1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 9, 2018
  5. Article

Annual Review of Condensed Matter Physics

Volume 9, 2018

Maxwell Lattices and Topological Mechanics

Abstract

This is a review on the emergent field of topological mechanics, where concepts from electronic topological states of matter are applied to mechanics. We focus on the subcategory of topological mechanics of Maxwell lattices, which are mechanical frames having average coordination numbers equal to twice their spatial dimension, 〈〉=2, leaving them on the verge of mechanical instability. We start by introducing examples of Maxwell lattices, describing their elastic properties, and discussing their general classification. We then focus on topological phonon modes of these lattices by reviewing recent theoretical progress on one-dimensional chains and two-dimensional lattices that exhibit topologically protected zero-frequency phonon modes on edges and domain walls. We also propose metamaterials based on Maxwell lattices with unusual topologically protected mechanical properties.

Keyword(s): continuum elasticity, mechanical metamaterials, mechanics of frames, surface mode, zero modes
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-033117-054235
2018-03-10
2024-04-20
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/9/1/annurev-conmatphys-033117-054235.html?itemId=/content/journals/10.1146/annurev-conmatphys-033117-054235&mimeType=html&fmt=ahah

Literature Cited

  1. Wen XG. 1.  1995. Adv. Phys. 44:405–73
  2. Hasan MZ, Kane CL. 2.  2010. Rev. Mod. Phys. 82:3045–67
  3. Qi XL, Zhang SC. 3.  2011. Rev. Mod. Phys. 83:1057–110
  4. Su WP, Schrieffer JR, Heeger AJ. 4.  1979. Phys. Rev. Lett. 42:1698–701
  5. Lu L, Joannopoulos JD, Soljačić M. 5.  2014. Nat. Photonics 8:821–29
  6. Prodan E, Prodan C. 6.  2009. Phys. Rev. Lett. 103:248101
  7. Kane CL, Lubensky TC. 7.  2014. Nat. Phys. 10:39–45
  8. Lubensky TC, Kane C, Mao X, Souslov A, Sun K. 8.  2015. Rep. Prog. Phys. 78:073901
  9. Wang P, Lu L, Bertoldi K. 9.  2015. Phys. Rev. Lett. 115:104302
  10. Nash LM, Kleckner D, Read A, Vitelli V, Turner AM, Irvine WT. 10.  2015. PNAS 112:14495–500
  11. Süsstrunk R, Huber SD. 11.  2015. Science 349:47–50
  12. Mousavi SH, Khanikaev AB, Wang Z. 12.  2015. Nat. Commun. 6:8682
  13. Yang Z, Gao F, Shi X, Lin X, Gao Z. 13.  et al. 2015. Phys. Rev. Lett. 114:114301
  14. Peano V, Brendel C, Schmidt M, Marquardt F. 14.  2015. Phys. Rev. X 5:031011
  15. Strohm C, Rikken G, Wyder P. 15.  2005. Phys. Rev. Lett. 95:155901
  16. Sheng L, Sheng D, Ting C. 16.  2006. Phys. Rev. Lett. 96:155901
  17. Pal RK, Schaeffer M, Ruzzene M. 17.  2016. J. Appl. Phys. 119:084305
  18. He C, Ni X, Ge H, Sun XC, Chen YB. 18.  et al. 2016. Nat. Phys. 12:1124–29
  19. Süsstrunk R, Huber SD. 19.  2016. PNAS 113:E4767–75
  20. Xiao M, Chen WJ, He WY, Chan C. 20.  2015. Nat. Phys. 11:11920–24
  21. Maxwell JC. 21.  1864. Philos. Mag. 27:294
  22. Phillips JC. 22.  1979. J. Non-Cryst. Solids 34:153–81
  23. Thorpe M. 23.  1983. J. Non-Cryst. Solids 57:355–70
  24. Phillips JC, Thorpe MF. 24.  1985. Solid State Commun 53:699–702
  25. He H, Thorpe MF. 25.  1985. Phys. Rev. Lett. 54:2107–10
  26. Boolchand P, Lucovsky G, Phillips J, Thorpe M. 26.  2005. Philos. Mag. 85:3823–38
  27. Feng S, Sen PN. 27.  1984. Phys. Rev. Lett. 52:216–19
  28. Jacobs DJ, Thorpe MF. 28.  1995. Phys. Rev. Lett. 75:4051–54
  29. Jacobs DJ, Thorpe MF. 29.  1996. Phys. Rev. E 53:3682–93
  30. Ellenbroek WG, Mao X. 30.  2011. Europhys. Lett. 96:554002
  31. Zhang L, Rocklin DZ, Chen BG, Mao X. 31.  2015. Phys. Rev. E 91:032124
  32. Souslov A, Liu AJ, Lubensky TC. 32.  2009. Phys. Rev. Lett. 103:205503
  33. Mao X, Xu N, Lubensky TC. 33.  2010. Phys. Rev. Lett. 104:085504
  34. Mao X, Lubensky TC. 34.  2011. Phys. Rev. E 83:011111
  35. Broedersz CP, Mao X, Lubensky TC, MacKintosh FC. 35.  2011. Nat. Phys. 7:983–88
  36. Mao X, Stenull O, Lubensky TC. 36.  2013. Phys. Rev. E 87:042602
  37. Mao X, Stenull O, Lubensky TC. 37.  2013. Phys. Rev. E 87:042601
  38. Feng J, Levine H, Mao X, Sander LM. 38.  2015. Phys. Rev. E 91:042710
  39. Feng J, Levine H, Mao X, Sander LM. 39.  2016. Soft Matter 12:1419–24
  40. Mao X, Souslov A, Mendoza CI, Lubensky TC. 40.  2015. Nat. Commun. 6:5968
  41. Zhang L, Mao X. 41.  2016. Phys. Rev. E 93:022110
  42. Liarte DB, Stenull O, Mao X, Lubensky T. 42.  2016. J. Phys.: Condens. Matter 28:165402
  43. Calladine C. 43.  1978. Int. J. Solids Struct. 14:161–72
  44. Pellegrino S, Calladine CR. 44.  1986. Int. J. Solids Struct. 22:409–28
  45. Guest SD, Hutchinson JW. 45.  2003. J. Mech. Phys. Solids 51:383–91
  46. Rocklin DZ, Zhou S, Sun K, Mao X. 46.  2017. Nat. Commun. 8:14201
  47. Stenull O, Lubensky TC. 47.  2014. Phys. Rev. Lett. 113:158301
  48. Rocklin DZ, Chen BGG, Falk M, Vitelli V, Lubensky TC. 48.  2016. Phys. Rev. Lett. 116:135503
  49. Landau LD, Lifshitz EM. 49.  1986. Theory of Elasticity New York: Pergamon
  50. Sun K, Souslov A, Mao X, Lubensky TC. 50.  2012. PNAS 109:12369–74
  51. Berry M. 51.  1984. Proc. R. Soc. A. 44:45–57
  52. Chen BG, Upadhyaya N, Vitelli V. 52.  2014. PNAS 111:13004–9
  53. Wan XG, Turner AM, Vishwanath A, Savrasov SY. 53.  2011. Phys. Rev. B 83:205101
  54. Burkov AA, Balents L. 54.  2011. Phys. Rev. Lett. 107:127205
  55. Burkov AA, Hook MD, Balents L. 55.  2011. Phys. Rev. B 84:235126
  56. Liu JP, Vanderbilt D. 56.  2014. Phys. Rev. B 90:155316
  57. Xu SY, Belopolski I, Alidoust N, Neupane M, Bian G. 57.  et al. 2015. Science 349:6248613–17
  58. Stenull O, Kane CL, Lubensky TC. 58.  2016. Phys. Rev. Lett. 117:068001
  59. Volovik G. 59.  2007. Lect. Notes Phys. 718:31–73
  60. Kim Y, Wieder BJ, Kane CL, Rappe AM. 60.  2015. Phys. Rev. Lett. 115:036806
  61. Yu R, Weng HM, Fang Z, Dai X, Hu X. 61.  2015. Phys. Rev. Lett. 115:036807
  62. Lu L, Fu L, Joannopoulos JD, Soljaić M. 62.  2013. Nat. Photonics 7:294–99
  63. Sussman D, Stenull O, Lubensky T. 63.  2016. Soft Matter 12:6079–87
  64. Paulose J, Meeussen AS, Vitelli V. 64.  2015. PNAS 112:7639–44
  65. Paulose J, Chen BGG, Vitelli V. 65.  2015. Nat. Phys. 11:153–56
  66. Rocklin DZ. 66.  2017. New J. Phys. 19:065004
  67. Chen BG, Liu B, Evans AA, Paulose J, Cohen I. 67.  et al. 2016. Phys. Rev. Lett. 116:135501
  68. Lawler MJ. 68.  2016. Phys. Rev. B 94:165101
  69. Roychowdhury K, Rocklin DZ, Lawler MJ. 69.  2017. arXiv1705.00015
  70. Meeussen AS, Paulose J, Vitelli V. 70.  2016. Phys. Rev. X 6:041029
  71. Socolar JES, Lubensky TC, Kane CL. 71.  2017. New J. Phys. 19:025003
  72. Kitaev A. 72.  2006. Ann. Phys. 321:2–111
  73. Wu GX, Cho Y, Choi IS, Ge DT, Li J. 73.  et al. 2015. Adv. Mater. 27:2747–52
/content/journals/10.1146/annurev-conmatphys-033117-054235
Loading
Maxwell Lattices and Topological Mechanics
Annual Review of Condensed Matter Physics 9, 413 (2018); https://doi.org/10.1146/annurev-conmatphys-033117-054235
/content/journals/10.1146/annurev-conmatphys-033117-054235
/content/journals/10.1146/annurev-conmatphys-033117-054235
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error