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The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model

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Abstract

Weyl fermions are shown to exist in a Drude-Sommerfeld topological model (DSTM), that features nearly free carriers in topological protected states under residual collisions. The Weyl fermion features a weak magnetic field around it, produced by its own currents, that dresses it, and is the key to its topological stability. The Weyl fermion state results from a Schroedinger like hamiltonian for particles with spin and magnetic energy which are momentum confined to a layer [M.M. Doria, A. Perali, Europhys. Lett. 119, 21001 (2017)]. The present mechanism for the onset of Weyl fermion breaks the reflection and time symmetries around the layer and displays an energy gap. Much above this gap the spectrum becomes linear (Dirac) and then momentum and spin become orthogonal (zero helicity state, ZHS). The collision time is shown to be renormalized by the inverse of the square of the gap in the linear Dirac spectrum limit. Hence the Weyl fermions are shown to be intrinsically ballistic in this limit. The Weyl fermion own magnetic field, although very weak, cannot be discarded because it yields a non zero Chern-Simons number, which is here calculated in the Dirac limit. The electrical and the thermal conductivities of the Weyl fermions are derived in the framework of a constant relaxation time. The Lorenz number coefficient associated to the Wiedemman-Franz law acquires asymptotic value of 6.5552 times the bulk value of π2∕3.

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References

  1. P. Miro, M. Audiffred, T. Heine, Chem. Soc. Rev. 43, 6537 (2014)

    Article  Google Scholar 

  2. J. Nevalaita, P. Koskinen, Phys. Rev. B 97, 035411 (2018)

    Article  ADS  Google Scholar 

  3. I. Tamm, Phys. Z. Soviet Union 1, 733 (1932)

    Google Scholar 

  4. W. Shockley, Phys. Rev. 56, c317 (1939)

    Article  ADS  Google Scholar 

  5. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 452, 970 (2008)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  7. I. Bozovic, C. Ahn, Nat. Phys. 10, 892 (2014)

    Article  Google Scholar 

  8. T. Uchihashi, Supercond. Sci. Technol. 30, 013002 (2017)

    Article  ADS  Google Scholar 

  9. C. Brun, T. Cren, D. Roditchev, Supercond. Sci. Technol. 30, 013003 (2017)

    Article  ADS  Google Scholar 

  10. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)

    Article  ADS  Google Scholar 

  11. J. Wang, S. Deng, Z. Liu, Z. Liu, Natl. Sci. Rev. 2, 22 (2015)

    Article  Google Scholar 

  12. S.M. Young, C.L. Kane, Phys. Rev. Lett. 115, 126803 (2015)

    Article  ADS  Google Scholar 

  13. P.R. Wallace, Phys. Rev. 71, 622 (1947)

    Article  ADS  Google Scholar 

  14. R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, 1998)

  15. A.A. Abrikosov, Phys. Rev. B 58, 2788 (1998)

    Article  ADS  Google Scholar 

  16. A.A. Abrikosov, Phys. Rev. B 60, 4231 (1999)

    Article  ADS  Google Scholar 

  17. A.A. Abrikosov, Europhys. Lett. 49, 789 (2000)

    Article  ADS  Google Scholar 

  18. A.A. Abrikosov, J. Phys. A: Math. General 36, 9119 (2003)

    Article  ADS  Google Scholar 

  19. W. Zhang, R. Yu, W. Feng, Y. Yao, H. Weng, X. Dai, Z. Fang, Phys. Rev. Lett. 106, 156808 (2011)

    Article  ADS  Google Scholar 

  20. R. Xu, A. Husmann, T.F. Rosenbaum, M.-L. Saboungi, J.E. Enderby, P.B. Littlewood, Nature 390, 57 (1997)

    Article  ADS  Google Scholar 

  21. S.L. Bud’ko, P.C. Canfield, C.H. Mielke, A.H. Lacerda, Phys. Rev. B 57, 13624 (1998)

    Article  ADS  Google Scholar 

  22. B. Péter, D. Balázs, M. Roderich, Phys. Status Solidi B 248, 2627 (2011)

    Article  Google Scholar 

  23. S. Sadeddine, H. Enriquez, A. Bendounan, P. Kumar Das, I. Vobornik, A. Kara, A.J. Mayne, F. Sirotti, G. Dujardin, H. Oughaddou, Sci. Rep. 7, 44400 (2017)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  25. M. Hirata, K. Ishikawa, K. Miyagawa, M. Tamura, C. Berthier, D. Basko, A. Kobayashi, G. Matsuno, K. Kanoda, Nat. Commun. 7, 12666 (2016)

    Article  ADS  Google Scholar 

  26. G. Li, B. Yan, Z. Wang, K. Held, Phys. Rev. B 95, 035102 (2017)

    Article  ADS  Google Scholar 

  27. M.Z. Hasan, S.-Y. Xu, I. Belopolski, S.-M. Huang, Annu. Rev. Condens. Matter Phys. 8, 289 (2017)

    Article  ADS  Google Scholar 

  28. Z.T. Liu, X.Z. Xing, M.Y. Li, W. Zhou, Y. Sun, C.C. Fan, H.F. Yang, J.S. Liu, Q. Yao, W. Li, Z.X. Shi, D.W. Shen, Z. Wang, Appl. Phys. Lett. 109, 042602 (2016)

    Article  ADS  Google Scholar 

  29. K.K. Huynh, Y. Tanabe, K. Tanigaki, Phys. Rev. Lett. 106, 217004 (2011)

    Article  ADS  Google Scholar 

  30. T. Terashima, H.T. Hirose, D. Graf, Y. Ma, G. Mu, T. Hu, K. Suzuki, S. Uji, H. Ikeda, Phys. Rev. X 8, 011014 (2018)

    Google Scholar 

  31. M. Sakano, K. Okawa, M. Kanou, H. Sanjo, T. Okuda, T. Sasagawa, K. Ishizaka, Nat. Commun. 6, 8595 (2015)

    Article  ADS  Google Scholar 

  32. M. Lee, T.F. Rosenbaum, M.-L. Saboungi, H.S. Schnyders, Phys. Rev. Lett. 88, 066602 (2002)

    Article  ADS  Google Scholar 

  33. L.P. He, X.C. Hong, J.K. Dong, J. Pan, Z. Zhang, J. Zhang, S.Y. Li, Phys. Rev. Lett. 113, 246402 (2014)

    Article  ADS  Google Scholar 

  34. T. Liang, Q. Gibson, M.N. Ali, M. Liu, R.J. Cava, N.P. Ong, Nat. Mater. 14, 280 (2014)

    Article  ADS  Google Scholar 

  35. A. Narayanan, M.D. Watson, S.F. Blake, N. Bruyant, L. Drigo, Y.L. Chen, D. Prabhakaran, B. Yan, C. Felser, T. Kong, P.C. Canfeld, A.I. Coldea, Phys. Rev. Lett. 114, 117201 (2015)

    Article  ADS  Google Scholar 

  36. X.Z. Xing, C.Q. Xu, N. Zhou, B. Li, J. Zhang, Z.X. Shi, X. Xu, Appl. Phys. Lett. 109, 122403 (2016)

    Article  ADS  Google Scholar 

  37. M.M. Doria, A. Perali, Europhys. Lett. 119, 21001 (2017)

    Article  ADS  Google Scholar 

  38. T. Stauber, N.M.R. Peres, F. Guinea, A.H. Castro Neto, Phys. Rev. B 75, 115425 (2007)

    Article  ADS  Google Scholar 

  39. D. Wickramaratne, F. Zahid, R.K. Lake, J. Appl. Phys. 118, 075101 (2015)

    Article  ADS  Google Scholar 

  40. I. Jo, Y. Liu, L.N. Pfeiffer, K.W. West, K.W. Baldwin, M. Shayegan, R. Winkler, Phys. Rev. B 95, 035103 (2017)

    Article  ADS  Google Scholar 

  41. N.M.R. Peres, J.M.B. Lopes dos Santos, T. Stauber, Phys. Rev. B 76, 073412 (2007)

    Article  ADS  Google Scholar 

  42. H.L. Stormer, L.N. Pfeiffer, K.W. Baldwin, K.W. West, Phys. Rev. B 41, 1278 (1990)

    Article  ADS  Google Scholar 

  43. D.K. Efetov, P. Kim, Phys. Rev. Lett. 105, 256805 (2010)

    Article  ADS  Google Scholar 

  44. N. Ashcroft, N. Mermin, Solid State Physics (Saunders College, 1976)

  45. R.C.V. Coelho, M. Mendoza, M.M. Doria, H.J. Herrmann, Phys. Rev. B 96, 184307 (2017)

    Article  ADS  Google Scholar 

  46. C.H. Li, O.M.J. van’t Erve, J.T. Robinson, Y. Liu, L. Li, B.T. Jonker, Nat. Nanotechnol. 9, 218 (2014)

    Article  ADS  Google Scholar 

  47. D. Hsieh, Y. Xia, D. Qian, L. Wray, J.H. Dil, F. Meier, J. Osterwalder, L. Patthey, J.G. Checkelsky, N.P. Ong, A.V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y.S. Hor, R.J. Cava, M.Z. Hasan, Nature 460, 1101 (2009)

    Article  ADS  Google Scholar 

  48. B. Dup’e, M. Hoffmann, C. Paillard, S. Heinze, Nat. Commun. 5, 4030 (2014)

    Article  ADS  Google Scholar 

  49. D. Bazeia, M. Doria, E. Rodrigues, Phys. Lett. A 380, 1947 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  50. S. Tsesses, E. Ostrovsky, K. Cohen, B. Gjonaj, N. Lindner, G. Bartal, Science 361, 993 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  51. M.M. Doria, M. Cariglia, A. Perali, Phys. Rev. B 94, 224513 (2016)

    Article  ADS  Google Scholar 

  52. S. Hoinka, P. Dyke, M.G. Lingham, J.J. Kinnunen, G.M. Bruun, C.J. Vale, Nat. Phys. 13, 943 (2017)

    Article  Google Scholar 

  53. A.A. Vargas-Paredes, M.M. Doria, J.A.H. Neto, J. Math. Phys. 54, 013101 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  54. M.M. Doria, A.A. Vargas-Paredes, M. Cariglia, Supercond. Sci. Technol. 27, 124008 (2014)

    Article  ADS  Google Scholar 

  55. A.A. Vargas-Paredes, M. Cariglia, M.M. Doria, J. Magn. Magn. Mater. 376, 40 (2015)

    Article  ADS  Google Scholar 

  56. E.I.B. Rodrigues, A.A. Vargas-Paredes, M.M. Doria, M. Cariglia, J. Supercond. Novel Magn. 30, 1327 (2017)

    Article  Google Scholar 

  57. E.I.B. Rodrigues, M.M. Doria, A.A. Vargas-Paredes, M. Cariglia, A. Perali, J. Supercond. Novel Magn. 30, 145 (2017)

    Article  Google Scholar 

  58. M. Cariglia, A.A. Vargas-Paredes, M.M. Doria, Europhys. Lett. 105, 31002 (2014)

    Article  ADS  Google Scholar 

  59. K.C. Fong, E.E. Wollman, H. Ravi, W. Chen, A.A. Clerk, M.D. Shaw, H.G. Leduc, K.C. Schwab, Phys. Rev. X 3, 041008 (2013)

    Google Scholar 

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Authors and Affiliations

  1. Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, Brazil

    Mauro M. Doria

  2. Instituto de Física “Gleg Wataghin”, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo, Brazil

    Mauro M. Doria

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Correspondence to Mauro M. Doria.

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Doria, M.M. The linear Dirac spectrum and the Weyl states in the Drude-Sommerfeld topological model. Eur. Phys. J. B 92, 64 (2019). https://doi.org/10.1140/epjb/e2019-90591-2

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  • DOI: https://doi.org/10.1140/epjb/e2019-90591-2

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