Carbon Monosulfide Nanostructures: Chains Arrays, Monolayers, And

July 22, 2018 Stable Carbon Monosulﬁde Nanostructures: Chains Arrays and Monolayers

T. Alonso-Lanza,1 F. Aguilera-Granja,1,2 J. W. González1 A. Ayuela1 1Centro de F´ısica de Materiales CFM-MPC CSIC-UPV/EHU, Donostia International Physics Center (DIPC), Departamento de F´ısica de Materiales, Fac. de Qu´ımicas, UPV-EHU, 20018 San Sebastián,Spain 2Instituto de F´ısica, Universidad Autónomade San Luis de Potos´ı,78000 San Luis Potos´ıS.L.P., México

Theoretical predictions have lead to the experimental synthesis of new low dimensional layered structures. Herein we show for the very first time that compounds of carbon monosulfide exhibit a great variety of layered nanostructures, such as chains arrays, monolayers, and thin films. We find that the chains arrays are the most stable because they are mainly dimensionality-driven by the sp2 hybridization of sulfur and carbon orbitals. Furthermore, the chains arrays are direct gap semiconductors. In contrast to thin films, the monolayers are stable at room temperature with a semiconductor phase followed in energy by a metallic phase. Then, we achieve a semiconductor- to-metal phase transition in carbon sulfur monolayers, which can be driven by strain engineering controlling conductivity and carrier mobility.

I. INTRODUCTION analyzed to obtain 2D materials with improved stability and new properties30; one of the hottest topic nowadays New phenomena in condensed matter physics are based focuses on phosphorene isoelectronics compounds. on two-dimensional materials. An example is a single There are two different approaches to obtain phos- layer of carbon atoms known as graphene1. Graphene phorene isoelectronic compounds, by taking elements of characterization shows outstanding structural and elec- the group V or by mixing elements of the groups IV-VI tronic properties such as high stiffness or flexibility, and also called group IV monochalcogenides31–36. The phos- massless Dirac fermions with low resistivity2–7, which al- phorene isoelectronic compounds of the group V are ni- low for many applications. The main drawback is the trogene, phosphorene, arsenene37–39 and antimonene39, absence of band gap in the graphene electronic structure and their binary compounds40,41. They are cur- and the small on/off ratio4,8, a band-gap may be opened rently undergoing characterization, for instance, by via different techniques, such as chemical tailoring, in- studying doping42, point defects42,43, and oxygen ducing strains, and geometric patterning9–13. Although contamination44. The group IV monochalcogenides in- graphene looks promising for the future, research is to- cludes a combination of light elements, such as in silicon day focusing on other carbon nanostructured materials monosulfide monolayers and thin films23–25, and a com- and other two-dimensional materials14. bination of heavy (Ge, Sn) and light (O, S) atoms45, such The possibility to exfoliate materials and the ex- as in silicon telluride46 and germanium monosulfide47 istence of accurate experimental techniques to study monolayers, which exhibit strain-tunable indirect band single-layer materials15–17 supposed a big boost to study gap. Nevertheless, none of the today proposed phospho- other layered materials. Layers with other elements in rene isoelectronic compounds is based on carbon. In fact, the carbon group have been studied to produce coun- the layered carbon compounds, such as carbon nitride48 terparts to graphene, such as silicene, germanene or and carbon phosphide49,50, are not isoelectronic to phos- stanene18–21. Graphene is flat because there is sp2 hy- phorene. Our aim is to design new layered nanostructures bridization, and these other compounds adopt a buckled isoelectronic to black phosphorus, but still composed of structure because they prefer sp3 hybridization. Other carbon. layered nanostructures isoelectronic to graphene are ob- We present here for the first time stable carbon mono- tained either combining III-V group elements, such as sulfide nanostructures covering chains, monolayers, and in hexagonal boron nitride22. 2D materials research is thin films. We have performed phonon and molecular recently widen to other new materials based on phos- dynamics calculations to ensure the stability of those arXiv:1703.02756v1 [cond-mat.mtrl-sci] 8 Mar 2017 phorus, whose isoelectronic counterparts are a central structures at room temperature. The carbon monosulfide issue nowadays23–25. Black phosphorus is formed by nanostructures vary from metallics in thin films to semi- single layers mediated by van der Waals interaction, so conductors in chains and most monolayers. The chains that analogously to graphene, few layers are isolated to and thin films are more stable than the monolayers be- form phosphorene26,27. Phosphorene has a two dimen- cause sulfur atoms have two bonds instead of three (or sional honeycomb puckered structure where each atom four) for the monolayers25. The large variety of nanos- is bonded to three neighbors. It displays a direct band tructures that we explored with either metallic or semi- gap, tunable attending to the number of layers and the conductor character makes this material an interesting stacking28,29. compound for several applications based on electronic More and more systems are being proposed and deeply transport within semiconductors devices. 2

II. COMPUTATIONAL DETAILS and electronic structure of the four most stable structures, and finally consider the ground state in more de- We use the SIESTA (Spanish Initiative for Electronic tail. Figure 1 shows four monolayers of carbon mono- Simulations with Thousands of Atoms) package to carry sulfide after structural relaxation including their relative out density functional theory (DFT) calculations for car- energies. The most stable α monolayer presents a simi- bon monosulfide nanostructures. For the exchange and lar structure to that of a single layer of black phosphorus. correlation potentials we used the generalized gradient This structure has also been reported recently for group 23,31 approximation (GGA) in the form of Perdew-Burke- IV monochalcogenides , and group V semiconductors 40,41,63 Ernzenhof51. We fully relax atomic positions and unit such as phosphorous-nitrogen or arsenic-nitrogen . cells until forces are below 0.006 eV/A.˚ The used unit The results obtained with VASP method yield energy cells have large vectors about 24.5 A˚ in the perpendic- differences slightly larger, although the stability order is ular direction to the layers in order to avoid interaction the same. Second in energy we find the δ monolayer with images. An electronic temperature of 25 meV and that is a regular structure composed of squares looked a meshcutoff of 250 Ry are used. The sampling of the from above. A side view reveals two different heights for Brillouin zone has a fine grid of 20×20×1 k points. The sulfur atoms. Next there is a similar structure, the κ atomic cores are described by nonlocal norm-conserving structure, with all the carbon atoms shifted towards one Troullier-Martins52 pseudopotentials factorized in the side producing long and short distances with the sulfur Kleynman-Bylander form. Orbitals are developed in ba- atoms. When the distortion is maximized the α structure sis sets on each atom, and the basis size is double zeta is reached. The κ layer seems an intermediate structure plus polarization orbitals. Details on the used pseu- between the α and δ monolayers, so that the three mono- dopotentials and basis were described previously9,25,53. layer monosulfide-carbon structures seems related, to be Anyhow our main results are checked by repeating cal- discussed at length in next section III A 2. Phonon dis- culations with the VASP code using the projected aug- persions, shown in Supplemental Information, indicate mented wave method (PAW) and within the PBE formal- that the α and δ structures are really stable, and the κ ism for the exchange and correlation54,55, and the Quan- structure is unstable because there are negative frequen- tum ESPRESSO method with equivalent parameters56. cies. Furthermore, molecular dynamics simulations show We estimate the van der Waals contribution to the to- that the α and δ structures are stable even at room tem- tal energy for a two dimensional array with well sepa- perature. Last we find the β structure which from a top rated chains using the implementation within the VASP view it displays a hexagonal pattern, and in a side view it code57,58 of the vdW-DF59 functional. Last but not has a buckled structure, reported for other phosphorene 23 least, we even confirm the stability of such highly stable isoelectronic compounds . The β structure is similar to 64,65 obtained structures by carrying out molecular dynam- that of blue phosphorene . The phonon dispersion ics calculations within the SIESTA code using the Nose curves show that the carbon monosulfide β phase is un- thermostat at room temperature. We employed a Nose stable. mass60–62 of 10 Ry fs2, and a time step of 1 fs. We have To gain insight on the electronic structure of the car- chosen 3000 as final time step and the relaxation time to bon monosulfide monolayers we consider the band struc- reach target temperature was 2500 fs. Phonon dispersion tures shown in Fig. 2. On the one hand, three of the curves are obtained using the Quantum ESPRESSO monolayers, labeled as α, κ and β, are semiconductors code, with details included in the Supplemental Informa- with indirect band gaps of 0.97, 0.77 and 1.64 eV, re- tion. spectively. For the α and κ layers, the minimum of the conduction band is located at the gamma point. For the α case, the highest occupied valence band is well sepa- III. RESULTS AND DISCUSSION rated from lower valence bands with a pseudogap of 2 eV. The κ structure has still a pseudogap opening in the We study three different types of carbon monosulfide valence band, although the value is reduced to 0.5 eV. nanostructures, monolayers, thin films, and chains ar- On the other hand, the δ structure is metallic. rays, following the order from lower to higher stability. The bands of the α, δ and κ structures appear similar Molecular dynamics simulations show that thin films are because they share common structural features as com- not stable at room temperature. Comments and analysis mented above. For the β monolayer the bands are degen- of thin film structures are therefore presented in the Sup- erated throughout the Brillouin zone due to the lattice plemental Information, together with further information symmetry. Most of the features of the bands are the same on monolayers and chains. for the α and κ cases; for instance there are two occupied bands just below the Fermi energy, extended along all Brillouin zone, and well separated from the deeper A. Monolayers states. However, the band structure of the δ case dif- fers because one of the two occupied bands close to the We explore a wide variety of structures for carbon Fermi energy becomes broad and metallized, going down monosulfide monolayers. We next present the geometry to deep energies following a parabolic shape. The two 3

FIG. 1: Geometries of the four carbon monosulfide monolayers in order of decreasing stability. Carbon (sulfur) atoms are represented by black (yellow) spheres through the article. The unit cell is shown in green for each case. Differences in the energy per atom using the SIESTA and VASP methods are shown on top and in parentheses for each structure, respectively. The energy differences are calculated relative to the energy per atom in the α structure.

FIG. 2: Band structures of the four carbon monosulfide monolayers. Fermi energies are denoted by horizontal dashed lines. Band gaps over the whole Brillouin zone are shown by shaded rectangles. occupied narrow bands for the α and κ cases are local- monolayer. ized within a interval of 2 eV, while the bands for the δ We furthermore study the charge transfer between car- case become broad expanding over more than 6 eV. We bon and sulfur atoms using the Mulliken scheme. The find two unoccupied conduction bands that mirror the charge values are 0.81, 0.92, 0.65 and 0.66 electrons for behavior of two nearest valence bands with respect to the α, δ, κ and β monolayers, respectively. We find that the Fermi energy. There are even bands for the δ struc- the charge transfer of almost one electron in some cases is ture crossing the Fermi energy, resulting in a conducting large and goes from carbon to sulfur atoms. This result 4

FIG. 3: Electronic properties of the ground α structure. (a) Density of states projected on carbon (up panel) and sulfur (down panel). (b) Spatial localized density of states for the energy peak marked up with a blue rectangle in (a). (c) Highest occupied orbital of the valence band at the Γ point. is surprising because carbon and sulfur have almost the 2 eV is included in panel (b). Most of the states are local- same Pauling electronegativity. It seems that the larger ized around carbon atoms with orbital lobes suggesting a size of sulfur atoms with respect to carbon atoms must large p-type contribution. The peak LDOS globally looks be taken into account in order to explain the charge gain like a dangling bond of the sp3 hybridization. However, by sulfur atoms. the wave function for the highest occupied orbital in Γ point, as shown in Fig. 3c, reveals a pz-like orbital over the carbon atoms, to be held responsible for the broad- 1. α monolayer ening of a band close to Fermi energy upon distortions. The projected sulfur LDOS shown in Fig. 3(a) has a We focus on the ground state monolayer given by the non negligible d contribution, especially for the highest α structure. Each carbon atom is bonded to three sulfur energy occupied peak. Therefore, spd hybridization on atoms and vice versa. There are two bonds of 1.82 A˚ and sulfur atoms seems crucial to describe the valence band one of 1.90 A.˚ The angles between the bonds from a car- close to the Fermi energy25. bon atom are 113◦ in two cases and 103◦ in the other. It We then compare carbon-sulfur and silicon-sulfur23,25 seems that carbon atoms present a sp3-like hybridization. compounds, both being isoelectronic to phosphorene, in We discuss on the relative contribution between car- the α structure. There are two well diﬀerentiated roles bon and sulfur atoms to discuss stability. The projected depending of the atom size, as shown in the α structure of density of states is shown in Fig. 3(a). The total states Fig. 1. The smaller atom, either carbon for CS or sulfur projected on sulfur contribute more than those on carbon for SiS, is the inner one, and the larger atom is the outer because sulfur has a larger number of electrons than car- one. The electronic structure produces similar trends bon. Nevertheless, the occupied peak close to the Fermi taking into account that the inner atom contributes with energy has a larger carbon contribution than sulfur. This pz orbitals to the highest occupied orbital at the Γ point. particular peak is related to the isolated valence band, Figure 3(c) shows a pz-type orbital for carbon atoms in discussed above when commenting Fig. 2. The density carbon-sulfur compounds. The main contribution to the of states (LDOS) in real space within the energy range of frontier orbitals in silicon-sulfur compound comes from 5

FIG. 4: Stretching the α and δ monolayer as shown in panel (a) yields an increasing energy as shown in panel (b), suggesting a barrier between those structures. (c) Relative position in energy of the three most stable monolayers sketching a possible energy proﬁle.

23 the pz orbitals in sulfur . These bands for the outer is characterized by the aspect ratio between length and atom project on a hybridized dangling bond. It has pd width, which is 1 for the δ phase and 1.4 for the α phase. hybridization for sulfur in CS, as shown by the projected For each calculation the unit cell remains fixed and the density of states in Fig. 3(a), and it has spd-like hy- inner atomic positions are relaxed. We expected that bridization for the frontier orbitals of silicon in SiS23,25. the δ monolayer changing aspect ratio would transform It is noteworthy that sulfur atoms can adopt the two into the α monolayer by relaxing the inner atomic posi- roles depending on the counterpart element involved in tions. However, we find that the inner atomic structure the isoelectronic compound to phosphorene. is retained when deforming the unit cell, and the energy increases continuously with the aspect ratio, as shown in Fig. 4(b). We also find a similar behavior when deform- 2. Strain-driven transition between two stable monolayer ing the α monolayer. The two curves of energy versus as- phases pect ratio cross at a point with a barrier of about 0.2 eV between the monolayers, a fact sufficient to confirm the We try to shed light over the striking metallization stability for the δ structure. The energy of the κ mono- of the δ monolayer. A distortion of the α atomic posi- layer, included in Fig. 4(b), is very close to the crossing tions could end in the δ structure, so that the monolayer point, which supports the idea of κ being a metastable could undergo a semiconductor-metal transition driven phase between α and δ monolayers. Figure 4(c) sketches by a strain field. The δ structure is isotropic and similar a possible energy profile following this picture. to a rippled square lattice. Sulfur atoms show spd hybridization as denoted by the projected density-of- states, similarly to the α structure. A detailed analysis of the B. Chains arrays localized density of states shows that the Fermi energy states are p-type on carbon, which could be seen as a We find other kind of structures for carbon monosul- square lattice of pz orbitals. Details on the geometry fide with chains arrays. The previously studied γ SiS and the projected and localized density-of-states of the δ monolayer25 is fully relaxed by substituting silicon with phase are found in the Supplemental Information. carbon atoms. A layer with chains of carbon monosul- We follow the transition between the α and δ mono- fide is then stabilized by more than half electronvolt per layers by changing aspect ratio, as shown schematically atom when compared to the most stable α monolayer. in Fig. 4(a). To this aim we modify the unit cell shape We obtained two different chains arrays with hexagonal step-by-step and transform the square cell into a rect- and pentagonal motifs. The hexa chains are more stable angular one. The unit cell following the transformation than the penta chains by more than 0.25 eV per atom, 6

FIG. 5: (a) Geometry of the hexa chains arrays, with the hexagon motif of the structure highlighted in blue color. The unit cell to compute the band structures are marked by vectors. The energies per atom obtained using SIESTA and VASP codes are given above referred to the ground state α monolayer. (b) Highest occupied molecular orbital (HOMO) at the Γ point for the hexa chains in the region marked with a black ellipse in panel (a). (c) Band structure of the hexa chains. so we focus on the hexa chains below. The penta chains the cases the angles are close to 120◦. The fact that the are commented in the Supplemental Information. The three bonds are planar and form angles close to 120◦ is as- 2 structure with hexa-motif chains, shown in Fig. 5(a), is signed to a sp hybridization. The remaining pz orbital is 0.766 eV per atom more stable than the ground state α used to form the double π bond with the neighboring car- monolayer, which results in a large rise of stability. The bon atom. Focusing now on the sulfur atoms, each atom distance between the closest atoms from two different establishes two bonds with carbon. The chain adopts a chains is larger than 3.7 A,˚ which means that interaction zigzag pattern with two consecutive sulfur atoms in kinks between adjacent chains is mediated by dispersion forces. followed by other in a straight stretch. The two types of Thus, the bonds between chains are much weaker than sulfur atoms seem to have the same hybridization. They those established within a single chain.69 contribute with p-orbitals to the highest occupied orbital We investigate in more detail the bonds between atoms at the Γ point, as shown in Fig. 5(b). However, the kinks in the chains. The top view in Fig. 5 (a) shows that effect is to tilt the pz orbitals by an angle θ of approxi- due to kinks, the hexa chains combines long and short mately 25◦, as presented in Fig. 5(b). stretches. The kinked chains are more stable by an 70 meV per atom than the straight chains. We check the structural stability of this structure with chains using molecular dynamics simulation for a single chain at room The analysis of the projected density of states for the temperature. Carbon atoms form covalent bonds with hexa chains array, attached in the Supplemental Infor- sulfur atoms. Each carbon atom is bonded to two sul- mation, shows that close to the Fermi energy there are fur atoms with two bond lengths of about 1.82 A˚ and to mainly p-type contributions, in contrast to the α and δ another carbon atom with a bond length of 1.38 A.˚ The monolayers. The charge reorganization under the Mul- short bond length between carbon atoms indicates the liken scheme results in a net transfer of approximately existence of a double bond with a σ bond and a π bond. 0.6 electrons from each carbon atom towards the sul- The π bond is spatially shown by the highest occupied fur atoms. Furthermore, we analyze the band structure molecular orbital at the Γ point in Fig. 5(b), formed shown in Fig. 5(c) along two directions, parallel and per- by two p-type orbitals from each pair of carbon atoms. pendicular to the chains. We find that the hexa chains Concerning the angles between the three bonds, there are array is semiconductor with a direct band gap of 1.03 two different carbon atoms depending on whether they eV at the Γ point, a fact that could be interesting for are in a short stretch or in a long stretch; however, for all electronic applications. 7

FIG. 6: Comparison of energetic stability, number of bonds, and hybridizations for carbon monosulﬁde layered nanostructures. Note that the most stable structures are the chains arrays.

IV. FINAL REMARKS fur atoms displaying sp2 hybridizations. These results pave the way so that this type of nanostructures with Finally, we comment on the stability order between carbon monosulfide chains can be synthesized as free- the different layered nanostructures of carbon monosul- standing chains, but probably better grown supported fide we have studied this far. We find chains, thin films on some substrates as chains arrays. On the other hand, 3 and monolayers in order of increasing energy. The en- the monolayers show sp and spd hybridizations for car- ergy is explained by hybridization and the numbers of bon and sulfur atoms, respectively. The ground state bonds for carbon and sulfur atoms in each structure, as α monolayer has the structure of a single layer of black summarized in Fig. 6. The α monolayer, taken as refer- phosphorus with an indirect band gap of approximately ence, presents a sp3 hybridization for carbon atoms with 1 eV. We find that strain can induce a transition be- three bonds and a dangling bond, and a spd hybridiza- tween the most stable α and δ monolayers. Because the tion for sulfur atoms with three bonds. The thin films α monolayer is semiconductor and the δ monolayer is have lower energies per atom because the carbon atoms metallic, the α to δ transition could just allow to con- establish a fourth bond and the sulfur atoms lost a bond. trol conductivity by applying strain, an effect that looks Note that sulfur atoms prefer to establish two bonds to promising for the design of new electronic devices. fulfill the octet rule24,25. The thin films are unstable at Acknowledgments room temperature in molecular simulations. Last but not least, the hexa chains array improves energy and stability with respect to thin films. The gain in stability for This work has been partially supported by the chains is ascribed to the carbon preference for the sp2 Projects FIS2013-48286-C02-01-P and FIS2016-76617- hybridization with two single bonds and a double bond P of the Spanish Ministry of Economy and Competi- over the fourfold coordination of the sp3 hybridization in tiveness MINECO, the Basque Government under the thin films. ELKARTEK project(SUPER), and the University of the In summary, we present brand new stable nanostruc- Basque Country (Grant No. IT-756-13). TA-L acknowl- tures for carbon monosulfide, which include stable chains edge the grant of the MPC Material Physics Center - San arrays and monolayers. On the one hand, the chains Sebastián. FA-G acknowledge the DIPC for their gen- arrays, which are more stable than monolayers, present erous hospitality. Authors also acknowledge the DIPC hexagonal and pentagonal patterns with carbon and sul- computer center.

1 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Commun. 146, 351 (2008). Y. Zhang, S. V. Dubonos, , I. V. Grigorieva, and A. A. 7 Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature Firsov, Science 306, 666 (2004). 438, 201 (2005). 2 K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, 8 F. Schwierz, Nat. Nanotechnol. 5, 487 (2010). M. G. Schwab, and K. Kim, Nature 490, 192 (2012). 9 T. Alonso-Lanza, A. Ayuela, and F. Aguilera-Granja, 3 X. Huang, Z. Yin, S. Wu, X. Qi, Q. He, Q. Zhang, Q. Yan, Phys. Chem. Chem. Phys. 18, 21913 (2016). F. Boey, and H. Zhang, Small 7, 1876 (2011). 10 G. W. Semenoﬀ, Physica Scripta 2012, 014016 (2012). 4 A. K. Geim, Science 324, 1530 (2009). 11 A. Diaz-Fernandez, L. Chico, J. W. Gonz´alez, and 5 A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, F. Dominguez-Adame, arXiv preprint arXiv:1702.08296 and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). (2017). 6 K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fuden- 12 S. Y. Zhou, G.-H. Gweon, A. Fedorov, P. First, berg, J. Hone, P. Kim, and H. L. Stormer, Solid State W. De Heer, D.-H. Lee, F. Guinea, A. C. Neto, and A. Lan- 8

zara, Nature materials 6, 770 (2007). Chem. Chem. Phys. 18, 8158 (2016). 13 J. W. González,M. Pacheco, L. Rosales, and P. Orellana, 43 L. C. Gomes, A. Carvalho, and A. C. Neto, Phys. Rev. B Phys. Rev. B 83, 155450 (2011). 94, 054103 (2016). 14 Y. Gogotsi, MRS Bulletin 40, 1110 (2015). 44 I. de Oliveira and R. Longuinhos, Phys. Rev. B 94, 035440 15 A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, and (2016). S. Iijima, Nature 430, 870 (2004). 45 Z. Ma, B. Wang, L. Ou, Y. Zhang, X. Zhang, and Z. Zhou, 16 Z. Liu, K. Suenaga, P. J. F. Harris, and S. Iijima, Phys. Nanotechnology 27, 415203 (2016). Rev. Lett. 102, 015501 (2009). 46 Y. Chen, Q. Sun, and P. Jena, J. Mater. Chem. C (2016). 17 C. Jin, H. Lan, L. Peng, K. Suenaga, and S. Iijima, Phys. 47 F. Li, X. Liu, Y. Wang, and Y. Li, J. Mater. Chem. C 4, Rev. Lett. 102, 205501 (2009). 2155 (2016). 18 P. Vogt, P. De Padova, C. Quaresima, J. Avila, 48 J. de Sousa, T. Botari, E. Perim, R. Bizao, and D. S. E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and Galvao, RSC Adv. 6, 76915 (2016). G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012). 49 J. Guan, D. Liu, Z. Zhu, and D. Tománek,Nano Lett. 16, 19 B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, 3247 (2016). B. Ealet, and B. Aufray, Appl. Phys. Lett. 97, 223109 50 G. Wang, R. Pandey, and S. P. Karna, Nanoscale 8, 8819 (2010). (2016). 20 B. Aufray, A. Kara, S. Vizzini, H. Oughaddou, C. Leandri, 51 J. P. Perdew, K. Burke, and M. Ernzerhof, Phy. Rev. Lett. B. Ealet, and G. Le Lay, Appl. Phys. Lett. 96, 183102 77, 3865 (1996). (2010). 52 N. Troullier and J. L. Martins, Phys. Rev. B 43, 1993 21 S. Balendhran, S. Walia, H. Nili, S. Sriram, and (1991). M. Bhaskaran, Small 11, 640 (2015). 53 T. Alonso-Lanza, A. Ayuela, and F. Aguilera-Granja, 22 A. Zunger, A. Katzir, and A. Halperin, Phys. Rev. B 13, ChemPhysChem 16, 3700 (2015). 5560 (1976). 54 P. E. Blöchl, Phys. Rev. B 50, 17953 (1994). 23 Z. Zhu, J. Guan, D. Liu, and D. Tománek,ACS Nano 9, 55 G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 8284 (2015). 56 P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, 24 J.-H. Yang, Y. Zhang, W.-J. Yin, X. Gong, B. I. Yakobson, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, and S.-H. Wei, Nano Lett. 16, 1110 (2016). I. Dabo, et al., J. Phys. Condens. Matter 21 (2009), URL 25 T. Alonso-Lanza, A. Ayuela, and F. Aguilera-Granja, http://www.quantum-espresso.org. Phys. Rev. B 94, 245441 (2016). 57 J. Klimeˇs,D. R. Bowler, and A. Michaelides, Phys. Rev. 26 H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, B 83, 195131 (2011). and P. D. Ye, ACS Nano 8, 4033 (2014). 58 G. Román-Pérezand J. M. Soler, Phys. Rev. Lett. 103, 27 A. Castellanos-Gómez,L. Vicarelli, E. Prada, J. O. Island, 096102 (2009). K. L. Narasimha-Acharya, S. I. Blanter, D. J. Groenendijk, 59 M. Dion, H. Rydberg, E. Schröder,D. C. Langreth, and M. Buscema, G. A. Steele, J. V. Alvarez, et al., 2D Mater. B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004). 1, 025001 (2014). 60 A. M. Souza, A. R. Rocha, A. Fazzio, and A. J. R. da Silva, 28 F. Xia, H. Wang, and Y. Jia, Nat. Commun. 5 (2014). AIP Adv. 2, 032115 (2012). 29 J. Dai and X. C. Zeng, J. Phys. Chem. Lett. 5, 1289 (2014). 61 Z. Zanolli and J.-C. Charlier, Phys. Rev. B 80, 155447 30 S. Beniwal, J. Hooper, D. P. Miller, P. S. Costa, G. Chen, (2009). S.-Y. Liu, P. A. Dowben, E. C. H. Sykes, E. Zurek, and 62 E. Hobi Jr, R. B. Pontes, A. Fazzio, and A. J. da Silva, A. Enders, ACS Nano (2017). Phys. Rev. B 81, 201406 (2010). 31 L. C. Gomes and A. Carvalho, Phys. Rev. B 92, 085406 63 L.-C. Zhang, G. Qin, W.-Z. Fang, H.-J. Cui, Q.-R. Zheng, (2015). Q.-B. Yan, and G. Su, Sci. Rep. 6 (2016). 32 J. Hong and O. Delaire, arXiv preprint arXiv:1604.07077 64 J. L. Zhang, S. Zhao, C. Han, Z. Wang, S. Zhong, S. Sun, (2016). R. Guo, X. Zhou, C. D. Gu, K. D. Yuan, et al., Nano Lett. 33 W. Fang, L.-C. Zhang, G. Qin, Q.-B. Yan, Q.-R. Zheng, 16, 4903 (2016). and G. Su, arXiv preprint arXiv:1603.01791 (2016). 65 Z. Zhu and D. Tománek, Phys. Rev. Lett. 112, 176802 34 L. C. Gomes, A. Carvalho, and A. H. C. Neto, Phys. Rev. (2014). B 92, 214103 (2015). 66 P. Giannozzi, S. De Gironcoli, P. Pavone, and S. Baroni, 35 B. R. Tuttle, S. M. Alhassan, and S. T. Pantelides, Phys. Phys. Rev. B 43, 7231 (1991). Rev. B 92, 235405 (2015). 67 S. Baroni, S. De Gironcoli, A. Dal Corso, and P. Giannozzi, 36 M. Mehboudi, A. M. Dorio, W. Zhu, A. van der Zande, Rev. Mod. Phys. 73, 515 (2001). H. O. Churchill, A. A. Pacheco-Sanjuan, E. O. Harriss, 68 We used the pseudopotentials c.pbe-n-kjpaw psl.0.1.upf P. Kumar, and S. Barraza-Lopez, Nano Lett. 16, 1704 and s.pbe-n-kjpaw psl.0.1.upf, http://www. (2016). quantum-espresso.org, accessed: 12/2016. 37 C. Kamal and M. Ezawa, Phys. Rev. B 91, 085423 (2015). 69 Although the interaction between chains by dispersion 38 S. Mardanya, V. K. Thakur, S. Bhowmick, and A. Agar- forces is beyond the actual scope of the paper, we have wal, Phys. Rev. B 94, 035423 (2016). tested the hexa chains including van der Waals interac- 39 S. Zhang, Z. Yan, Y. Li, Z. Chen, and H. Zeng, Angew. tion using the VASP code, obtaining that the stability is Chem. Int. Ed. 54, 3112 (2015). enhanced by approximately 70 meV per atom. 40 W. Yu, C.-Y. Niu, Z. Zhu, X. Wang, and W.-B. Zhang, J. Mater. Chem. C 4, 6581 (2016). 41 H. Xiao, F. Hao, X. Liao, X. Shi, Y. Zhang, and X. Chen, arXiv preprint arXiv:1603.01957 (2016). 42 Q. Wang, W. Yu, X. Fu, C. Qiao, C. Xia, and Y. Jia, Phys. 9

Supplemental Information are hybridized at deep energies. Close to the Fermi energy all the states come from the p orbitals centered in A. Monolayers carbon and sulfur atoms. The d orbitals for chains arrays give just residual contributions. 1. Monolayers parameters

2. Penta chains arrays

TABLE I: Lattice-vectors, first-neighbor distances, and Because the carbon-carbon bond seems the cause of stability we next investigate structures in which the C thickness ∆z (in A)˚ for the four carbon monosulfide 2 monolayers. Band gap (in eV). unit has rotated, as in Stone-Wales rotations. Figure 8(b) shows a penta array with chains interacting through ~ ~a b dC−S ∆z gap their edges. The presence of pentagons motivates the α (4.00, 0) (0, 2.85) 1.90, 1.82 (×2) 1.89 0.97 structure name. The distances between carbon and sulfur ˚ δ (3.65, 0) (0, 3.65) 1.93 (×4) 1.31 0.77 atoms between chains are larger than 3.5 A. Therefore, there are few atoms interacting through dispersion forces, κ (4.42, 0) (0, 2.94) 1.93 (×2), 1.96, 2.53 1.61 - which means that van der Waals contribution would be β (2.55, 1.47) (2.55, -1.47) 1.99 (×3) 1.03 1.64 lower than for the hexa motif. Focusing on a single penta chain, there are two remarkable facts that explain the loss of stability with respect to the hexa chains. First, the penta motif is similar to the hexa motif with a carbon- ◦ 2. δ monolayer carbon double bond rotated 90 , so that instead of having two hexagons we have the two less stable pentagons. The double bonds are preserved with typical bond lengths be- We further study the striking metallization of the tween carbon atoms of 1.39 A˚ in most of the cases, and δ monolayer. A distortion of the α atomic positions 1.45 A˚ close to a terrace. The carbon-sulfur bond length could end in the δ structure, meaning that by engi- is around 1.8 A.˚ Second, the individual chains have steps neering with a strain field the monolayer could undergo each couple of two pentagons linked by a carbon double a semiconductor-metal transition. The δ structure is bond. The angles of carbon bonds are close to 120◦, a isotropic and similar to a rippled square lattice. All the characteristic of sp2-like hybridization. The two bonds carbon-sulfur bonds are equal with a distance of 1.93 A.˚ of sulfur atoms have angles about 95◦, except for the sul- The consecutive carbon bonds have four angles of 96◦, fur atoms close to terraces where the angle values ( e.g. the opposite bonds have two angles of 141◦. The angles 99◦ and 115◦) are slightly larger. The charge transfer between the sulfur bonds are four of 84◦. The right angles goes from carbon to sulfur with a value larger than 0.5 for sulfur atoms are related to d orbitals taken part in spd electrons. Thus, the penta array with chains presents hybridization, as shown using the density of states in Fig. hybridizations and a bonding scheme similar as those for 7(a). However, the occupied states close to the Fermi en- the hexa motif. It seems that having arrays with chains ergy present a major contribution from the states p of formed by carbon molecules separated by sulfur atoms is carbon and a small contribution with d-character from crucial for having high stability with respect to monolay- sulfur. The spatial localized density of states (LDOS) for ers. two energy intervals is shown in Fig. 7 (b). Around to the Fermi energy, the states in interval 1 are localized on carbon atoms, like a square lattice of p orbitals explain- z C. Thin films ing metallic behavior. They become metallic along the ΓM direction in reciprocal space, equivalent to the (110) direction in real space among carbon atoms. Along the Carbon group elements form buckled monolayers, such 3 ΓX direction, there are also empty states very close to as in silicene and germanene, because sp hybridization 2 the Fermi energy, but with a small gap of 0.22 eV. These is favored rather than sp hybridization. Silicon nanos- states plotted in interval 2 are now including lobules on tructures are expected to gain energy when higher silicon sulfur towards the outer part of the δ monolayer. coordination is allowed, as reported for silicon monosulfide thin films24,25. We study carbon monosulfide following the silicon monosulfide thin films structures. We find that there is a large energy gain with respect to B. Chains arrays the α monolayer because a fourth bond is achieved for the carbon having sp3 hybridization. On the one hand, 1. Density of states for the hexa chains the most stable monolayer do not exhibit a purely carbon sp2 hybridization, but it has a strong sp3 character Figure 8(a) shows the projected density of states re- with a dangling bond. On the other hand, sulfur prefers solved per atom site. We find that the s and p orbitals to have two bonds instead of three in order to fulfill the 10

FIG. 7: Electronic properties of the δ monolayer. (a) Density of states projected on carbon (top) and sulfur (bottom). (b) Spatial localized density of states for the two energy intervals marked in the band structure around the Fermi energy. octet rule24. Consequently the energy per atom increases ate bands of P mma. The conduction bands close to the notably with respect to monolayers because the carbon Fermi energy expand within a broad range of more than 4 dangling bond is passivated and a sulfur bond is lost. eV. We find that there is no band gap, which means the Figure 9 shows the detailed geometries of P ma2 and carbon monosulfide thin films are metallic. The states P mma structures. The coordination number, number of are metallic in the band crossing the Fermi energy around bonds, and distances are very similar for both structures. the Γ point and in the ΓX direction, regions to be held The difference between the P ma2 and P mma structures responsible for electronic conduction. is the slight distortion around sulfur atoms, which re- The projected density of states of the P ma2 and quires considering a large unit cell. The unit cell of P ma2 P mma structures shown in Fig. 9 for both cases are is large than that of P mma, as shown by the unit cell vec- similar, as expected. For carbon we distinguish three tors in Fig. 9. For the P ma2 structure, the sulfur angle zones: an interval [-15,-10] eV with sp hybridization, an between the two C-S bonds is 99◦. Carbon atoms bind interval [-10,-4] with almost all the p-type contribution, to two carbon atoms located at 1.71 A˚ and two sulfur and an interval [-4,0] where the contribution from car- atoms at 1.86 A.˚ The angles between bonds established bon is very small compared to that of sulfur. For sulfur by carbon atoms are all close to 109.5◦, the typical angle there is large s-type contribution very deep in energy for for an sp3 hybridization as for methane. The description the interval [-15,-11], and p-type contribution is largely for the P mma case reveals almost identical findings. predominant in energies around the Fermi level. In fact, The band structures of the P ma2 and P mma struc- the sulfur p-type states near the Fermi energy are mostly tures are presented in Fig. 9. The electronic structure of responsible for conduction. these structures look similar as expected. However, the Molecular dynamics simulations show that the two pro- structural distortion of P ma2 is splitting the degener- posed thin films P ma2 and P mma are not stable at room 11

FIG. 8: (a) Density of states projected on carbon (up) and sulfur (down) for the hexa chains array. (b) Geometry and energy of the penta chains array. Energy origin is relative to the α monolayer of Fig. 1. temperature. The structures break into separated parts, for the two most stable monolayers α and δ and for the showing preference for chain-like geometries in agreement hexa chains arrays, which are found to be stable at room with our results given above. The absence of a band gap temperature, in Fig. 11 and Fig. 12. Molecular dynamics for the P ma2 and P mma structures could be related to simulations of the thin film geometries P ma2 and P mma the low stability of carbon monosulfide thin films. for carbon monosulfide show that they are not stable at room temperature. Phonon dispersions are calculated using linear re- D. Phonon dispersion and molecular dynamics sponse in the Quantum ESPRESSO56,66,67 method, a plane wave code that uses ultrasoft pseudopotentials68 We have carried out molecular dynamics simulations with a cutoff energy of 50 Ry and the PBE GGA. We using the Nose-Hoover thermostat in order to study the have also computed the phonon dispersion curves for α stability of the carbon monosulfide chains, thin films, and and δ carbon monosulfide monolayers, as shown in Fig. monolayers at room temperature. We show the results 10. There are no negative frequencies. 12

FIG. 9: Geometries for two carbon-sulfur thin ﬁlms in the (a) Pma2 and (b) Pmma structures. The unit cells employed for the electronic analysis are shown in green. Energies per atom with the SIESTA and VASP methods relative to the α monolayer are given on top and within parenthesis, respectively. Band structures and projected density of states are shown in the lower part. 13

FIG. 10: Phonon dispersions of the (a) α, (b) δ , (c) κ, and (d) β carbon monosulﬁde monolayers. 14

FIG. 11: Energy versus time step for the α (a) and δ (b) monolayers in a Nose thermostat at 300K. Structural snapshots are shown below at the four steps marked up in the graph for each case. 15

FIG. 12: Energy versus time step for the hexa chains in a Nose thermostat at 300K. Structural snapshots are shown below at the four steps marked up in the graph.