase, their stress-strain behaviors become nonlinear and show difference changing trends along the x and y directions. Particularly, for $\alpha$- and $\beta$-BS, along y direction, both the peak strengths and the corresponding critical strains are higher than along x direction, while the opposite trends occurred in $\gamma$- and $\delta$-BS sheets. The $\alpha$-BS can sustain stress up to 13 N m*-1* and 18 N m*-1* in the x and y directions, respectively. The corresponding critical trains are 0.1 (x) and 0.22 (y). The ideal strengths for the $\beta$-BS are 16 N m*-1* and 20 N m*-1* in the x and y directions, respectively, and their critical strains are 0.12 (x) and 0.24 (y). Figure 3d presents the results for $\delta$-BS, its peak strength is 25 N m*-1* at ${\epsilon}_{x}$ = 0.34 and 6 N m*-1* at ${\epsilon}_{y}$ = 0.06, respectively. Thus, the ideal strengths of BS sheets are significantly higher than other 2D materials, such as borophenes, MoS2, and phosphorene.zhang2017elasticity

Electronic Structures. The computed HSE06 band structures of the proposed sheets are shown in Figure 4. For $\alpha$- and $\beta$-BS, clearly, they are indirect band gap semiconductors: the conduction band minimum (CBM) is at the M point, while the valence band maximum (VBM) lies between the $\Gamma$ and K points, which is only slightly higher in energy than at the $\Gamma$ point (6.6 meV for $\alpha$-BS and 16.2 meV for $\beta$-BS at HSE06 level). However, for $\gamma$-BS, both CBM and VBM are located at the $\Gamma$ point, generating a direct band gap of 2.94 eV. For those three semiconductors, their band structures show strong anisotropy of the conduction band, which finally leads to the anisotropy of the effective masses. (see Figure S3)

Interestingly, the top valence bands of $\alpha$- and $\beta$-BS sheets are nearly flat near around the $\Gamma$ point, leading to the Mexican-hat shape of the valence band edges, which render sharp peaks in the DOS and strong van Hove singularities near the Fermi level.miao2017tunable ; cao2015tunable ; kuc2017high The Mexican-hat shape valence bands are mostly contributed by the 2p and 2p orbitals of B and S atoms, respectively, and these orbitals are strongly overlapping in the full energy range, suggesting covalent bonding characters of B-S bonds. (see Figure S4) The covalent features in the proposed 2D materials are also demonstrated by the analysis of the electron localization functions (ELFs), as shown in Figure S5. Obviously, ELFs show two localization areas: one is located around the B-S bonds and the other is between B-B bonds, reflecting the valence electrons are shared between the adjacent atoms.

Tunable Band Gaps and Superconducting. One of the promising avenue to tune the electronic property of 2D materials is strain engineering. The band gaps of $\alpha$-, $\beta$-, and $\gamma$-BS structures with respect to the uniaxial stress are shown in Figure 5a. Approximately, the band gaps of the $\alpha$- and $\beta$-BS monolayers decrease gradually with either tensile or compressive strains, showing a nonmonotonic relationship. This unusual behavior is attributed to Mexican-hat shape valence bands near the Fermi level, akin to InP3 monolayer.miao2017tunable Their outstanding properties with heavy effective masses and wide band gaps render these materials suitable candidates for future applications in ultrashort (i.e., sub-5nm regime) channel logical devices.kuc2017high ; fiori2014electronics

Additionally, the metallic property of $\delta$-BS inspire us to investigate its potential superconducting property. Figure 4b shows the Eliashberg spectral function $\alpha$2$F$($\omega$) together with the integrated EPC parameter $\lambda$($\omega$) at the PBE level. $\alpha$2$F$($\omega$) exhibits a strong peak around 5 THz, and $\lambda$($\omega$) increases sharply in the range of 0-7 THz. As expected, the main contributor to the EPC is derived from the vibration of the heavy S atoms. The resulting coupling strength of $\lambda$ = 1.51, is rather strong. Superconducting transition temperature ($T_{c}$) of $\delta$-BS is estimated through the Allen-Dynes modified McMillan formula equation,allen1975transition

[TABLE]

by using the calculated logarithmic average frequency ($\omega$log) and a series of Coulomb pseudopotential parameters ($m*$) from 0.10 to 0.13, as shown in Table S2. At $m*$ = 0.10, the highest $T_{c}$ value of $\delta$-BS is 21.56 K, originating from its strong EPC and high logarithmic average frequency ($\omega$log = 189.06 K). Thus, the evaluated $T_{c}$ is in the range of 21.56 K ($m*$ = 0.10) to 19.08 K ($m*$ = 0.13), indicating that the $\delta$-BS is an intrinsic Bardeen-Cooper-Schrieffer (BCS) type superconductor. Notably, this $T_{c}$ is higher than that of other previously reported 2D superconductors, such as borophenes ($\approx$ 10-20 K), and boron carbides ($\approx$ 21.20 K).penev2016can ; fan2018two

Exfoliation of $\alpha$-BS. The most common techniques to prepare 2D materials from their bulk counterparts are mechanical or liquid phase exfoliation.novoselov2004electric ; kim2009large Here, to explore the possibility of fabricating the energetically favorable $\alpha$-BS from the surface of its layered bulk r-BS crystal (see Figure S6),sasaki2001high ; cherednichenko2018boron we then simulated the exfoliation process and calculated exfoliation energy with respect to separation, as shown in Figure 5. We first test the computing method using graphite as a benchmark, and the calculated exfoliation energy for graphene is 0.30 J m*-2*, which is is consistent with the previous experimental (0.32 $\pm$ 0.03 J m*-2*)zacharia2004interlayer and theoretical value (0.31 J m*-2*).miao2017tunable For $\alpha$-BS, the calculated exfoliation energy is 0.96 J m*-2*, which is higher than that of graphene, but still less than some layered materials, i.e., InP3 (1.32 J m*-2*),miao2017tunable Ca2N (1.08 J m*-2*),zhao2014obtaining and GeP3 (1.14 J m*-2*),jing2017gep3 indicating the $\alpha$-BS sheet could be prepared experimentally from its bulk counterpart. Therefore, the moderate vdW interactions of $\alpha$-BS suggests the preparation of mono- or few-layer $\alpha$-BS heterostructures is feasible.tan2015epitaxial

IV CONCLUSION

In summary, we have reported novel 2D BS binary sheets with high stability, high mechanical strength, and unique electronic properties. Importantly, $\delta$-BS phase is identified as the first discovery of intrinsic superconducting material among all 2D group IIIA chalcogenides. All monolayers show good dynamical and thermal stability, and $\alpha$-BS is expected to be prepared from its layered bulk $r$-BS by exfoliation. These advantaged features promote 2D BS sheets as promising candidates for future applications in future nano-devices. We also believe our results will further stimulate the experimentally preparation and investigation of 2D BS materials.

V ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11504325, 50972129, and 50602039), and Natural Science Foundation of Zhejiang Province (LQ15A040004). This work was also supported by the international science technology cooperation program of China (2014DFR51160), the National Key Research and Development Program of China (No. 2016YFE0133200), the European Union’s Horizon 2020 Research and Innovation Staff Exchange (RISE) Scheme (No. 734578), and the One Belt and One Road International Cooperation Project from Key Research and Development Program of Zhejiang Province (2018C04021).