Computationally Driven Two-Dimensional Materials Design: What Is Next? Jie Pan,*,† Stephan Lany,† and Yue Qi‡ †
Materials Science Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824, United States
‡
ABSTRACT: Two-dimensional (2D) materials offer many key advantages to innovative applications, such as spintronics and quantum information processing. Theoretical computations have accelerated 2D materials design. In this issue of ACS Nano, Kumar et al. report that ferromagnetism can be achieved in functionalized nitride MXene based on first-principles calculations. Their computational results shed light on a potentially vast group of materials for the realization of 2D magnets. In this Perspective, we briefly summarize the promising properties of 2D materials and the role theory has played in predicting these properties. In addition, we discuss challenges and opportunities to boost the power of computation for the prediction of the “structure−property−process (synthesizability)” relationship of 2D materials.
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2D magnetic order can be introduced extrinsically by doping transition metal elements or through defect engineering, the search for stable, intrinsic 2D magnets above absolute zero temperature is ongoing.1 Two recent studies have demonstrated that intrinsic 2D magnetism at finite temperature can be realized by adding magnetic anisotropy in chromium triiodide10 (CrI3; Figure 1c) and Cr2Ge2Te6.11 This is a significant step, but thus far, the intrinsic 2D magnetic ordering is maintained only far below room temperature (−228 °C for CrI3), and the challenge remains to realize room temperature non-air-sensitive intrinsic 2D magnets. Two-dimensional transition metal carbides, carbonitrides, and nitridesMXenes in shortwere synthesized in 201112 and present a rich area for the design of 2D materials, including 2D magnets. A typical MXene structure, Ti3C3 with OH functional groups, is shown in Figure 1d. Derived from MAX phases (M is an early transition metal, A is a group IIIA or IVA element, and X refers to either carbon or nitrogen), MXenes have the general chemical formula Mn+1XnTx (n = 1,2,3). MXenes come in a variety of structures, with different 2D layer thicknesses (described by the index n), different transition metal cations (M = Ti, V, Nb, Ta, etc.), or combinations in either disordered solid solutions or ordered arrangements, as well as different terminal functional groups (Tx, where T = F, Cl, O, OH, etc. and the value of x depends on the surface termination groups).7 This chemical and atomic structural diversity adds an enormous chemical space to fill the “property gap” that
ver the past decade, the development of twodimensional (2D) materials has established an entire research field dedicated to phenomena, properties, and functionalities that are not present in the bulk phases.1 Not limited to single-element phases, such as graphene or silicene, these one- to several-atoms-thick materials have rapidly expanded into a nontrivial set of chemical compounds (as shown in Figure 1a), most prominently including hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDs). These 2D materials can be metallic (e.g., NbSe2), semiconducting (e.g., WSe2, MoS2), or insulating (e.g., hBN). They have extraordinary combinations of mechanical, electronic, and optic properties, offering a plethora of opportunities in advanced technical applications. MoS2 (Figure 1b) is the prototypical TMD material. In its single-layer structure, MoS2 is a direct band gap semiconductor,2 highly flexible, and mechanically strong;3 these properties not only make MoS2 suitable for flexible electronic devices but also enable the optoelectronic properties to be tuned by mechanical strain for solar energy capture.4 Two-dimensional materials host a wealth of physical phenomena, but the realization of intrinsic 2D magnetism at finite temperature remains a challenge. Just as semiconducting 2D materials could revolutionize electronics,8 2D magnets could be “game-changing” materials for spintronic devices that manipulate the spin degree of freedom. However, the fundamental physics of intrinsic 2D magnetism depends on subtleties, where the Ising model predicts finite temperature ferromagnetic but the isotropic Heisenberg model does not.9 Although © 2017 American Chemical Society
Published: July 17, 2017 7560
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Figure 1. (a) Family of two-dimensional (2D) materials. Reproduced with permission from ref 1. Copyright 2015 American Chemical Society. (b) MoS2 structure in three dimensions, and each layer can be separated as 2D-MoS2. Reproduced with permission from ref 5. Copyright 2012 Nature Publishing Group. (c) 2D-CrI3 crystal structure with magnetic moments aligned with the out-of-plane axis (green arrows). Reproduced with permission from ref 6. Copyright 2017 Nature Publishing Group. (d) Typical MXene structure (Ti3C2TX) with OH functional groups on the surface. Reproduced with permission from ref 7. Copyright 2017 Macmillan Publishers Limited.
in nanotechnology. Ever since the discovery of graphene in 2004,14 a variety of 2D materials have been found to have useful electronic, optical, mechanical, and thermal properties. Most notably, the electronic structure changes with the layer thickness, for example, leading in MoS2 to a transition from an indirect bulk band gap to a direct gap in the single-layer material (Figure 2a) and causing profound changes in the photoluminescence and absorption spectra.15 Hybrid functional calculations with spin−orbit coupling (SOC) also show that the band structure can be tuned by applying strain or by varying terminating functional groups.8 Furthermore, 2D materials also exhibit superior carrier mobility (e.g., graphene has a room temperature electron mobility of about 104 cm2 V−1 s−1), which enables the fabrication of fast operation transistors (Figure 2b).1 In the semiconducting TMDs, SOC and the lack of inversion symmetry result in new electron/hole behaviors, such as the “valley” degree of freedom.8 In addition, the reduced dielectric screening in 2D materials alters their optical properties by increasing exciton binding. As shown in Figure 2c, transitions A and B represent two exciton transitions from conduction band minimum to two SOC split valence band maximum. These optical responses due to excitonic transitions in MoS2 have been verified by first-principles-based GW calculations (GW-Bethe-Salpeter equation approach).16 These new emerging properties provide alternatives for optimizing optoelectronic devices, such as light-emitting devices and solar cells. The prospect of 2D and van der Waals heterostructures adds yet another dimension to the design of novel devices and functionalities.17 Notwithstanding the fundamental questions about magnetic ordering in two dimensions, extensive research has been devoted to the search for 2D magnets, due to their potential
other types of 2D materials may not fulfill, for example, providing magnetic interaction for room temperature 2D magnets. In this issue of ACS Nano, Kumar et al. report a density functional theory (DFT)-based computational study for screening magnetic properties of MXenes.13 By mapping the DFT energies onto an Ising model, they predict robust half-metallic ferromagnetism at or even above room temperature in Mn- and Cr-based MXenes, thereby guiding exploratory syntheses of novel 2D magnetic materials.
In this issue of ACS Nano, Kumar et al. report a density functional theory (DFT)-based computational study for screening magnetic properties of MXenes. In this Perspective, we discuss the prospects of 2D materials design on the computational horizon. We briefly summarize the interesting properties of 2D materials and their potential technical applications, with a detailed discussion of magnetism. Because of the crucial role computations have played in the discovery and development of 2D materials (the article from Kumar et al. in this issue of ACS Nano is a good example13), we focus in particular on the power of computation on 2D materials structures and property predictions and the associated opportunities and challenges.
TWO-DIMENSIONAL MATERIALS AND THEIR APPLICATIONS Due to their reduced dimensions and symmetry, 2D materials offer remarkable physical properties for potential applications 7561
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Figure 2. (a) Band structure calculated from density functional theory (GGA-PBE functional) for bulk and monolayer MoS2. Reproduced with permission from ref 2. Copyright 2011 American Physical Society. (b) Schematic drawing of a monolayer MoS2-based field-effect transistor device. Reproduced with permission from ref 5. Copyright 2012 Nature Publishing Group. (c) Band structure of MoS2 showing the bulk indirect band gap Eg′, monolayer direct band gap Eg, and two exitonic transitions A and B. Reproduced with permission from ref 18. Copyright 2010 American Physical Society.
Figure 3. (a) Schematic illustration of spintronic devices. Reproduced with permission from ref 21. Copyright 2012 Nature Publishing Group. (b) Schematic density of states for two spin states: in ferromagnetic transition metals, the transport of electrons is spin-dependent due to the strong scattering to down-spin electrons from the half-filled d-bands. Reproduced with permission from ref 22. Copyright 2015 Nature Publishing Group. (c) First-principles calculations predict antiferromagnetic Cr2CF2 atomic structure. Blue and yellow colors are the isosurface of electron density with majority and minority spin, respectively. Reproduced with permission from ref 19. Copyright 2017 The Royal Society of Chemistry. 7562
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able to form a different type of 2D structure. It is possible that entire families of other 2D structures are waiting to be discovered. As an example, Caskey et al. recently reported the synthesis of a novel mixed-valent Sn(II)Sn(IV)N2 nitride (Sn2N2) by sputtering.27 Although the structural assignment was initially inconclusive, recent first-principles structure predictions suggest a layered structure, where the three-fold coordinated Sn(II) cations sandwich the five-fold coordinated Sn(IV) inner cations.28 As an 8-atom-thick, single-layer 2D material, Sn2N2 is expected to have a sizable band gap and could be of great interest if the isolation of single layers can be achieved.
importance in applications such as spintronics. Figure 3a illustrates the basic operating principles for a spin-gate/valve that allows electrons with selective spin to pass. This character can be achieved in ferromagnetic metals. For example, in ferromagnetic nickel, the transport of electrons is spin-dependent due to the different scattering strengths from immobile d-electrons for electrons with up-spin and down-spin (Figure 3b). MXenes are promising candidates for 2D magnetism due to their rich chemistry and their morphology. Through spinpolarized DFT calculations, researchers have predicted that some of the pristine MXenes (without functional groups on the surface), such as Ti2C and Ti2N, have half-metallic ferromagnetic ground states.19 However, ferromagnetic ordering is not sustained after functionalization by F, Cl, OH, or H termination on the surface (Cr2CF2, as a example, is shown in Figure 3c).19 Recently, DFT+U calculations have shown that Cr2N can be ferromagnetic only after O surface passivation.20 These scattered theoretical studies have established the possibility of magnetic MXenes, but a more comprehensive approach is clearly needed. In this issue of ACS Nano, researchers from University of Pennsylvania and Drexel University report theoretical predictions of magnetism in a series of nitride MXenes.13 They used DFT+U calculations to calculate energies and electronic structures for different magnetic orderings and then analyzed and rationalized the DFT results with a crystal field theory model. They found that O termination is preferred for ferromagnetic nitride MXenes (Mn2NO2, Ti2NO2, and Cr2NO2), and Mn2N can be ferromagnetic with other terminations, such as F and OH. They attributed this interesting phenomenon to the competition between superexchange and double-exchange interactions, which can rationally narrow down the possibilities of 2D magnets. Furthermore, they also tested the robustness of the ferromagnetism at finite temperatures by constructing an Ising model Hamiltonian for large-scale Monte Carlo simulations. Based on this statistical simulation, they found that the Curie temperature for these nitride MXenes could be above room temperature.
It is possible that entire families of other two-dimensional structures are waiting to be discovered. As 2D materials are envisioned for a wide range of applications, the materials by design approach will guide research directions. New types of electronics are based on tunneling devices, and optoelectronic applications could lead to revolutionary light-emitting diodes, photodetectors, or even photovoltaics.17 Harnessing half-metallic ferromagnetism, as predicted by Kumar et al. in nitride-based MXenes, could lead to novel spintronic applications.13 A further application area of increasing interest is catalysis,29 where the natural high specific surface area of 2D materials is of great advantage. All these applications require the control of several materials properties simultaneously, including the electronic structure, magnetic structure, optical properties, and transport. In addition, emergent properties arise from atomic or electronic correlations particular to the 2D form, as is illustrated by the prediction of ferromagnetic ordering.13 The design space for 2D materials is vast, and it continues to expand as 1) the materials base for 2D layers is augmented by new discoveries; 2) the properties are tailored by different layer terminations and functionalizations; and 3) van der Waals heterostructures are built from combinations of different 2D materials. Therefore, materials-by-design approaches, with efficient methods that can identify materials with targeted properties from a large pool of candidates, are essential for accelerated discovery. In addition, the role of computational design will shift from predicting which structures to make toward also describing how to synthesize them.30 Twodimensional materials are generally metastable phases and are often realized via kinetic routes. Thus, computational descriptions cannot be agnostic to the synthesis technique, and the integration of computations and experimental synthesis becomes particularly important.
MATERIALS BY DESIGN FOR TWO-DIMENSIONAL MATERIALS Computation has played indispensable roles in predicting the structure and properties of 2D materials. The development of MXenes has been accompanied from the beginning by firstprinciples calculations, which have provided insight into MXenes’ atomic and electronic structure, magnetism, and elastic and phonon properties.12,23,24 Initial steps toward computational design of 2D materials have been undertaken, for example, in evaluating the atomic ordering patterns in double-transition metal layers25 and predicting adsorption energies for intercalation ions.26 In the work reported in this issue, Kumar et al. have predicted the magnetism in new nitride-based MXenes obtained by introducing different transition metal cations into the MXene structure.13 Similarly, a total of about 70 elemental hypothetical MXenes have been suggested theoretically by varying the elements within the atomic structures of the currently known MXenes. As both an opportunity and a challenge for computational design of 2D materials, the next logical step is to search for new atomic structures in 2D materials. The MXene structure can be viewed as being derived from the rock-salt crystal of the binary carbide or nitride (e.g., TiC, TiN). However, the binaries of other transition metals form different crystal structures and may be
Harnessing half-metallic ferromagnetism, as predicted by Kumar et al. in nitride-based MXenes, could lead to novel spintronic applications. PROSPECTS AND OUTLOOK In this Perspective, we highlighted the relevance of theoretical calculations on the prediction of the structures and properties of 2D materials. The emergence of new properties of 2D materials enables a wide range of potential technologies. We envision the challenges and opportunities for theory to promote the advancement of 2D materials further. We anticipate 7563
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the significant future development of 2D materials to include computational materials design as a driving force.
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Jie Pan: 0000-0002-9993-1379 Yue Qi: 0000-0001-5331-1193 Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS J.P. and S.L. acknowledge support as part of the “Center for the Next Generation of Materials by Design”, an Energy Frontier Research Center (EFRC) funded by U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under Contract No. DE-AC36-08GO28308 to the National Renewable Energy Laboratory (NREL). Y.Q. acknowledges the support by the Nanostructures for Electrical Energy Storage (NEES), an Energy Frontier Research Center funded by DOE, Office of Science, Basic Energy Sciences under Award Number DESC0001160. The authors thank Alfred Hicks at the Communications and Public Affairs Department of the National Renewable Energy Laboratory for the design of graphics for the Table of Contents. REFERENCES (1) Bhimanapati, G. R.; Lin, Z.; Meunier, V.; Jung, Y.; Cha, J.; Das, S.; Xiao, D.; Son, Y.; Strano, M. S.; Cooper, V. R.; Liang, L.; Louie, S. G.; Ringe, E.; Zhou, W.; Kim, S. S.; Naik, R. R.; Sumpter, B. G.; Terrones, H.; Xia, F.; Wang, Y.; Zhu, J.; Akinwande, D.; Alem, N.; Schuller, J. A.; Schaak, R. E.; Terrones, M.; Robinson, J. A. Recent Advances in Two-Dimensional Materials beyond Graphene. ACS Nano 2015, 9, 11509−11539. (2) Kuc, A.; Zibouche, N.; Heine, T. Influence of Quantum Confinement on the Electronic Structure of the Transition Metal Sulfide TS2. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 245213. (3) Bertolazzi, S.; Brivio, J.; Kis, A. Stretching and Breaking of Ultrathin MoS2. ACS Nano 2011, 5, 9703−9709. (4) Feng, J.; Qian, X.; Huang, C.-W.; Li, J. Strain-Engineered Artificial Atom as a Broad-Spectrum Solar Energy Funnel. Nat. Photonics 2012, 6, 866−872. (5) Wang, Q. H.; Kalantar-Zadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides. Nat. Nanotechnol. 2012, 7, 699−712. (6) Bourzac, K. Physicists Have Finally Created a 2D Magnet. Nature 2017, DOI: 10.1038/nature.2017.22115. (7) Anasori, B.; Lukatskaya, M. R.; Gogotsi, Y. 2D Metal Carbides and Nitrides (MXenes) for Energy Storage. Nat. Rev. Mater. 2017, 2, 16098. (8) Butler, S. Z.; Hollen, S. M.; Cao, L.; Cui, Y.; Gupta, J. A.; Gutiérrez, H. R.; Heinz, T. F.; Hong, S. S.; Huang, J.; Ismach, A. F.; Johnston-Halperin, E.; Kuno, M.; Plashnitsa, V. V.; Robinson, R. D.; Ruoff, R. S.; Salahuddin, S.; Shan, J.; Shi, L.; Spencer, M. G.; Terrones, M.; Windl, W.; Goldberger, J. E. Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene. ACS Nano 2013, 7, 2898−2926. (9) Mermin, N. D.; Wagner, H. Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models. Phys. Rev. Lett. 1966, 17, 1133−1136. (10) Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; Jarillo-Herrero, P.; Xu, X. Layer7564
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