Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds


Two-dimensional (2D) materials have emerged as promising candidates for next-generation electronic and optoelectronic applications. Yet, only a few dozen 2D materials have been successfully synthesized or exfoliated. Here, we search for 2D materials that can be easily exfoliated from their parent compounds. Starting from 108,423 unique, experimentally known 3D compounds, we identify a subset of 5,619 compounds that appear layered according to robust geometric and bonding criteria. High-throughput calculations using van der Waals density functional theory, validated against experimental structural data and calculated random phase approximation binding energies, further allowed the identification of 1,825 compounds that are either easily or potentially exfoliable. In particular, the subset of 1,036 easily exfoliable cases provides novel structural prototypes and simple ternary compounds as well as a large portfolio of materials to search from for optimal properties. For a subset of 258 compounds, we explore vibrational, electronic, magnetic and topological properties, identifying 56 ferromagnetic and antiferromagnetic systems, including half-metals and half-semiconductors.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Screening for low-dimensional manifolds in a parent 3D crystal.
Fig. 2: Binding energies of the bulk 3D compounds identified as geometrically layered.
Fig. 3: Statistics on the 2D and 3D databases.
Fig. 4: The most common 2D structural prototypes.


  1. 1.

    Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nat. Nanotechnol. 6, 147–150 (2011).

    Article  Google Scholar 

  2. 2.

    Chhowalla, M., Jena, D. & Zhang, H. Two-dimensional semiconductors for transistors. Nat. Rev. Mater. 1, 16052 (2016).

    Article  Google Scholar 

  3. 3.

    Butler, S. Z. et al. Progress, challenges, and opportunities in two-dimensional materials beyond graphene. ACS Nano 7, 2898–2926 (2013).

    Article  Google Scholar 

  4. 4.

    Geim, A. & Grigorieva, I. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  Google Scholar 

  5. 5.

    Villars, P., Onodera, N. & Iwata, S. The Linus Pauling file (LPF) and its application to materials design. J. Alloys Compd. 279, 1–7 (1998).

    Article  Google Scholar 

  6. 6.

    Inorganic Crystal Structure Database (ICSD);

  7. 7.

    Gražulis, S. et al. Crystallography open database (COD): an open-access collection of crystal structures and platform for world-wide collaboration. Nucleic. Acids. Res. 40, D420–D427 (2012).

    Article  Google Scholar 

  8. 8.

    Lebègue, S., Björkman, T., Klintenberg, M., Nieminen, R. M. & Eriksson, O. Two-dimensional materials from data filtering and ab initio calculations. Phys. Rev. X 3, 031002 (2013).

    Google Scholar 

  9. 9.

    Romdhane, F. B. et al. Quasi-2D Cu2S crystals on graphene: in-situ growth and ab-initio calculations. Small 11, 1253–1257 (2015).

    Article  Google Scholar 

  10. 10.

    Miró, P., Audiffred, M. & Heine, T. An atlas of two-dimensional materials. Chem. Soc. Rev. 43, 6537–6554 (2014).

    Article  Google Scholar 

  11. 11.

    Rasmussen, F. A. & Thygesen, K. S. Computational 2D materials database: electronic structure of transition-metal dichalcogenides and oxides. J. Phys. Chem. C 119, 13169–13183 (2015).

    Article  Google Scholar 

  12. 12.

    Ashton, M., Paul, J., Sinnott, S. B. & Hennig, R. G. Topology-scaling identification of layered solids and stable exfoliated 2D materials. Phys. Rev. Lett. 118, 106101 (2017).

    Article  Google Scholar 

  13. 13.

    Cheon, G. et al. Data mining for new two- and one-dimensional weakly bonded solids and lattice-commensurate heterostructures. Nano Lett. 17, 1915–1923 (2017).

    Article  Google Scholar 

  14. 14.

    Jain, A. et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).

    Article  Google Scholar 

  15. 15.

    Gould, T., Lebègue, S., Björkman, T. & Dobson, J. in Semiconductors and Semimetals 2D Materials Vol. 95 (eds Iacopi, F. et al.) Ch. 1, 1–33 (Elsevier, 2016).

  16. 16.

    Franceschetti, A. & Zunger, A. The inverse band-structure problem of finding an atomic configuration with given electronic properties. Nature 402, 60–63 (1999).

    Article  Google Scholar 

  17. 17.

    Johannesson, G. H. et al. Combined electronic structure and evolutionary search approach to materials design. Phys. Rev. Lett. 88, 255506 (2002).

    Article  Google Scholar 

  18. 18.

    Curtarolo, S., Morgan, D., Persson, K., Rodgers, J. & Ceder, G. Predicting crystal structures with data mining of quantum calculations. Phys. Rev. Lett. 91, 135503 (2003).

    Article  Google Scholar 

  19. 19.

    Curtarolo, S. et al. The high-throughput highway to computational materials design. Nat. Mater. 12, 191–201 (2013).

    Article  Google Scholar 

  20. 20.

    Jain, A., Shin, Y. & Persson, K. A. Computational predictions of energy materials using density functional theory. Nat. Rev. Mater. 1, 15004 (2016).

    Article  Google Scholar 

  21. 21.

    Mueller, T., Hautier, G., Jain, A. & Ceder, G. Evaluation of tavorite-structured cathode materials for lithium-ion batteries using high-throughput computing. Chem. Mater. 23, 3854–3862 (2011).

    Article  Google Scholar 

  22. 22.

    Saal, J., Kirklin, S., Aykol, M., Meredig, B. & Wolverton, C. Materials design and discovery with high-throughput density functional theory: the Open Quantum Materials Database (OQMD). JOM 65, 1501–1509 (2013).

    Article  Google Scholar 

  23. 23.

    Ozolins, V., Majzoub, E. H. & Wolverton, C. First-principles prediction of thermodynamically reversible hydrogen storage reactions in the Li-Mg-Ca-B-H system. J. Am. Chem. Soc. 131, 230–237 (2009).

    Article  Google Scholar 

  24. 24.

    Ortiz, C., Eriksson, O. & Klintenberg, M. Data mining and accelerated electronic structure theory as a tool in the search for new functional materials. Comput. Mater. Sci. 44, 1042–1049 (2009).

    Article  Google Scholar 

  25. 25.

    Greeley, J., Jaramillo, T. F., Bonde, J., Chorkendorff, I. & Norskov, J. K. Computational high-throughput screening of electrocatalytic materials for hydrogen evolution. Nat. Mater. 5, 909–913 (2006).

    Article  Google Scholar 

  26. 26.

    Yu, L. & Zunger, A. Identification of potential photovoltaic absorbers based on first-principles spectroscopic screening of materials. Phys. Rev. Lett. 108, 068701 (2012).

    Article  Google Scholar 

  27. 27.

    Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  Google Scholar 

  28. 28.

    Nicolosi, V., Chhowalla, M., Kanatzidis, M. G., Strano, M. S. & Coleman, J. N. Liquid exfoliation of layered materials. Science 340, 1226419 (2013).

    Article  Google Scholar 

  29. 29.

    Pizzi, G., Cepellotti, A., Sabatini, R., Marzari, N. & Kozinsky, B. AiiDA: automated interactive infrastructure and database for computational science. Comput. Mater. Sci. 111, 218–230 (2016).

    Article  Google Scholar 

  30. 30.

    Merkys, A. et al. COD::CIF::Parser: an error-correcting CIF parser for the Perl language. J. Appl. Crystallogr. 49, 292–301 (2016).

    Article  Google Scholar 

  31. 31.

    Ong, S. P. et al. Python Materials Genomics (pymatgen): a robust, open-source python library for materials analysis. Comput. Mater. Sci. 68, 314–319 (2013).

    Article  Google Scholar 

  32. 32.

    Togo, A. spglib;

  33. 33.

    Alvarez, S. A cartography of the van der Waals territories. Dalton Trans. 42, 8617–8636 (2013).

    Article  Google Scholar 

  34. 34.

    Lee, K., Murray, É. D., Kong, L., Lundqvist, B. I. & Langreth, D. C. Higher-accuracy van der Waals density functional. Phys. Rev. B 82, 081101 (2010).

    Article  Google Scholar 

  35. 35.

    Cooper, V. R. Van der Waals density functional: an appropriate exchange functional. Phys. Rev. B 81, 161104 (2010).

    Article  Google Scholar 

  36. 36.

    Hamada, I. & Otani, M. Comparative van der Waals density-functional study of graphene on metal surfaces. Phys. Rev. B 82, 153412 (2010).

    Article  Google Scholar 

  37. 37.

    Vydrov, O. A. & Van Voorhis, T. Nonlocal van der Waals density functional made simple. Phys. Rev. Lett. 103, 063004 (2009).

    Article  Google Scholar 

  38. 38.

    Vydrov, O. A. & Van Voorhis, T. Nonlocal van der Waals density functional: the simpler the better. J. Chem. Phys. 133, 244103 (2010).

    Article  Google Scholar 

  39. 39.

    Sabatini, R., Gorni, T. & de Gironcoli, S. Nonlocal van der Waals density functional made simple and efficient. Phys. Rev. B 87, 041108 (2013).

    Article  Google Scholar 

  40. 40.

    Björkman, T., Gulans, A., Krasheninnikov, A. V. & Nieminen, R. M. Van der Waals bonding in layered compounds from advanced density-functional first-principles calculations. Phys. Rev. Lett. 108, 235502 (2012).

    Article  Google Scholar 

  41. 41.

    Zhang, Y. & Yang, W. Comment on “generalized gradient approximation made simple”. Phys. Rev. Lett. 80, 890–890 (1998).

    Article  Google Scholar 

  42. 42.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  Google Scholar 

  43. 43.

    Dion, M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004).

    Article  Google Scholar 

  44. 44.

    Cordero, B. et al. Covalent radii revisited. Dalton Trans. 2832–2838 (2008).

  45. 45.

    Sohier, T., Gibertini, M., Calandra, M., Mauri, F. & Marzari, N. Breakdown of optical phonons’ splitting in two-dimensional materials. Nano Lett. 17, 3758–3763 (2017).

    Article  Google Scholar 

  46. 46.

    Samarth, N. Condensed-matter physics: magnetism in flatland. Nature 546, 216–218 (2017).

    Article  Google Scholar 

  47. 47.

    Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).

    Article  Google Scholar 

  48. 48.

    Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).

    Article  Google Scholar 

  49. 49.

    Drozdov, I. K. et al. One-dimensional topological edge states of bismuth bilayers. Nat. Phys. 10, 664–669 (2014).

    Article  Google Scholar 

  50. 50.

    Wang, A., Wang, Z., Du, A. & Zhao, M. Band inversion and topological aspects in a TiNI monolayer. Phys. Chem. Chem. Phys. 18, 22154–22159 (2016).

    Article  Google Scholar 

  51. 51.

    Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds (data download). Materials Cloud Archive (2017);

  52. 52.

    Grosse-Kunstleve, R. W. & Adams, P. D. Algorithms for deriving crystallographic space-group information. II. Treatment of special positions. Acta. Crystallogr. A58, 60–65 (2002).

    Article  Google Scholar 

  53. 53.

    Hinuma, Y., Togo, A., Hayashi, H. & Tanaka, I. Choice of basis vectors for conventional unit cells revisited. Preprint at (2015).

  54. 54.

    Hundt, R., Schön, J. C. & Jansen, M. CMPZ—an algorithm for the efficient comparison of periodic structures. J. Appl. Crystallogr. 39, 6–16 (2006).

    Article  Google Scholar 

  55. 55.

    Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

  56. 56.

    Standard solid-state pseudopotentials (SSSP);

  57. 57.

    Garrity, K. F., Bennett, J. W., Rabe, K. M. & Vanderbilt, D. Pseudopotentials for high-throughput DFT calculations. Comput. Mater. Sci. 81, 446–452 (2014).

    Article  Google Scholar 

  58. 58.

    Kucukbenli, E. et al. Projector augmented-wave and all-electron calculations across the periodic table: a comparison of structural and energetic properties. Preprint at (2014).

  59. 59.

    Dal Corso, A. Pseudopotentials periodic table: from H to Pu. Comput. Mater. Sci. 95, 337–350 (2014).

    Article  Google Scholar 

  60. 60.

    Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).

    Article  Google Scholar 

  61. 61.

    Willand, A. et al. Norm-conserving pseudopotentials with chemical accuracy compared to all-electron calculations. J. Chem. Phys. 138, 104109 (2013).

    Article  Google Scholar 

  62. 62.

    Topsakal, M. & Wentzcovitch, R. Accurate projected augmented wave (PAW) datasets for rare-earth elements (RE = La-Lu). Comput. Mater. Sci. 95, 263–270 (2014).

    Article  Google Scholar 

  63. 63.

    Lejaeghere, K. et al. Reproducibility in density functional theory calculations of solids. Science 351, aad3000 (2016).

    Article  Google Scholar 

  64. 64.

    Lejaeghere, K., Van Speybroeck, V., Van Oost, G. & Cottenier, S. Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals. Crit. Rev. Solid State Mater. Sci. 39, 1–24 (2014).

    Article  Google Scholar 

  65. 65.

    Björkman, T. Van der Waals density functional for solids. Phys. Rev. B 86, 165109 (2012).

    Article  Google Scholar 

  66. 66.

    Björkman, T. Testing several recent van der Waals density functionals for layered structures. J. Chem. Phys. 141, 074708 (2014).

    Article  Google Scholar 

  67. 67.

    Berland, K. et al. Van der Waals forces in density functional theory: a review of the vdW-DF method. Rep. Prog. Phys. 78, 066501 (2015).

    Article  Google Scholar 

  68. 68.

    Marzari, N., Vanderbilt, D., De Vita, A. & Payne, M. C. Thermal contraction and disordering of the Al(110) surface. Phys. Rev. Lett. 82, 3296 (1999).

    Article  Google Scholar 

  69. 69.

    Sohier, T., Calandra, M. & Mauri, F. Density functional perturbation theory for gated two-dimensional heterostructures: theoretical developments and application to flexural phonons in graphene. Phys. Rev. B 96, 075448 (2017).

    Article  Google Scholar 

  70. 70.

    Sohier, T., Calandra, M. & Mauri, F. Two-dimensional Fröhlich interaction in transition-metal dichalcogenide monolayers: theoretical modeling and first-principles calculations. Phys. Rev. B 94, 085415 (2016).

    Article  Google Scholar 

  71. 71.

    Togo, A. & Tanaka, I. Evolution of crystal structures in metallic elements. Phys. Rev. B 87, 184104 (2013).

    Article  Google Scholar 

  72. 72.

    Hart, G. L. W. & Forcade, R. W. Algorithm for generating derivative structures. Phys. Rev. B 77, 224115 (2008).

    Article  Google Scholar 

  73. 73.

    Hart, G. L. W. & Forcade, R. W. Generating derivative structures from multilattices: algorithm and application to hcp alloys. Phys. Rev. B 80, 014120 (2009).

    Article  Google Scholar 

  74. 74.

    Hart, G. L., Nelson, L. J. & Forcade, R. W. Generating derivative structures at a fixed concentration. Comput. Mater. Sci. 59, 101–107 (2012).

    Article  Google Scholar 

  75. 75.

    Soluyanov, A. A. & Vanderbilt, D. Computing topological invariants without inversion symmetry. Phys. Rev. B 83, 235401 (2011).

    Article  Google Scholar 

  76. 76.

    Gresch, D. et al. Z2Pack: numerical implementation of hybrid Wannier centers for identifying topological materials. Phys. Rev. B 95, 075146 (2017).

    Article  Google Scholar 

  77. 77.

    Mostofi, A. A. et al. An updated version of wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 185, 2309–2310 (2014).

    Article  Google Scholar 

  78. 78.

    Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).

    Article  Google Scholar 

  79. 79.

    Pseudo-Dojo library;

Download references


This work was supported by the MARVEL National Centre of Competence in Research of the Swiss National Science Foundation. Simulation time was provided by the Swiss National Supercomputing Centre (CSCS) under project IDs s580, mr0 and ch3, amounting to 60,000 DFT calculations and 5 million core hours. D.C., A.Ma. and N.Ma. gratefully acknowledge support from the EU Centre of Excellence MaX ‘MAterials design at the eXascale’ (grant no. 676598). D.C. acknowledges support from the ‘EPFL Fellows’ fellowship programme co-funded by Marie Skłodowska-Curie, Horizon 2020 grant agreement no. 665667. The authors would also like to acknowledge useful discussions with F. Ambrosio, and thank M. Giantomassi, M. J. van Setten and G. M. Rignanese for providing their fully relativistic ONCV pseudopotentials (

Author information




M.G., G.P., N.Mo. and N.Ma. conceived the project. N.Mo., A.C., G.P., A.Me., T.S. and I.E.C. provided the necessary input, software tools and AiiDA workflows. N.Mo., P.S. and M.G. extracted and refined the structures from the source databases. P.S., N.Mo. and M.G. performed the geometrical screening of layered materials. N.Mo., D.C. and A.Ma. performed all first-principles simulations. N.Mo., M.G., G.P., D.C., A.Ma. and N.Ma. analysed the data. All authors contributed to the redaction of the manuscript.

Corresponding authors

Correspondence to Nicolas Mounet or Nicola Marzari.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figures 1–4, Supplementary Tables 1–6, Supplementary Structures 1–6, Supplementary References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mounet, N., Gibertini, M., Schwaller, P. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nature Nanotech 13, 246–252 (2018).

Download citation

Further reading


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research