Skip to main content

Advertisement

SpringerLink
Log in

A topological twist on materials science

  • Technical Feature
  • Published:
MRS Bulletin Aims and scope Submit manuscript

Abstract

The primary objective of this article is twofold: to address the key concept of topology that impacts materials science in a major way and to convey the excitement to the materials community of recent significant advances in our understanding of the important topological notions in a wide class of materials with potential technological applications. A paradigm of topology/geometry → property → functionality is emerging that goes beyond the traditional microscopic structure → property → functionality relationship. The new approach delineates the active roles of topology and geometry in design, fabrication, characterization, and predictive modeling of novel materials properties and multifunctionalities. After introducing the essentials of topology and geometry, we elucidate these concepts through a gamut of nanocarbon allotropes of de novo carbons, hierarchical self-assembled soft- and biomaterials, supramolecular assemblies, and nanoporous materials. Applications of these topological materials range from sensing, energy storage/conversion, and catalysis to nanomedicine.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6

Similar content being viewed by others

References

  1. M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics (Taylor & Francis, Boca Raton, FL, 1990).

  2. J.R. Munkres, Topology, 2nd ed. (Pearson, London, 2000).

  3. G.K. Francis, A Topological Picturebook (Springer, NY, 2006).

  4. M. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

    Google Scholar 

  5. D. Massiot, R.J. Messinger, S. Cadars, M. Deschamps, V. Montouillout, N. Pellerin, E. Veron, M. Allix, P. Florian, F. Fayon, Acc. Chem. Res. 46, 1975 (2013).

    Google Scholar 

  6. X. Zou, H. Ren, G. Zhu, Chem. Commun. 49, 3911 (2013).

    Google Scholar 

  7. A.G. Evans, J.W. Hutchinson, N.A. Fleck, M.F. Ashby, H.N.G. Wadley, Prog. Mater. Sci. 46, 309 (2001).

    Google Scholar 

  8. S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, P. Boni, Science 323, 915 (2009).

    Google Scholar 

  9. S. Gupta, A. Saxena, J. Raman Spectrosc. 39, 1127 (2009).

    Google Scholar 

  10. S. Gupta, A. Saxena, J. Appl. Phys. 109, 074316 (2011).

    Google Scholar 

  11. S.H. Yook, Z.N. Oltvai, A.L. Barabasi, Proteomics 4, 928 (2004).

    Google Scholar 

  12. H. Yang, N. Coombs, G.A. Ozin, Nature 386, 692 (1997).

    Google Scholar 

  13. D. Zhao, D.J. Timmons, D. Yuan, H.-C. Zhou, Acc. Chem. Res. 44, 123 (2011).

    Google Scholar 

  14. N.J. Turro, M. Garcia-Garibay, in Photochemistry in Organized and Constrained Media, V. Ramamurthy, Ed. (VCH Publishers, New York, 1991), pp. 1–21.

  15. S.T. Hyde, G.E. Schröder-Turk, Interface Focus 2, 529 (2012).

    Google Scholar 

  16. http://www.topos.samsu.ru.

  17. http://epinet.anu.edu.au/reference.

  18. B. Yan, S.-C. Zhang, Rep. Prog. Phys. 75, 096501 (2012).

    Google Scholar 

  19. J. Cayssol, Condens. Matter (2013), available at http://arxiv.org/abs/1310.0792.

  20. S. Gupta, A. Saxena, J. Appl. Phys. 112, 114316 (2012).

    Google Scholar 

  21. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004).

    Google Scholar 

  22. H. Kroto, J.R. Heath, S.C. O’Brien, R.E. Curl, R.E. Smalley, Nature 318, 162 (1985).

    Google Scholar 

  23. A. Hirsch, M. Brettreich, Fullerenes-Chemistry and Reactions (Wiley, NY, 2004).

  24. S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya, N. Hatakenaka, Nature 417, 397 (2002).

    Google Scholar 

  25. A. Yamashiro, Y. Shimoi, K. Harigaya, K. Wakabayashi, Physica E 22, 688 (2004).

    Google Scholar 

  26. J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Matthias, A.P. Seitsonen, S. Moussa, X. Feng, K. Muellen, R. Fasel, Nature 466, 470 (2010).

    Google Scholar 

  27. S.B. Sinnott, R. Andrews, Crit. Rev. Solid State Mater. Sci. 26, 145 (2001).

    Google Scholar 

  28. A. Rubio, J. Corkill, M.L. Cohen, Phys. Rev. B 49, 5081 (1994).

    Google Scholar 

  29. Y. Oshima, A. Onga, K. Takayanagi, Phys. Rev. Lett. 91, 205503 (2003).

    Google Scholar 

  30. D. Ajami, O. Oeckler, A. Simon, R. Herges, Nature 426, 819 (2003).

    Google Scholar 

  31. N. Hadjichristidis, S. Pispas, G. Floudas, Block Copolymers: Synthetic Strategies, Physical Properties, and Applications (Wiley, NY, 2003).

  32. X. Michalet, D. Bensimon, Science 269, 666 (1995).

    Google Scholar 

  33. R. Lipowsky, Encyclopedia of Applied Physics 23, 199 (1998).

    Google Scholar 

  34. V. Saranathan, C.O. Osuji, S.G. Mochrie, H. Noh, S. Narayanan, A. Sandy, E.R. Dufresne, R.O. Prum, Proc. Natl. Acad. Sci. U.S.A. 107, 11676 (2010).

    Google Scholar 

  35. E.J.W. Crossland, M. Kamperman, M. Nedelcu, C. Ducati, U. Wiesner, D.-M. Smilgies, G.E.S. Toombes, M.A. Hillmyer, S. Ludwigs, U. Steiner, H.J. Snaith Nano Lett. 9, 2807 (2009).

  36. R.B. King, J. Chem. Inf. Comput. Sci. 38, 180 (1998).

    Google Scholar 

  37. S. Hutzler, D. Weaire, The Physics of Foams (Oxford University Press, UK, 1999).

  38. S. Bohn, Eur. Phys. J. E 11, 177 (2003).

    Google Scholar 

  39. A.T. Skjeltorp, Knots and Applications to Biology, Chemistry and Physics (Springer, NY, 1996).

  40. B. Christensen, J. Nielsen, Adv. Biochem. Eng. Biotechnol. 66, 209 (2000).

    Google Scholar 

  41. L.H. Sperling, J. Polym. Sci. Macromol. Rev. 12, 141 (1977).

    Google Scholar 

  42. E.A. Lazar, J.K. Mason, R.D. MacPherson, D.J. Srolovitz, Phys. Rev. Lett. 109, 095505 (2012).

    Google Scholar 

  43. X. Huang, A. Radman, Y.M. Xie, Comput. Mater. Sci. 50, 1861 (2011).

    Google Scholar 

  44. L.W. Hobbs, C.E. Jesurum, V. Pulim, B. Berger, Philos. Mag. A 78, 679 (1998).

    Google Scholar 

  45. T. Ishøy, K. Mortensen, Langmuir 21, 1766 (2005).

    Google Scholar 

  46. R.D. Hills Jr., S.V. Kathuria, L.A. Wallace, I.J. Day, C.L. Brooks 3rd, C.R. Matthews, J. Mol. Biol. 398, 332 (2010).

    Google Scholar 

  47. W.L. Wang, O.V. Yazyev, S. Meng, E. Kaxiras, Phys. Rev. Lett. 102, 157201 (2009).

    Google Scholar 

  48. O.D. Lavrentovich, in Patterns of Symmetry Breaking, H. Arodz, J. Dziarmaga, W.H. Zurek, Eds. (Kluwer Academic, The Netherlands, 2003), pp. 161–195.

  49. E.A. Matsumoto, G.P. Alexander, R.D. Kamien, Phys. Rev. Lett. 103, 257804 (2009).

    Google Scholar 

  50. A.H. Schoen, NASA Technical Note TN D-5541 (1970).

  51. E. Sezgin, H.-J. Kaiser, T. Baumgart, P. Schwille, K. Simons, I. Levental, Nat. Protoc. 7, 1042 (2012).

    Google Scholar 

  52. J. Katsaras, T. Gutberlet, Eds., in Lipid Bilayers – Structure and Interactions (Springer-Verlag, Berlin-Heidelberg, 2001).

  53. M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, L.G. Cancádo, A. Jorio, R. Saito, Phys. Chem. Chem. Phys. 9, 1276 (2007), and references therein.

  54. M.S. Dresselhaus, P.C. Eklund, Adv. Phys. 49, 705 (2000).

    Google Scholar 

  55. J.-C. Charlier, Acc. Chem. Res. 35, 1063 (2002).

    Google Scholar 

  56. S. Iijima, T. Ichihashi, Y. Ando, Nature 356, 776 (1992).

    Google Scholar 

  57. L. Chico, V.H. Crespi, L.X. Benedict, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 76, 971 (1996).

    Google Scholar 

  58. J.K. Pachos, Contemp. Phys. 50, 375 (2009).

    Google Scholar 

  59. I. Zsoldos, J. Nanotechnol. Sci. Appl. 3, 101 (2010).

    Google Scholar 

  60. E.J. Duplock, M. Scheffler, P.J.D. Lindan, Phys. Rev. Lett. 92, 225502 (2004).

    Google Scholar 

  61. S. Gupta, R.J. Patel, J. Raman Spectrosc. 38, 188 (2007).

    Google Scholar 

  62. V.N. Mochalin, O. Shenderova, D. Ho, Y. Gogotsi, Nat. Nanotechnol. 7, 11 (2011).

    Google Scholar 

  63. X. Blasé, L.X. Benedict, E.L. Shirley, S.G. Louie, Phys. Rev. Lett. 72, 1878 (1994).

    Google Scholar 

  64. A.C. Ferrari, D.M. Basko, Nat. Nanotechnol. 8, 235 (2013).

    Google Scholar 

  65. L. Dunsch, F. Ziegs, J. Fröhner, U. Kirbach, K. Klostermann, A. Bartl, U. Feist, Electronic Properties of Fullerenes, Springer Series in Solid-State Sciences (Springer, NY, 1993), vol. 117, pp. 39–43.

  66. E. Yamamoto, M. Tansho, T. Tomiyama, H. Shinohara, H. Kawahara, Y. Kobayashi, Am. Chem. Soc. 118, 2293 (1996).

    Google Scholar 

  67. M. Takata, E. Nishibori, B. Umeda, M. Sakata, E. Yamamoto, H. Shinohara, Phys. Rev. Lett. 78, 3330 (1997).

    Google Scholar 

  68. H. Wang, M. Chhowalla, N. Sano, S. Jia, G.A.J. Amaratunga, Nanotechnology 15, 546 (2004).

    Google Scholar 

  69. K. Murata, J. Miyawaki, M. Yudasaka, S. Iijima, K. Kaneko, Carbon 43, 2826 (2005).

    Google Scholar 

  70. M. Yudasaka, T. Komatsu, T. Ichihashi, Y. Achiba, S. Iijima, J. Phys. Chem. B 107, 4681(2003).

  71. P. Tan, S. Dimovski, Y. Gogotsi, Philos. Trans. R. Soc. London, A 362, 2289 (2004).

    Google Scholar 

  72. V. Meunier, Ph. Lambin, A.A. Lucas, Phys. Rev. B 57, 14886 (1998).

    Google Scholar 

  73. J.C. Charlier, G.M. Rignanese, Phys. Rev. Lett. 86, 5970 (2001).

    Google Scholar 

  74. R.P. Vidano, D.B. Fishbach, L.J. Willis, T.M. Loehr, Solid State Commun. 39, 341 (1981).

    Google Scholar 

  75. A.V. Baranov, A.N. Bekhterev, Y.S. Bobovich, V.I. Petrov, Opt. Spectrosc. 62, 1036 (1987).

    Google Scholar 

  76. C. Thomsen, S. Reich, Phys. Rev. Lett. 85, 5214 (2000).

    Google Scholar 

  77. V. Mennella, G. Monaco, L. Colangeli, E. Bussoletti, Carbon 33, 115 (1995).

    Google Scholar 

  78. H.-J. Vogel, Lecture Notes in Physics, K.R. Mecke, D. Stoyan, Eds. (Springer-Verlag, Berlin, 2002), vol. 600, pp. 75–92.

  79. H.K. Chae, D.Y. Siberio-Perez, J. Kim, Y.-B. Go, M. Eddaoudi, A.J. Matzger, M. O’Keefe, O.M. Yaghi, Nature 427, 523 (2004).

    Google Scholar 

  80. G.-H. Lee, R.C. Cooper, S.J. An, S. Lee, A. van der Zande, N. Petrone, A.G. Hammerberg, C. Lee, B. Crawford, W. Oliver, J.W. Kysar, J. Hone, Science 340, 1073 (2013).

    Google Scholar 

  81. R. Gröger, T. Lookman, A. Saxena, Phys. Rev. B 78, 184101 (2008).

    Google Scholar 

  82. T. Dauxois, M. Peyrard, Physics of Solitons (Cambridge University Press, UK, 2006).

  83. S. Seki, X.Z. Yu, S. Ishiwata, Y. Tokura, Science 336, 198 (2012).

    Google Scholar 

  84. J. Fukuda, S. Zumer, Nat. Commun. 2, 246 (2011).

    Google Scholar 

  85. S. Zhang, I. Gilbert, C. Nisoli, G.-W. Chern, M.J. Erickson, L. O’Brien, C. Leighton, P.E. Lammert, V.H. Crespi, P. Schiffer, Nature 500, 553 (2013).

    Google Scholar 

  86. P. Milde, D. Kohler, J. Seidel, L.M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Muhlbauer, C. Pfleiderer, S. Buhrandt, C. Schutte, A. Rosch, Science 340, 1076 (2013).

    Google Scholar 

  87. M. Tasinkevych, N.M. Silvestre, M.M. Telo da Gama, New J. Phys. 14, 073030 (2012).

    Google Scholar 

  88. G.S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer-Verlag, Berlin, 2001).

  89. I. Dierking, O. Marshall, J. Wright, N. Bulleid, Phys. Rev. E 71, 061709 (2005).

    Google Scholar 

  90. S.C. Chae, Y. Horibe, D.Y. Jeong, S. Rodan, N. Lee, S.W. Cheong, Proc. Natl. Acad. Sci. U.S.A. 107, 21366 (2010).

    Google Scholar 

  91. B.G. Chen, P.J. Ackerman, G.P. Alexander, R.D. Kamien, I.I. Smalyukh, Phys. Rev. Lett. 110, 237801 (2013).

    Google Scholar 

  92. J. Fischer, M. Wegener, Laser Photonics Rev. 7, 22 (2013).

    Google Scholar 

  93. B. Senyuk, Q. Liu, S. He, R.D. Kamien, R.B. Kusner, T.C. Lubensky, I.I. Smalyukh, Nature 493, 200 (2013).

    Google Scholar 

  94. C. Quillet, S.A. Talebi, D. Rabaud, J. Kafer, S.J. Cox, F. Graner, Philos. Mag. Lett. 88, 651 (2008).

    Google Scholar 

  95. J. Benoit, A. Saxena, T. Lookman, J. Phys. A 34, 9417 (2001).

    Google Scholar 

  96. Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984).

    Google Scholar 

  97. Y. Aharonov, J. Anandan, Phys. Rev. Lett. 58, 1593 (1987).

    Google Scholar 

  98. V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, Science 336, 1003 (2012).

    Google Scholar 

  99. F.D.M. Haldane, S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).

    Google Scholar 

  100. M. Verbin, O. Zilberberg, Y.E. Kraus, Y. Lahini, Y. Silberberg, Phys. Rev. Lett. 110, 076403 (2013).

    Google Scholar 

  101. V.M. Mostepanenko, N.N. Trunov, The Casimir Effect and Its Applications (Clarendon, Oxford, 1997).

  102. S. Bellucci, A.A. Saharian, Phys. Rev. D 80, 105003 (2009).

    Google Scholar 

  103. S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, M. Sato, Y. Ando, Phys. Rev. Lett. 107, 217001 (2011).

    Google Scholar 

  104. L. Fu, Phys. Rev. Lett. 106, 106802 (2011).

    Google Scholar 

  105. E. Rossi, J.H. Bardarson, M.S. Fuhrer, S. Das Sarma, Phys. Rev. Lett. 109, 096801 (2012).

    Google Scholar 

  106. A.V. Balatsky, I. Vekhter, J.-X. Zhu, Rev. Mod. Phys. 78, 373 (2006).

    Google Scholar 

  107. T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Adv. Phys., in press (2014).

  108. W.T.M. Irvine, A.D. Hollingsworth, D.G. Grier, P.M. Chaikin, Proc. Nat. Acad. Sci. U.S.A. 110, 15544 (2013).

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by the US Department of Energy (A.S. and S.G. through LANL-CINT Gateway).

Author information

Authors and Affiliations

  1. Western Kentucky University, USA

    Sanju Gupta

  2. Los Alamos National Laboratory, NM, USA

    Avadh Saxena

Authors
  1. Sanju Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Avadh Saxena
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sanju Gupta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, S., Saxena, A. A topological twist on materials science. MRS Bulletin 39, 265–279 (2014). https://doi.org/10.1557/mrs.2014.28

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/mrs.2014.28

Search

Navigation