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 optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

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


  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

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

  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).

  6. 6.

    Inorganic Crystal Structure Database (ICSD); http://www.fiz-karlsruhe.com/icsd.html

  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).

  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).

  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).

  10. 10.

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

  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).

  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).

  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).

  14. 14.

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

  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).

  17. 17.

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

  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).

  19. 19.

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

  20. 20.

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

  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).

  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).

  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).

  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).

  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).

  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).

  27. 27.

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

  28. 28.

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

  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).

  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).

  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).

  32. 32.

    Togo, A. spglib; https://atztogo.github.io/spglib/

  33. 33.

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

  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).

  35. 35.

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

  36. 36.

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

  37. 37.

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

  38. 38.

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

  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).

  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).

  41. 41.

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

  42. 42.

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

  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).

  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).

  46. 46.

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

  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).

  48. 48.

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

  49. 49.

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

  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).

  51. 51.

    Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds (data download). Materials Cloud Archive (2017); https://doi.org/10.24435/materialscloud:2017.0008/v1

  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).

  53. 53.

    Hinuma, Y., Togo, A., Hayashi, H. & Tanaka, I. Choice of basis vectors for conventional unit cells revisited. Preprint at http://arXiv.org/abs/1506.01455 (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).

  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).

  56. 56.

    Standard solid-state pseudopotentials (SSSP); http://www.materialscloud.org/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).

  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 http://arXiv.org/abs/1404.3015 (2014).

  59. 59.

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

  60. 60.

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

  61. 61.

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

  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).

  63. 63.

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

  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).

  65. 65.

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

  66. 66.

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

  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).

  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).

  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).

  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).

  71. 71.

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

  72. 72.

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

  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).

  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).

  75. 75.

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

  76. 76.

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

  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).

  78. 78.

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

  79. 79.

    Pseudo-Dojo library; http://www.pseudo-dojo.org/

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 (https://github.com/abinit/pseudo_dojo).

Author information


  1. Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    • Nicolas Mounet
    • , Marco Gibertini
    • , Philippe Schwaller
    • , Davide Campi
    • , Andrius Merkys
    • , Antimo Marrazzo
    • , Thibault Sohier
    • , Ivano Eligio Castelli
    • , Andrea Cepellotti
    • , Giovanni Pizzi
    •  & Nicola Marzari
  2. Vilnius University Institute of Biotechnology, Vilnius, Lithuania

    • Andrius Merkys


  1. Search for Nicolas Mounet in:

  2. Search for Marco Gibertini in:

  3. Search for Philippe Schwaller in:

  4. Search for Davide Campi in:

  5. Search for Andrius Merkys in:

  6. Search for Antimo Marrazzo in:

  7. Search for Thibault Sohier in:

  8. Search for Ivano Eligio Castelli in:

  9. Search for Andrea Cepellotti in:

  10. Search for Giovanni Pizzi in:

  11. Search for Nicola Marzari in:


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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Nicolas Mounet or Nicola Marzari.

Supplementary information

  1. Supplementary Information

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

About this article

Publication history






Further reading