Skip to main content
SpringerLink
Log in

Edge physics in two-dimensional topological insulators

  • Published:
La Rivista del Nuovo Cimento Aims and scope

Summary

Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by spin-momentum locking and protected by time-reversal symmetry. We focus in particular on their transport properties in the presence of electron interactions, which can allow the onset of different backscattering mechanisms, thus leading to deviations from the quantized conductance observed in the ballistic regime. The combined presence of helicity and electron interactions creates a new paradigm of the one-dimensional world called helical Luttinger liquid, whose theoretical properties and experimental observations are reviewed.

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

Similar content being viewed by others

References

  1. Shen S.-Q., Topological insulators: Dirac equation in condensed matters, Vol. 174 (Springer) 2013.

  2. König M., Wiedmann S., Brüne C, Roth A., Buhmann H., Molenkamp L. W., Qi X.-L. and Zhang S.-C., Science, 318 (2007) 766.

    Article  ADS  Google Scholar 

  3. Hasan M. Z. and Kane C. L., Rev. Mod. Phys., 82 (2010) 3045.

    Article  ADS  Google Scholar 

  4. Tkachov G., Topological insulators: The physics of spin helicity in quantum transport (Pan Stanford Publishing) 2015.

  5. Klitzing K., Dorda G. and Pepper M., Phys. Rev. Lett., 45 (1980) 494.

    Article  ADS  Google Scholar 

  6. Laughlin R., Phys. Rev. B, 23 (1981) 5632.

    Article  ADS  Google Scholar 

  7. Halperin B., Phys. Rev. B, 25 (1982) 2185.

    Article  ADS  Google Scholar 

  8. Haldane F., Phys. Rev. Lett., 61 (1988) 2015.

    Article  ADS  MathSciNet  Google Scholar 

  9. Kane C. L. and Mele E. J., Phys. Rev. Lett., 95 (2005) 226801.

    Article  ADS  Google Scholar 

  10. Kane C. L. and Mele E. J., Phys. Rev. Lett., 95 (2005) 146802.

    Article  ADS  Google Scholar 

  11. Bernevig B. A., Hughes T. L. and Zhang S.-C., Science, 314 (2006) 1757.

    Article  ADS  Google Scholar 

  12. Liu C.-C., Feng W. and Yao Y., Phys. Rev. Lett., 107 (2011) 076802.

    Article  ADS  Google Scholar 

  13. Ezawa M., New J. Phys., 14 (2012) 033003.

    Article  ADS  Google Scholar 

  14. Ezawa M., J. Phys. Soc. Jpn., 84 (2015) 121003.

    Article  ADS  Google Scholar 

  15. Qian X., Liu J., Fu. L. and Li J., Science, 346 (2014) 1344.

    Article  ADS  Google Scholar 

  16. Nie S. M., Song Z., Weng H. and Fang Z., Phys. Rev. B, 91 (2015) 235434.

    Article  ADS  Google Scholar 

  17. Oreg Y., Sela E. and Stern A., Phys. Rev. B, 89 (2014) 115402.

    Article  ADS  Google Scholar 

  18. Sagi E. and Oreg Y., Phys. Rev. B, 90 (2014) 201102.

    Article  ADS  Google Scholar 

  19. Sagi E. and Oreg Y., Phys. Rev. B, 92 (2015) 195137.

    Article  ADS  Google Scholar 

  20. Neupert T., Chamon C., Mudry C. and Thomale R., Phys. Rev. B, 90 (2014) 205101.

    Article  ADS  Google Scholar 

  21. Zhang H., Liu C.-X., Qi X.-L., Dai X., Fang Z. and Zhang S.-C., Nat. Phys., 5 (2009) 438.

    Article  Google Scholar 

  22. Liu C.-X., Qi X.-L., Zhang H., Dai X., Fang Z. and Zhang S.-C., Phys. Rev. B, 82 (2010) 045122.

    Article  ADS  Google Scholar 

  23. Xia Y., Qian D., Hsieh D., Wray L., Pal A., Lin H., Bansil A., Grauer D., Hor Y., Cava R. and Hasan M. Z., Nat. Phys., 5 (2009) 398.

    Article  Google Scholar 

  24. Chen Y., Analytis J., Chu J.-H, Liu Z., Mo S.-K., Qi X.-L., Zhang H., Lu D., Dai X., Fang Z., Zhang S.-C., Fisher I. R., Hussain Z. and Shen Z.-X., Science, 325 (2009) 178.

    Article  ADS  Google Scholar 

  25. Hsieh D., Xia Y., Wray L., Qian D., Pal A., Dil J., Osterwalder J., Meier F., Bihlmayer G., Kane C L., Hor Y. S., Cava R. J. and Hasan M. Z., Science, 323 (2009) 919.

    Article  ADS  Google Scholar 

  26. Qi X.-L. and Zhang S.-C., Rev. Mod. Phys., 83 (2011) 1057.

    Article  ADS  Google Scholar 

  27. Kitaev A. Y., Ann. Phys., 303 (2003) 2.

    Article  ADS  Google Scholar 

  28. Beenakker C., Annu. Rev. Condens. Matter Phys., 4 (2012) 113.

    Article  ADS  Google Scholar 

  29. Alicea J., Rep. Prog. Phys., 75 (2012) 076501.

    Article  ADS  Google Scholar 

  30. Oreg Y., Refael G. and Von Oppen F., Phys. Rev. Lett., 105 (2010) 177002.

    Article  ADS  Google Scholar 

  31. Lutchyn R. M., Sau J. D. and Das-Sarma S., Phys. Rev. Lett., 105 (2010) 077001.

    Article  ADS  Google Scholar 

  32. Mourik V., Zuo K., Frolov S., Plissard S., Bakkers E. and Kouwenhoven L., Science, 336 (2012) 1003.

    Article  ADS  Google Scholar 

  33. Das A., Ronen Y., Most Y., Oreg Y., Heiblum M. and Shtrikman H., Nat. Phys., 8 (2012) 887.

    Article  Google Scholar 

  34. Fu L. and Kane C. L., Phys. Rev. Lett., 100 (2008) 096407.

    Article  ADS  Google Scholar 

  35. Fu L. and Kane C. L., Phys. Rev. B, 79 (2009) 161408.

    Article  ADS  Google Scholar 

  36. Hart S., Ren H., Wagner T., Leubner P., Mühlbauer M., Brüne C, Buhmann H., Molenkamp L. W. and Yacoby A., Nat. Phys., 10 (2014) 638.

    Article  Google Scholar 

  37. Pribiag V. S., Beukman A. J., Qu F., Cassidy M. C., Charpentier C., Wegscheider W. and Kouwenhoven L. P., Nat. Nanotech., 10 (2015) 593.

    Article  ADS  Google Scholar 

  38. Cayssol J., Dóra B., Simon F. and Moessner R., Phys. Status Solidi RRL, 7 (2013) 101.

    Article  Google Scholar 

  39. Lindner N. H., Refael G. and Galitski V., Nat. Phys., 7 (2011) 490.

    Article  Google Scholar 

  40. Torres L. F., Perez-Piskunow P., Balseiro C. and Usaj G., Phys. Rev. Lett., 113 (2014) 266801.

    Article  ADS  Google Scholar 

  41. Katan Y. T. and Podolsky D., Phys. Rev. Lett., 110 (2013) 016802.

    Article  ADS  Google Scholar 

  42. Wang J. J., Li W., Chen S., Xianlong G., Rontani M. and Polini M., Phys. Rev. B, 86 (2012) 075110.

    Article  ADS  Google Scholar 

  43. Balents L., Physics, 4 (2011) 36.

    Article  Google Scholar 

  44. Burkov A. and Balents L., Phys. Rev. Lett., 107 (2011) 127205.

    Article  ADS  Google Scholar 

  45. Turner A. M. and Vishwanath A., in Contemporary Concepts of Condensed Matter Science: Topological Insulators, chapter 11 Vol. 6 (Elsevier) 2013.

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

    Article  ADS  Google Scholar 

  47. Hsieh T. H., Lin H., Liu J., Duan W., Bansil A. and Fu L., Nat. Commun., 3 (2012) 982.

    Article  ADS  Google Scholar 

  48. Sun K., Gu Z., Katsura H. and Sarma S. D., Phys. Rev. Lett., 106 (2011) 236803.

    Article  ADS  Google Scholar 

  49. Sheng D., Gu Z.-C., Sun K. and Sheng L., Nat. Commun., 2 (2011) 389.

    Article  ADS  Google Scholar 

  50. Tsui D., Stormer H. and Gossard A., Phys. Rev. Lett., 48 (1982) 1559.

    Article  ADS  Google Scholar 

  51. Laughlin R. B., Phys. Rev. Lett., 50 (1983) 1395.

    Article  ADS  Google Scholar 

  52. Jain J., Phys. Rev. Lett., 63 (1989) 199.

    Article  ADS  Google Scholar 

  53. Wen X.-G., Phys. Rev. Lett., 66 (1991) 802.

    Article  ADS  MathSciNet  Google Scholar 

  54. Levin M. and Stern A., Phys. Rev. Lett., 103 (2009) 196803.

    Article  ADS  Google Scholar 

  55. Levin M. and Stern A., Phys. Rev. B, 86 (2012) 115131.

    Article  ADS  Google Scholar 

  56. Neupert T., Santos L., Ryu S., Chamon C. and Mudry C., Phys. Rev. B, 84 (2011) 165107.

    Article  ADS  Google Scholar 

  57. Santos L., Neupert T., Ryu S., Chamon C. and Mudry C., Phys. Rev. B, 84 (2011) 165138.

    Article  ADS  Google Scholar 

  58. Li T., Wang P., Fu H., Du L., Schreiber K.-A., Mu X., Liu X., Sullivan G., Csàthy G. A., Lin X. and Du R.-R., Phys. Rev. Lett., 115 (2015) 136804.

    Article  ADS  Google Scholar 

  59. Dirac P. A. M., Principles of Quantum Mechanics, (Clarendon Press) 1982.

  60. Nielssen H. and Ninomiya N., Phys. Lett. B, 130 (1983) 389.

    Article  ADS  MathSciNet  Google Scholar 

  61. Cardona M., Phys. Today, 63 (2010) 10.

    Article  Google Scholar 

  62. Liu C., Hughes T. L., Qi X.-L., Wang K. and Zhang S.-C., Phys. Rev. Lett., 100 (2008) 236601.

    Article  ADS  Google Scholar 

  63. Rothe D., Reinthaler R., Liu C., Molenkamp L. W., Zhang S.-C. and Hankiewicz E. M., New J. Phys., 12 (2010) 065012.

    Article  ADS  Google Scholar 

  64. Maciejko J., Qi X.-L. and Zhang S.-C., Phys. Rev. B, 82 (2010) 155310.

    Article  ADS  Google Scholar 

  65. Schmidt T. L., Rachel S., Von Oppen F. and Glazman L. I., Phys. Rev. Lett., 108 (2012) 156402.

    Article  ADS  Google Scholar 

  66. Orth C. P., Strübi G. and Schmidt T. L., Phys. Rev. B, 88 (2013) 165315.

    Article  ADS  Google Scholar 

  67. Kainaris N., Gornyi I. V., Carr S. T. and Mirlin A. D., Phys. Rev. B, 90 (2014) 075118.

    Article  ADS  Google Scholar 

  68. Rod A., Schmidt T. L. and Rachel S., Phys. Rev. B, 91 (2015) 245112.

    Article  ADS  Google Scholar 

  69. Tkachov G. and Hankiewicz E. M., Phys. Rev. Lett., 104 (2010) 166803.

    Article  ADS  Google Scholar 

  70. Roth A., Brüne C., Buhmann H., Molenkamp L. W., Maciejko J., Qi X.-L. and Zhang S.-C., Science, 325 (2009) 294.

    Article  ADS  Google Scholar 

  71. Brüne C, Roth A., Buhmann H., Hankiewicz E. M., Molenkamp L. W., Maciejko J., Qi X.-L. and Zhang S.-C., Nat. Phys., 8 (2012) 485.

    Article  Google Scholar 

  72. Knez I., Du R.-R. and Sullivan C, Phys. Rev. Lett., 107 (2011) 136603.

    Article  ADS  Google Scholar 

  73. Du L., Knez I., Sullivan G. and Du R.-R., Phys. Rev. Lett., 114 (2015) 096802.

    Article  ADS  Google Scholar 

  74. Nowack K. C., Spanton E. M., Baenninger M., König M., Kirtley J. R., Kalisky B., Ames C, Leubner P., Brüne C, Buhmann H., Molenkamp L., W., Goldhaber-Gordon D. and Moler K. A., Nat. Mater, 12 (2013) 787.

    Article  ADS  Google Scholar 

  75. Spanton E. M., Nowack K. C., Du L., Sullivan G., Du R.-R. and Moler K. A., Phys. Rev. Lett., 113 (2014) 026804.

    Article  ADS  Google Scholar 

  76. Leijnse M. and Flensberg K., Semicond. Sci. Technol., 27 (2012) 124003.

    Article  ADS  Google Scholar 

  77. Nayak C., Simon S., Stern A., Freedman M. and Das-Sarma S., Rev. Mod. Phys., 80 (2008) 1083.

    Article  ADS  Google Scholar 

  78. Knez I., Du R.-R. and Sullivan G., Phys. Rev. Lett., 109 (2012) 186603.

    Article  ADS  Google Scholar 

  79. Adroguer P., Grenier C., Carpentier D., Cayssol J., Degiovanni P. and Orignac E., Phys. Rev. B, 82 (2010) 081303.

    Article  ADS  Google Scholar 

  80. Tomonaga S. I., Prog. Theor. Phys., 5 (1950) 544.

    Article  ADS  Google Scholar 

  81. Luttinger J., J. Math. Phys., 4 (1963) 1154.

    Article  ADS  MathSciNet  Google Scholar 

  82. Giamarchi T., Quantum Physics in One Dimension, International Series of Monographs on Physics (Clarendon Press) 2003.

  83. Haldane F., J. Phys. C, 14 (1981) 2585.

    Article  ADS  Google Scholar 

  84. Deshpande V. V. and Bockrath M., Nat. Phys., 4 (2008) 314.

    Article  Google Scholar 

  85. Auslaender O. M., Steinberg H., Yacoby A., Tserkovnyak Y., Halperin B. I., Baldwin K. W., Pfeiffer L. N. and West K. W., Science, 308 (2005) 88.

    Article  ADS  Google Scholar 

  86. Lorenz T., Hofmann M., Grüninger M., Freimuth A., Uhrig G., Dumm M. and Dressel M., Nature, 418 (2002) 614.

    Article  ADS  Google Scholar 

  87. Bockrath M., Cobden D. H., Lu J., Rinzler A. G., Smalley R. E., Balents L. and McEuen P. L., Nature, 397 (1999) 598.

    Article  ADS  Google Scholar 

  88. Safi I. and Schulz H., Phys. Rev. B, 52 (1995) R17040.

    Article  ADS  Google Scholar 

  89. Maslov D. L. and Stone M., Phys. Rev. B, 52 (1995) R5539.

    Article  ADS  Google Scholar 

  90. Steinberg H., Barak G., Yacoby A., Pfeiffer L. N., West K. W., Halperin B. I. and Le Hur K., Nat. Phys., 4 (2007) 116.

    Article  Google Scholar 

  91. Kamata H., Kumada N., Hashisaka M., Muraki K. and Fujisawa T., Nat. Nanotechnol., 9 (2014) 177.

    Article  ADS  Google Scholar 

  92. Chang A., Rev. Mod. Phys., 75 (2003) 1449.

    Article  ADS  Google Scholar 

  93. Wu C., Bernevig B. A. and Zhang S.-C., Phys. Rev. Lett., 96 (2006) 106401.

    Article  ADS  Google Scholar 

  94. Kane C. L. and Fisher M. P., Phys. Rev. B, 46 (1992) 15233.

    Article  ADS  Google Scholar 

  95. Zhang F. and Kane C. L., Phys. Rev. Lett., 113 (2014) 036401.

    Article  ADS  Google Scholar 

  96. Orth C. P., Tiwari R. P., Meng T. and Schmidt T. L., Phys. Rev. B, 91 (2015) 081406.

    Article  ADS  Google Scholar 

  97. Ziani N. T., Crépin F. and Trauzettel B., Phys. Rev. Lett., 115 (2015) 206402.

    Article  ADS  Google Scholar 

  98. Xu C. and Moore J. E., Phys. Rev. B, 73 (2006) 045322.

    Article  ADS  Google Scholar 

  99. Santos R. A. and Gutman D., Phys. Rev. B, 92 (2015) 075135.

    Article  ADS  Google Scholar 

  100. Crépin F., Budich J. C., Dolcini F., Recher P. and Trauzettel B., Phys. Rev. B, 86 (2012) 121106.

    Article  ADS  Google Scholar 

  101. Ström A., Johannesson H. and Japaridze G. I., Phys. Rev. Lett., 104 (2010) 256804.

    Article  ADS  Google Scholar 

  102. Lezmy N., Oreg Y. and Berkooz M., Phys. Rev. B, 85 (2012) 235304.

    Article  ADS  Google Scholar 

  103. Geissler F., Crépin F. and Trauzettel B., Phys. Rev. B, 89 (2014) 235136.

    Article  ADS  Google Scholar 

  104. Budich J. C., Dolcini F., Recher P. and Trauzettel B., Phys. Rev. Lett., 108 (2012) 086602.

    Article  ADS  Google Scholar 

  105. Maciejko J., Liu C., Oreg Y., Qi X.-L., Wu C. and Zhang S.-C., Phys. Rev. Lett.102 (2009) 256803.

    Article  ADS  Google Scholar 

  106. Tanaka Y., Furusaki A. and Matveev K., Phys. Rev. Lett., 106 (2011) 236402.

    Article  ADS  Google Scholar 

  107. Väyrynen J. I., Goldstein M. and Glazman L. I., Phys. Rev. Lett., 110 (2013) 216402.

    Article  ADS  Google Scholar 

  108. Väyrynen J. I., Goldstein M., Gefen Y. and Glazman L. I., Phys. Rev. B, 90 (2014) 115309.

    Article  ADS  Google Scholar 

  109. Grabecki G., Wróbel J., Czapkiewicz M., Gierałtowska S., Guziewicz E., Zholudev M., Gavrilenko V., Mikhailov N. N., Dvoretski S. A., Teppe F., Knap W. and Dietl T., Phys. Rev. B, 88 (2013) 165309.

    Article  ADS  Google Scholar 

  110. Gusev G., Kvon Z., Olshanetsky E., Levin A., Krupko Y., Portal J., Mikhailov N. and Dvoretsky S., Phys. Rev. B, 89 (2014) 125305.

    Article  ADS  Google Scholar 

  111. Tikhonov E. S., Shovkun D. V., Khrapai V. S., Kvon Z. D., Mikhailov N. N. and Dvoretsky S. A., JETP Lett., 101 (2015) 708.

    Article  ADS  Google Scholar 

  112. Pikulin D. and Hyart T., Phys. Rev. Lett., 112 (2014) 176403.

    Article  ADS  Google Scholar 

  113. Zhou B., Lu H.-Z., Chu R.-L., Shen S.-Q. and Niu Q., Phys. Rev. Lett., 101 (2008) 246807.

    Article  ADS  Google Scholar 

  114. Zhang L., Cheng F., Zhai F. and Chang K., Phys. Rev. B, 83 (2011) 081402.

    Article  ADS  Google Scholar 

  115. Chamon C., Freed D., Kivelson S., Sondhi S. and Wen X., Phys. Rev. B, 55 (1997) 2331.

    Article  ADS  Google Scholar 

  116. De-Picciotto R., Reznikov M., Heiblum M., Umansky V., Bunin G. and Mahalu D., Nature, 389 (1997) 162.

    Article  ADS  Google Scholar 

  117. Saminadayar L., Glattli D. C., Jin Y. and Etienne B., Phys. Rev. Lett., 79 (1997) 2526.

    Article  ADS  Google Scholar 

  118. Radu I. P., Miller J., Marcus C., Kastner M., Pfeiffer L. and West K., Science, 320 (2008) 899.

    Article  ADS  Google Scholar 

  119. Carrega M., Ferraro D., Braggio A., Magnoli N. and Sassetti M., Phys. Rev. Lett., 107 (2011) 146404.

    Article  ADS  Google Scholar 

  120. Inhofer A. and Bercioux D., Phys. Rev. B, 88 (2013) 235412.

    Article  ADS  Google Scholar 

  121. Büttiker M., Phys. Rev. B, 46 (1992) 12485.

    Article  ADS  Google Scholar 

  122. Moskalets M. V., Scattering matrix approach to non-stationary quantum transport (World Scientific) 2012.

  123. Sternativo P. and Dolcini F., Phys. Rev. B, 89 (2014) 035415.

    Article  ADS  Google Scholar 

  124. Liu C.-X., Budich J. C., Recher P. and Trauzettel B., Phys. Rev. B, 83 (2011) 035407.

    Article  ADS  Google Scholar 

  125. Dolcetto G., Barbarino S., Ferraro D., Magnoli N. and Sassetti M., Phys. Rev. B, 85 (2012) 195138.

    Article  ADS  Google Scholar 

  126. Väyrynen J. and Ojanen T., Phys. Rev. Lett., 106 (2011) 076803.

    Article  ADS  Google Scholar 

  127. Ström A. and Johannesson H., Phys. Rev. Lett., 102 (2009) 096806.

    Article  ADS  Google Scholar 

  128. Lee Y.-W., Lee Y.-L. and Chung C.-H., Phys. Rev. B, 86 (2012) 235121.

    Article  ADS  Google Scholar 

  129. Teo J. C. and Kane C. L., Phys. Rev. B, 79 (2009) 235321.

    Article  ADS  Google Scholar 

  130. Hou C.-Y., Kim E.-A. and Chamon C., Phys. Rev. Lett., 102 (2009) 076602.

    Article  ADS  Google Scholar 

  131. Schmidt T. L., Phys. Rev. Lett., 107 (2011) 096602.

    Article  ADS  Google Scholar 

  132. Chou Y.-Z., Levchenko A., Foster M. S., Phys. Rev. Lett., 115 (2015) 186404.

    Article  ADS  Google Scholar 

  133. Souquet J.-R. and Simon P., Phys. Rev. B, 86 (2012) 161410.

    Article  ADS  Google Scholar 

  134. Basset J., Bouchiat H. and Deblock R., Phys. Rev. Lett., 105 (2010) 166801.

    Article  ADS  Google Scholar 

  135. Chamon C., Freed D. and Wen X., Phys. Rev. B, 51 (1995) 2363.

    Article  ADS  Google Scholar 

  136. Krueckl V. and Richter K., Phys. Rev. Lett., 107 (2011) 086803.

    Article  ADS  Google Scholar 

  137. Dolcetto G., Cavaliere F., Ferraro D. and Sassetti M., Phys. Rev. B, 87 (2013) 085425.

    Article  ADS  Google Scholar 

  138. Romeo F. and Citro R., Phys. Rev. B, 90 (2014) 155408.

    Article  ADS  Google Scholar 

  139. Dolcini F., Phys. Rev. B, 92 (2015) 155421.

    Article  ADS  Google Scholar 

  140. Datta S. and Das B., Appl. Phys. Lett., 56 (1990) 665.

    Article  ADS  Google Scholar 

  141. Grenier C., Hervé R., Fève G. and Degiovanni P., Mod. Phys. Lett. B, 25 (2011) 1053.

    Article  ADS  Google Scholar 

  142. Bocquillon E., Freulon V., Berroir J.-M., Degiovanni P., Plac¸ais B., Cavanna A., Jin Y. and Fève G., Science, 339 (2013) 1054.

    Article  ADS  Google Scholar 

  143. Bocquillon E., Freulon V., Parmentier F. D., Berroir J.-M., Plac¸ais B., Wahl C, Rech J., Jonckheere T., Martin T., Grenier C, Ferraro D., Degiovanni P. and Fève G., Ann. Phys. (Berlin), 526 (2014) 1.

    Article  ADS  Google Scholar 

  144. Wahl C., Rech J., Jonckheere T. and Martin T., Phys. Rev. Lett., 112 (2014) 046802.

    Article  ADS  Google Scholar 

  145. Jullien T., Roulleau P., Roche B., Cavanna A., Jin Y. and Glattli D. C., Nature, 514 (2014) 603.

    Article  ADS  Google Scholar 

  146. Chu R.-L., Li J., Jain J. and Shen S.-Q., Phys. Rev. B, 80 (2009) 081102.

    Article  ADS  Google Scholar 

  147. Dolcini F., Phys. Rev. B, 83 (2011) 165304.

    Article  ADS  Google Scholar 

  148. Citro R., Romeo F. and Andrei N., Phys. Rev. B, 84 (2011) 161301.

    Article  ADS  Google Scholar 

  149. Romeo F., Citro R., Ferraro D. and Sassetti M., Phys. Rev. B, 86 (2012) 165418.

    Article  ADS  Google Scholar 

  150. Ferraro D., Dolcetto G., Citro R., Romeo F. and Sassetti M., Phys. Rev. B, 87 (2013) 245419.

    Article  ADS  Google Scholar 

  151. Calzona A., Carrega M., Dolcetto G. and Sassetti M., Phys. Rev. B, 92 (2015) 195414.

    Article  ADS  Google Scholar 

  152. Calzona A., Carrega M., Dolcetto G. and Sassetti M., Physica E, 74 (2015) 630.

    Article  ADS  Google Scholar 

  153. Fève G., Mahe A., Berroir J.-M., Kontos T., Plac¸ais B., Glattli D., Cavanna A., Etienne B. and Jin Y., Science, 316 (2007) 1169.

    Article  ADS  Google Scholar 

  154. Mahé A., Parmentier F., Bocquillon E., Berroir J.-M., Glattli D., Kontos T., Plac¸ais B., Fève G., Cavanna A. and Jin Y., Phys. Rev. B, 82 (2010) 201309.

    Article  ADS  Google Scholar 

  155. Büttiker M., Thomas H. and Préetre A., Phys. Lett. A, 180 (1993) 364.

    Article  ADS  Google Scholar 

  156. Dubois J., Jullien T., Grenier C., Degiovanni P., Roulleau P. and Glattli D., Phys. Rev. B, 88 (2013) 085301.

    Article  ADS  Google Scholar 

  157. Dubois J., Jullien T., Portier F., Roche P., Cavanna A., Jin Y., Wegscheider W., Roulleau P. and Glattli D., Nature, 502 (2013) 659.

    Article  ADS  Google Scholar 

  158. Hofer P. P. and Büttiker M., Phys. Rev. B, 88 (2013) 241308.

    Article  ADS  Google Scholar 

  159. Ferraro D., Wahl C., Rech J., Jonckheere T. and Martin T., Phys. Rev. B, 89 (2014) 075407.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SPIN-CNR, Via Dodecaneso 33, 16146, Genova, Italy

    G. Dolcetto & M. Sassetti

  2. Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146, Genova, Italy

    M. Sassetti

  3. Physics and Materials Science Research Unit, University of Luxembourg, L-1511, Luxembourg, Luxembourg

    G. Dolcetto & T. L. Schmidt

Authors
  1. G. Dolcetto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Sassetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. L. Schmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Dolcetto.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dolcetto, G., Sassetti, M. & Schmidt, T.L. Edge physics in two-dimensional topological insulators. Riv. Nuovo Cim. 39, 113–154 (2016). https://doi.org/10.1393/ncr/i2016-10121-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1393/ncr/i2016-10121-7

Search

Navigation