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Research 1..6 ajs00 | ACSJCA | JCA10.0.1465/W Unicode | research.3f (R3.6.i12 HF03:4459 | 2.0 alpha 39) 2017/11/27 07:41:00 | PROD-JCAVA | rq_13107282 | 3/26/2018 14:43:14 | 6 | JCA-DEFAULT Letter pubs.acs.org/JPCL 1 A New Anisotropic Dirac Cone Material: A B2S Honeycomb 2 Monolayer 3 Yu Zhao, Xiaoyin Li, Junyi Liu, Cunzhi Zhang, and Qian Wang* 4 Department of Materials Science and Engineering, Center for Applied Physics and Technology, College of Engineering, Peking 5 University, Beijing 100871, China 6 ABSTRACT: Different from the isotropic Dirac cones existing in other two- 7 dimensional (2D) materials, anisotropic Dirac cones have the merit of anisotropic 8 carrier mobility for applications in direction-dependent quantum devices. Motivated by 9 the recent experimental finding of an anisotropic Dirac cone in borophene, here we report fi 10 a new 2D anisotropic Dirac cone material, B2S monolayer, identi ed by using a global 11 structure search method and first-principles calculation combined with a tight-binding 12 model. The B2S monolayer is found to be stable mechanically, thermally, and 13 dynamically and exhibits an anisotropic Dirac cone exactly at the Fermi level, showing a 6 14 Fermi velocity of 10 m/s in the same order of magnitude as that of graphene. Moreover, fi 15 B2S monolayer is the rst anisotropy Dirac cone material with a pristine honeycomb 16 structure stabilized by S in free-standing conditions where each atom has four valence 17 electrons on average being isoelectronic to C. This study would expand the Dirac cone 18 material family with new features. 19 he passion for two-dimensional (2D) Dirac cone materials geometry is unstable for a 2D B sheet in its freestanding state. 52 1 20 T was ignited by graphene, which is characterized by a Although it can be stabilized by adding two electrons to each 53 18,19 21 linear energy dispersion at the Fermi level, exhibiting ballistic boron hexagonal ring via doping metal atoms, in all the 54 2 22 charge transport and ultrahigh carrier mobility. Its Fermi metal-stabilized B sheets, metal atoms occupy all the intrinsic 55 6 23 velocity is as high as 0.8 × 10 m/s, only 2 orders of magnitude hexagonal hollow sites. Thus, the resulting geometries are very 56 24 lower than the velocity of light, offering a new way of different from the simple honeycomb configuration of 57 25 developing electronic devices. The fascinating properties and graphene. 58 26 vast applications displayed in graphene have stimulated a In this work, we chose boron and sulfur for a B−S 59 27 growing interest in studying 2D Dirac cone materials. honeycomb monolayer because of their special electronic 60 3 20−31 28 Currently, extensive efforts have been devoted to silicene, configurations and flexible bonding ability. In addition, a 61 4 5−8 9,10 11 29 germanene, carbon allotropes, boron allotropes, SiC3, binary compound with an atomic ratio greater than 1 could 62 12 13 fi 32 30 C4N, and Be3C2, which are identi ed as Dirac materials. generate crystals with low symmetry compared with graphene 63 31 2D boron-based Dirac cone materials have attracted a lot of and might lead to the materials with anisotropic Dirac cones, 64 32 current attention because boron is positioned on the left side of thus providing Fermi velocities in practical devices that are 65 fl 33 carbon in the periodic table with a smaller covalent radius and more exible and tunable than those of the isotropic Dirac 66 33−36 34 the capacity of flexible bonding. For instance, it has been found cone. On the basis of the global structure search and state- 67 β 14 fi 68 35 that a Dirac cone can exist in a boron 12 monolayer that was of-the-art theoretical simulations, we have identi ed a desirable 15 8 36 successfully synthesized consisting of 5−6−7 boron rings, B2S honeycomb monolayer with an anisotropic Dirac cone 69 7 16 37 triangular B chain-based porous sheet, 8B-Pmmn borophene, located at the high symmetric line in k-space. In this structure, 70 38 etc. Very recently, 2D anisotropic Dirac cones in χ3 borophene each atom has four valence electrons on average making B2S 71 39 were experimentally discovered by using high-resolution angle- isoeletronic to graphene, while the lower symmetry induced by 72 17 ff 40 resolved photoemission spectroscopy, where the anisotropic the two di erent species of elements is responsible for the 73 41 Dirac cone exhibits anisotropic carrier mobility that may have anisotropic Dirac cone. 74 42 advantages in direction-dependent transport for quantum Computational Methods. The ground-state structure of 2D 75 43 B2S is predicted by using the particle swarm optimization 76 devices. To date for all the reported 2D boron-based Dirac 37−42 44 cone materials, their geometries are much more complicated (PSO) algorithm implemented in the CALYPSO package. 77 45 than that of the pristine honeycomb structure of graphene The population size and the number of generations are both set 78 46 because of the different electronic configuration of the boron to 30 to ensure the convergence. The number of formula units 79 47 atom, which has one fewer electron than carbon. The electron- per unit cell are set to be 1, 2, 3, and 4, corresponding to B2S, 80 48 deficient boron tends to form multiple center bonds in the 2D 49 boron allotropes, where the pz orbital is not dominating the Received: February 27, 2018 50 interactions between electrons, which is different from the Accepted: March 25, 2018 51 situation in graphene. Accordingly, the pristine honeycomb Published: March 26, 2018 © XXXX American Chemical Society A DOI: 10.1021/acs.jpclett.8b00616 J. Phys. Chem. Lett. XXXX, XXX, XXX−XXX The Journal of Physical Chemistry Letters Letter ff 81 B4S2,B6S3, and B8S4, respectively. To accommodate the di erent covalent radii and electronegativities. The bond 124 37 82 structure buckling, we set the buffering thickness to 0.1 Å. lengths of B−B and B−S are 1.62 and 1.82 Å, respectively. 125 83 Atomic structure optimization, total energy, and electronic This deviation from ideal honeycomb structure finally 126 84 structure calculations are performed based on density func- contributes to the anisotropic properties of this material, such 127 85 tional theory (DFT), as implemented in the Vienna ab initio as mechanical and electric properties. 128 43 86 simulation package (VASP). The projector augmented wave To get more insight into the chemical bonding of the B2S 129 44 87 (PAW) method is employed to treat the interactions between monolayer, we calculate its electron localization function 130 53 88 ion cores and valence electrons with a kinetic energy cutoff of (ELF) to analyze the electron distribution. The ELF is a 131 89 450 eV. The first Brillouin zone is sampled by a 6 × 10 × 1 k- useful tool for chemical bond classification, which can be 132 45 90 point grid within the Monkhorst−Pack scheme. The described in the form of a contour plot in real space with values 133 91 exchange−correlation potential is treated using the Perdew− renormalized between 0.00 and 1.00. The values of 1.00 and 134 46 92 Burke−Ernzerh (PBE) functional within the generalized 0.50 correspond to fully localized and fully delocalized 135 47 93 gradient approximation (GGA) in most cases, while the electrons, respectively, while the value 0.00 refers to very low 136 48,49 94 HSE06 hybrid functional is used to obtain a more accurate charge density. The calculated results are plotted in Figure 1d, 137 95 electronic band structure. The atomic positons are fully relaxed where the region with a large ELF value is portrayed in red, 138 −4 96 until the energy and atomic forces converge to 10 eV and showing the paired electrons with local bosonic character and 139 −2 97 10 eV/Å, respectively. A large vacuum space of 20 Å in the the strong covalent electron states of the σ bond formed by the 140 2 98 perpendicular direction of the sheet is used to avoid the sp -hybridized orbitals of B and S atoms. 141 fi fi 99 interactions between periodic images. The nite displacement To examine the stability of the B2S monolayer, we rst 142 50 100 method implemented in the phonopy package is used to fi − calculate its cohesive energy, which is de ned by Ecoh = (EB2S 143 101 calculate the phonon spectra. Ab initio molecular dynamics − − 8EB 4ES)/12, where EB and ES are the total energies of a 144 102 (AIMD) simulations are carried out to confirm the thermal single B atom and single S atom, respectively, and EB S is the 145 103 stability. The tight-binding (TB) matrix elements are calculated 2 total energy of a B S unit cell. Our calculated value is 5.3 eV/ 146 104 by projecting Bloch states onto the maximally localized 2 51 atom, which is comparable to that of some bulk boron sulfide 147 105 Wannier functions (MLWFs), using the Wannier90 package 54 52 148 106 interfaced with Quantum ESPRESSO. phases recorded in the materials project data set, including B12S (5.8 eV/atom), B2S3 (4.9 eV/atom), and BS2 (4.6 eV/ 149 107 Through the global structure searching for a B2S monolayer atom), indicating that the B2S sheet is energetically favorable. 150 108 sheet, we obtain three energetically favorable monolayer B2S 151 109 phases. The optimized geometries and the relative energies These cohesive energies are calculated at the same theoretical 152 f1 110 with respect to the lowest energy (0 eV) are plotted in Figure level.
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