A Large Family of Synthetic Two-Dimensional Metal Hydrides

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A Large Family of Synthetic Two-Dimensional Metal Hydrides Xiaocheng Zhou, Yang Hang, Liren Liu, Zhuhua Zhang, and Wanlin Guo J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.9b02279 • Publication Date (Web): 25 Apr 2019 Downloaded from http://pubs.acs.org on April 25, 2019

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Journal of the American Chemical Society

A Large Family of Synthetic Two-Dimensional Metal Hydrides Xiaocheng Zhou‡, Yang Hang‡, Liren Liu, Zhuhua Zhang* and Wanlin Guo* State Key Laboratory of Mechanics and Control of Mechanical Structures, Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education, and Institute of Nanoscience, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China ABSTRACT: Synthetic two-dimensional (2D) materials without layered bulk allotropes are approaching a new frontier of materials flatland, one with properties richer than those of graphene-like materials. This is the case even as only a few chemical elements and blends have shown synthetic 2D forms. While hydrogen and metals are earth-abundant and form numerous compounds, rarely are 2D materials with only robust metal-hydrogen bonds. Here, a large new family of 2D materials is found from metal hydrides by highthroughput computational search augmented with first principles calculations. There are 110 thermally and dynamically stable 2D materials that range from metallic materials to wide-gap semiconductors. A subgroup of these materials even varies from topological insulators to nodal-loop semimetals as well as from antiferromagnetic semiconductors to ferromagnetic half-metals. Unexpectedly, these monolayers resemble graphene in an ability to form weak interlayer interaction due to the variable multicenter bonding of hydrogen that eliminates the otherwise prevalent dangling bonds, rather than the covalent bonds between stacked layers as in previously reported synthetic 2D materials. This feature will favor potential experimental synthesis of these metal hydride monolayers.

INTRODUCTION Two-dimensional (2D) materials that are one or several atoms thick have dominated the current phase of materials research. Since the exfoliation of graphene from graphite,1 a number of crystals with a layered ground state have displayed their 2D suits,2 such as h-BN,3, 4 MoS25 and black phosphorus.6 These naturally layered 2D materials have exhibited complementary properties enabling rapid advances in functional devices. Recently, research interest in the materials flatland has resulted in significant development of those materials that do not have layered allotropes. These synthetic 2D materials provide access to a wider range of properties through flexible structural options and an elemental choice for compositions. Notable examples of synthetic 2D materials are the so-called 2D-Xenes,7 such as borophene,8-10 silicene,11, 12 stanene,13, 14 all predicted in theory and successfully realized in subsequent experiments. Nevertheless, these synthetic elemental 2D materials are subject to strong interlayer bonding in bilayers or multilayers, which limits their potential applications. Expanding synthetic 2D materials beyond those with only single-elements provides an opportunity to achieve new, tailorable properties upon more diverse combinations of constituent elements. In the last few years, 2D nitrides,15, 16 oxides17 and carbides18, 19 have been reported, but synthetic 2D compounds remain limited; and few are potentially exfoliable from their nearest neighbors. As the third most abundant element on Earth's surface, hydrogen has a moderate electronegativity that supports its strong bonding capability. It forms greatly diversified binary compounds in gas, liquid, and solid phases with most other elements. Among all the compounds, metal hydrides bear potential applications in a series of technical fields, including catalysis,20 organic synthesis,21 and energy storage,22 but hydrogen in metals can

also cause well-known embrittlement.23 A fundamental understanding of structures and properties of metal hydrides at nanoscale is essential for further enriching their application. Despite their promise, 2D forms of metal hydrides have received little attention. Here, we report on a systematic structural search for 2D metal hydrides with high structural stability, peculiar electronic properties, and weak interlayer interaction, using highthroughput computations augmented with ab initio calculations. It was performed by combining hydrogen with all metals in the periodic table and then testing them with known layered lattice structures. We establish over 100 stable metal hydride monolayers, which are potentially exfoliable due to van der Waals interlayer interaction in their bilayers. Furthermore, these monolayers present a rich variety of electronic properties from metals to wide-gap semiconductors, including 25 monolayers with magnetic orderings and 5 monolayers with novel topological electronic phases. This portfolio of 2D metal hydrides greatly enriches the materials family in the flatland with customized properties and increased potential applications. RESULTS AND DISCUSSION The high-throughput computational search starts from a comprehensive initial set of 2D metal hydrides with reported lattice structures for 2D materials by literature, as exemplified by the representative structural prototypes shown in Figure. 1a. For each structural prototype, we carry out elemental mutation by scanning all metals in the periodic table and then trying different-sized supercells to consider possible structural distortions in the 2D monolayers. As such, the initial set contains ~1000 2D structures. Then, we screen out 2D structures that can be exfoliated from their nearest neighbors by

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Figure 1. Screening 2D metal hydrides. (a) A workflow of the high-throughput computation starting from structural prototypes illustrated by insets. Gray and pink balls stand for metal and hydrogen, respectively. (b) Interlayer binding energy, Eb, in bilayer 2D metal hydrides relaxed using the optB88-vdW functional. Circles colored blue, cyan, and light blue represent materials classified as easily exfoliable, potentially exfoliable, and unexfoliable, respectively. (c) Interlayer distance (d) in the relaxed bilayers, defined as the distance between two originally equivalent metal atoms in two layers. Materials with different prototypes are distinguished by labels and the materials shaded in light gray are considered to have 2D structures.

calculating the interlayer binding energy, Eb, i.e. the total energy difference between two isolated monolayers and a fully relaxed bilayer system, using a dispersion-corrected optB88vdW functional. Test calculations using this functional determine Eb to be 25 meV/Å2 for graphene and 24 meV/Å2 for h-BN, and are in good agreement with the previous results[24] of random phase approximation calculations. In this process, we directly exclude those structures that release H2 molecules upon the staking in their bilayers. This step results in 574 2D materials that enable weak interlayer interactions (Figure 1b), grounded in Eb < 130 meV/Å2. These materials can be classified into two groups according to the calculated Eb. The materials in the first group have Eb < 30 meV/Å2, thus having mechanical exfoliability similar to graphene; materials in the second group have Eb distributed between 30 and 130 meV/Å2, which are potentially exfoliable. There are 231 2D metal hydrides in the first group, which is entirely unexpected considering that no layered bulk metal hydride exists in a natural state. In contrast, silicene, germanene, stanene and borophene result in strong covalent bonds between the stacked layers. The next step of our protocol is to assess the dynamic and thermodynamic stability of the 574 structures by calculating their phonon frequencies and their formation energies. Finally, their electronic properties are systematically studied. We consider a structure to be dynamically stable if its phonon spectrum does not display an imaginary frequency. With this criterion, 110 2D metal hydrides out of the 574 materials are identified to be dynamically stable (Figure S1). According to point groups of lattices, these metal hydrides can be classified into 8 different prototypes: MH2 with P-6m2, P-3m1, P-4m2 and Pmmn, MH3 with P-31m and P4/nmm, M2H3 with P-3m1, and MH4 with P4/mmm symmetries, respectively. In these

prototypes, metal and hydrogen form various bonding configurations, accommodated by their flexibility in forming different multicenter bonds.25 The bonding between metal and hydrogen is revealed to vary from three-center, two-electron (3c-2e) bonds to up to eighteen-center, two-electron (18c-2e) bonds (Figure S2). Owing to the variable multicenter bonding, no dangling bond appears on the surfaces of most of these monolayers, as further supported by negligible charge redistribution between the stacked layers (Figure S3). This contrasts the cases of O- or C-terminated MXenes that need to be passivated to avoid the reaction between stacked layers. We then discuss the correspondence of various metals to the structural prototypes of 2D metal hydrides. Figure 2a presents a distribution of structural prototypes in terms of metal species in the periodic table. It is found that all alkali metals cannot form any stable 2D monolayers with hydrogen because these metals are strong electron donors that disfavor the formation of stable multi-center bonding with hydrogen. Moreover, no stable 2D metal hydride is identified with Ag, Au, Hg, Tc and Lu either, possibly due to the chemical inertness of these metals. Surprisingly, all other 30 metals can form structurally stable, chemically diverse 2D compounds with hydrogen. They will be referred to as metals unless specified otherwise. Figure 2a shows that all the metals are able to form MH2 monolayers, which exist with different point groups for each given metal. The P-3m1 MH2 monolayers are most common, visible to all the alkaline-earth and transition metals other than Zn and Cd, and amounting to 28 monolayers. The P-6m2 MH2 monolayers can exist with 18 transition metals from the group IV B to I B. The lattice structures of P-3m1 and P-6m2 MH2 monolayers are identical to the 1T and 2H phases of 2D metal dichalcogenides, respectively. Obviously, hydrogen is more capable than chalcogens in forming 2D metal compounds with more exotic structures. This is supported by additional 19 MH2


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Figure 2. Statistics of stable 2D metal hydrides. (a) A correspondence of stable monolayers with different structural prototypes to metal elements in the periodic table. (b) Number of materials (Nm1) as a function of the number of atoms (Nat) in the unit cell. (c) Formation energies per atom of the MxH1-x monolayers. (d) Binding energies for the stable metal hydride monolayers calculated with the optB88-vdW functional. The corresponding value of graphene is given by the dashed line for comparison. In this figure, different structural prototypes are distinguished by colors in a, b and by labels in c, d.

monolayers with a tetragonal lattice (Pmmn) and 4 monolayers with a square lattice (P-4m2), where metals are in a nearly square planar coordination. Aside from the MH2 composition, we also identify 13 P-3m1 M2H3, 10 P4/mmm MH4 compounds as well as 9 P-31m and 9 P4/nmm MH3 compounds, mostly for the transition metals from the groups IIIV B to VIII B. Note that the transition metals with partly filled 3d orbitals are distinguished in their ability to form both stable 2D hydrides with different stoichiometry and varied lattice point groups. We now look into structural details of these 2D materials. Figure 2b plots the distribution of these 2D compounds in terms of the number of atoms per unit cell, Nat. As apparent from the plot, a majority of the compounds have Nat < 9. Especially, we find Nat ≤ 3 for 28 P-3m1 MH2, 16 P-6m2 MH2 and 3 P-4m2 MH2 compounds, whereas Nat ≤ 8 for 13 P-3m1 M2H3, 19 Pmmn MH2, 7 P4/mmm MH4, 6 P-31m MH3 and 8 P4/nmm MH3 compounds. The remaining compounds with Nat ≥ 9 atoms are distorted due to the structural instability captured by large supercells (Figure S5). Regarding thickness, the Pmmn MH2, P3m1 M2H3 and P4/nmm MH3 compounds containing two atomic layers of metals are 0.39~0.48 nm thick (the thickness is defined by the distance between the top and bottom atomic planes of hydrogen), whereas other compounds have their thicknesses in the range of 0.19~0.26 nm, thinner than the MoS2 monolayer (0.31 nm thick). The 2D metal hydrides have a high possibility of experimental synthesis according to their formation energies, Ef. For a composition of MxH1-x, Ef is calculated as Ef = Et – xEM – (1–x)EH + △EZPE, where Et, EM and EH are total energies per atom of the 2D compound, bulk metal M and a H2 molecule in gas phase, respectively, and △EZPE is the difference of the zero point energy induced by the compound formation. Figure 2c plots Ef for the 110 compounds. It is gratifying that 24 compounds are thermodynamically stable as their Ef are

negative. The MH2 (P-3m1) and M2H3 (P-3m1) monolayers have Ef located at the plot bottom, suggesting that experimental synthesis can be first attempted for these monolayers. The remaining compounds are metastable since they have positive Ef, but 40 of them have Ef < 0.2 eV/atom, which can be regulated by overlaying the compounds on substrates. For example, a weakly interacting graphene substrate can turn Ef of 16 compounds into negative. Experimental realization of these monolayers will further benefit from weak interlayer interactions. Figure 2d shows that the Eb of most monolayers are less than 42 meV/Å2, due largely to their surface termination by hydrogen, which has the lightest mass to contribute little to Eb. In particular, 50 compounds have Eb < 25 meV/Å2; if synthesized, these are expected to be weakly interacted with substrates to allow for separation. The thermal stability of the 110 2D metal hydrides is further checked by carrying out ab initio molecular dynamics simulation using 5×5 supercells. No significant structural disruption is observed for all the compounds in the groups P6m2, P-3m1, P-31m, P-3m1, P4/nmm and P4/mmm throughout simulations for 10 picoseconds at a temperature of 500 K, as evidenced by snapshots shown in Figure S6. Extensive simulations show that most of these monolayers will not disrupt their structures until the temperature is raised to 700 K, confirming their high thermal stability. The monolayers in the P-4m2 and Pmmn groups undergo structural disruption at 500 K, but they are quite stable at 300 K. Mechanical properties are also tested by biaxially stretching selected monolayers. By applying incrementally increased tensile strains, we find that three tested monolayers with P-3m1 and P-4m2 point groups will not undergo phonon instability until the tensile strain is raised to 15%, and three tested monolayers with P-6m2, P-3m1 and P4/mmm point groups can withstand a tensile strain of 10% (Figure S7), which is comparable to the mechanical stability of 2D MoS2.26 The



Figure 3. Electronic properties of stable 2D metal hydrides. (a) A summary of the electronic properties of 2D hydrides versus metals in the periodic table, coded by colors and patterns of the blocks. (b) The number of 2D hydrides (Nm2) classified by electronic properties. SC, NM, FM and AFM stand for semiconductor, normal metal, ferromagnet, and antiferromagnet, respectively. (c,d) Bandgaps and carrier mobility of 2D semiconductors. The top and bottom parts of the graph correspond to normal and antiferromagnetic semiconductors, respectively. The colors for different structural prototypes are the same as that in Figure 2. Solid and striated bars in the graph represent the electron and hole mobility, respectively.

results indicate remarkably strong M-H bonds in these monolayers, further supported by their stretching frequencies of up to 1000-1500 cm-1, as shown in Figure S1, which is only slightly lower than the stretching frequencies for two-center HZn and H-Mg bonds on ZnO(0001) and MgO(001) surfaces, respectively.25 Moreover, we have also performed ab-initio molecular dynamics simulations for selected 2D metal hydrides under different biaxial tensile strains, showing that the 2D monolayers can exhibit high thermal stability against mechanical strain (Figure S8). The chemical stability of 2D metal hydrides is examined by adsorbing an O2 molecule on the surfaces of selected monolayers. Taking the TiH2 monolayer for example, an O2 molecule can be physisorbed on it. The physisorbed O2 can further evolve into a more stable chemisorbed state with newly formed metal-oxygen bonds by overcoming a 0.53 eV barrier, suggesting that this monolayer is quite inert against oxidation at ambient condition (Figure S9). In contrast, C, O and N adatoms can be chemisorbed on this monolayer and distort the structure, similar to the case of 2D black phosphorus.27 This occurs because these adatoms have a higher electro-negativity than H and thus have a stronger affinity to metal atoms. Thus, it is important to avoid elements with high electronegativity in the chamber during the chemical synthesis of 2D metal hydrides. After ensuring the structural stability of 2D metal hydrides, we then discuss the exciting properties they offer and their potential applications. By calculating the electronic band structures of the 110 compounds, we summarize their electronic properties in Figure 3a. The results show that the 2D metal hydrides exhibit a rich variety of properties, spanning from normal metals to wide-gap semiconductors, from antiferromagnetic (AFM) semiconductors to ferromagnetic (FM) half-metals, and from Dirac semimetals to nontrivial topological insulators, as is discussed below.

First, we identify 21 semiconducting compounds, with 14 normal semiconductors and 7 AFM semiconductors (Figure 3b). The normal semiconductors are formed with metals in the group IIA and Mn, Co, Zn, Mo, Rh, Cd and Ir. Structural prototypes of the semiconductors include P4/mmm MH4, MH3 with P-31m and P4/nmm point groups, as well as MH2 with P3m1, P-4m2 and Pmmn point groups. The AFM semiconductors include hexagonal VH2, CrH2, FeH2, NiH2, tetragonal VH4 and NbH4 and hexagonal CrH3. Bandgaps of these semiconductors can continuously vary from 0.07 eV for the CrH3 monolayer to 4.87 eV for the MgH2 monolayer (Figure 3c). The bandgaps of MH2 compounds are larger than 3 eV while those of the MH3 compounds are less than 1 eV. Electronic analyses show that near-gap states are predominantly contributed by the metals’ orbitals, as is similar to the case of 2D metal dichalcogenides. The weak interlayer interaction in bilayers of semiconducting 2D metal hydrides only slightly modifies the bandgap from the monolayer case, as shown in Figure S4. Following the bandgap, the carrier mobility of semiconducting compounds also varies across a wide range. For example, the electronic mobility can increase from 4 cm2V-1s-1 in the CaH2 monolayer to 2.9 × 104 cm2V-1s-1 in the MgH2 monolayer. The combined large bandgap and high carrier mobility are suitable for high-frequency device applications. It is worth mentioning that the IrH3 monolayer combines a bandgap of ~1.0 eV with an electronic mobility of ~103 cm2V1s-1, both similar to those of silicon. This decent combination is rarely seen in the materials flatland. Another useful point is that a number of semiconducting monolayers, e.g. BaH2, CaH2, FeH2, NiH2, SrH2, MoH3 and VH4, have direct bandgaps, offering a wealth of opportunity for photoelectronic applications. We have also obtained 89 metallic compounds, of which 14 are FM metals. The metallic compounds can be seen with all


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Figure 4. Topological states in 2D metal hydrides. (a-c) Band structures of the TiH2, RuH2 and CuH3 monolayers. Band structures with the spin-orbit coupling are shown by symbols, with the metal 3d or 4d orbitals being thickness coded and color coded, whereas those without such coupling are shown by gray lines. (d,e) The 3D band structures of TiH2 and RuH2 monolayers around the Fermi level. (f) Topological states on the zigzag edge of the CuH3 monolayer.

the transition metals except Zn, following suits with the eight structural prototypes. The FM metals mainly include P-6m2, P3m1 and Pmmn MH2 as well as P4/nmm MH3 and P-3m1 M2H3 with M = Fe, Co, Mn etc. Interestingly, the CoH2 monolayer is an intrinsic FM half-metal, consistent with very recent predictions.28 The half-metallic monolayer can serve as a spin filter for the creation of a completely spin-polarized spin current that is desirable for spintronic applications. More interesting, perhaps, is that we identify several 2D metal hydrides that exhibit symmetry-protected topological phases, including Dirac cones, nodal-loop semimetals, and topological insulators. The search for a topological character based on DFT calculations shows that the P-3m1 MH2 monolayers (M=Ti and Zr ) display two Dirac cones near the Fermi level, denoted as Dirac points I and II, as shown in Figure 4a for the TiH2 monolayer. The Dirac points I and II are located at the K point and on the line from Г to K, respectively, contributed primarily by the metal 3d orbitals. These two Dirac points have six equal images in the Brillouin zone (Figure 4d), presenting a multi-Dirac feature that differs from the single Dirac point in graphene. Including spin-orbital coupling causes the bands at the Dirac points to repel each other, opening a bandgap of 42 and 98 meV in the TiH2 and ZrH2 monolayers, respectively. The linear bands can also cross each other along a closed curve instead of at discrete points in the momentum space, giving rise to another topological family called nodal-loop semimetals. This topological nature can be materialized in the RuH2 and OsH2 monolayers with a P-6m2 point group. Figure 4b shows that the RuH2 monolayer exhibits two Dirac points that are both off the high-symmetry points, again with the Dirac states predominately originating from the metal d orbitals. These Dirac points form a nodal-loop in the 3D energymomentum plot, as marked by the black line in Figure 4e.

Likewise, the inclusion of spin-orbital coupling opens a bandgap of, for example, 70 meV in the RuH2 monolayer. Among the topological metal hydrides, the P-31m CuH3 monolayer is distinct in that the Cu atoms form a planar hexagonal lattice. As such, the CuH3 monolayer has a single Dirac point, similar to graphene (Figure 4c). More distinct is its wave function parity calculated using the Wilson loop method, which gives a topological invariant Z2 = 1. In contrast, both the Z2 numbers of ZrH2 and RuH2 monolayers are zero. The spinorbital coupling opens a band gap of 55 meV at the band crossing point for the CuH3 monolayer, ending up a topological insulator protected by time reversal symmetry. The metallic zigzag edge states of the CuH3 monolayer manifest as two topologically entangled Rashba-split states near the Fermi level that cross at the Г point (see Figure 4f). These states should be detectable by photoelectron spectroscopy. More complicated topological properties of these 2D hydrides deserve further investigation. CONCLUSIONS We have identified 110 thermally and dynamically stable 2D metal hydrides with diverse lattice structures using highthroughput computations augmented with ab initio calculations. These 2D metal hydrides are distinguished by their weak interlayer binding and versatile properties. Despite having no bulk layered allotropes, they all can be stacked layer-by-layer via a weak interlayer interaction, in contrast to common synthetic 2D materials that covalently bond with each other. This feature will benefit their experimental synthesis, and 17 monolayers are summarized to hold a high possibility of being synthesized due to their negative Ef and high stability. It is even more compelling that these monolayers span from normal metals to wide-gap semiconductors. A subgroup of monolayers even varies from ferromagnetic half-metals to antiferromagnetic semiconductors and from Dirac semimetals



to topological insulators. Notably, the IrH3 monolayer gathers a bandgap and electronic mobility which are comparable to those of silicon and thus holds great promise for nanoelectronic applications. The results, which suggest that exfoliable and functional 2D materials can be created with no bulk layered allotropes, open up a new paradigm for the development of synthetic 2D materials. Beyond the monolayers, future efforts can be devoted to reassembling these versatile 2D metal hydrides into designer van der Waals heterostructures with coded sequences and enriched functionalities. METHODS First-principles calculations are implemented in the Vienna Abinitio Simulation Package (VASP) code29 within the framework of density-functional theory (DFT)30,31 based on generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional.32 The core region is described by projector augmented wave method,33 with a plane-wave kinetic energy cutoff of 500 eV. To include the dispersion interaction between monolayers, we use the optB88-vdW functional.34 A vacuum region of 20 Å is set to isolate neighboring periodic images and the Brillouin zone is densely sampled. The structures are fully relaxed until the force on each atom is less than 0.01 eV/Å. Phonon spectra are calculated using finite displacement method and then the mapped out by the Phonopy code.35 Ab-initio molecular dynamics simulations are carried out using the canonical ensemble with a Nosé thermostat and a time step of 1 fs. The chemical bonding analysis is performed with the adaptive natural density partitioning (AdNDP) method,36, 37 for which we adopt models of nanoflakes cut from metal hydride monolayers.

ASSOCIATED CONTENT Supporting Information. Explanation about ‘high throughput”, phonon spectra of stable 2D metal hydrides, chemical bonding patterns, charge density difference of bilayers, electronic properties of bilayers, structures of compounds with ≥ 9 atoms per unit cell, snapshots of 2D metal hydrides of ab-initio molecular dynamics simulations, phonon spectra of monolayers under biaxial stretches, snapshots of selected metal hydrides structures of ab-initio molecular dynamics simulations under biaxial tensile strains, and calculation of the energy barrier. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *[email protected] *[email protected]

Author Contributions Z.Z. conceived this project. W.G. and Z.Z. supervised the research. X.Z. performed stability and electronic structure calculations. Y.H. performed calculations of the high-throughput structural search and the topological portion of the study. L.L. analyzed the chemical bonding of the monolayers. . ‡These authors contributed equally.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China (11772153, 51535005, and 51472117), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0417G01, MCMS-I-0418 K01, and MCMS-I-0418Y01), the Fundamental Research Funds for the Central Universities (NE2018002, NC2018001), and Youth Thousand Talents Program.

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8 ACS Paragon Plus Environment

A Large Family of Synthetic Two-Dimensional Metal Hydrides

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