Linear response theory for shear modulus C66 and Raman quadrupole susceptibility: Evidence for nematic orbital fluctuations in Fe-based superconductors

Physical Review Letters

Volumn 113, Issue 4, 2014, Pages

  Kontani, Hiroshi ^a   Yamakawa, Youichi ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ELASTIC MODULI; SHEAR STRAIN;

FE-BASED SUPERCONDUCTORS; LINEAR-RESPONSE THEORY; NEMATIC ORDER; ORBITAL FLUCTUATIONS; ORBITAL ORDER; QUADRUPOLES; VERTEX CORRECTION;

SUPERCONDUCTING MATERIALS;

EID: 84905001109     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.113.047001     Document Type: Article

References (47)

1. F.L. Ning, K. Ahilan, T. Imai, A.S. Sefat, M.A. McGuire, B.C. Sales, D. Mandrus, P. Cheng, B. Shen, and H.-H Wen, Phys. Rev. Lett. 104, 037001 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.037001
2. R.M. Fernandes, L.H. VanBebber, S. Bhattacharya, P. Chandra, V. Keppens, D. Mandrus, M.A. McGuire, B.C. Sales, A.S. Sefat, and J. Schmalian, Phys. Rev. Lett. 105, 157003 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.157003
3. M. Yoshizawa, D. Kimura, T. Chiba, S. Simayi, Y. Nakanishi, K. Kihou, C.-H. Lee, A. Iyo, H. Eisaki, M. Nakajima, and S. Uchida, J. Phys. Soc. Jpn. 81, 024604 (2012). JUPSAU 0031-9015 10.1143/JPSJ.81.024604
4. S. Simayi, K. Sakano, H. Takezawa, M. Nakamura, Y. Nakanishi, K. Kihou, M. Nakajima, C.-H. Lee, A. Iyo, H. Eisaki, S. Uchida, and M. Yoshizawa, J. Phys. Soc. Jpn. 82, 114604 (2013). JUPSAU 0031-9015 10.7566/JPSJ.82.114604
5. A.E. Böhmer, P. Burger, F. Hardy, T. Wolf, P. Schweiss, R. Fromknecht, M. Reinecker, W. Schranz, and C. Meingast, Phys. Rev. Lett. 112, 047001 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.047001
6. T. Goto, R. Kurihara, K. Araki, K. Mitsumoto, M. Akatsu, Y. Nemoto, S. Tatematsu, and M. Sato, J. Phys. Soc. Jpn. 80, 073702 (2011). JUPSAU 0031-9015 10.1143/JPSJ.80.073702
7. H.-H. Kuo, J.G. Analytis, J.-H. Chu, R.M. Fernandes, J. Schmalian, and I.R. Fisher, Phys. Rev. B 86, 134507 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.134507
8. M. Yoshizawa (private communication).
9. R. Zhou, Z. Li, J. Yang, D.L. Sun, C.T. Lin, and G. Zheng, Nat. Commun. 4, 2265 (2013). NCAOBW 2041-1723 10.1038/ncomms3265
10. F. Krüger, S. Kumar, J. Zaanen, and J. van den Brink, Phys. Rev. B 79, 054504 (2009). PRBMDO 1098-0121 10.1103/PhysRevB.79.054504
11. W. Lv, J. Wu, and P. Phillips, Phys. Rev. B 80, 224506 (2009); PRBMDO 1098-0121 10.1103/PhysRevB.80.224506
12. W. Lv, F. Krüger, and P. Phillips, Phys. Rev. B 82, 045125 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.045125
13. C.-C. Lee, W.-G. Yin, and W. Ku, Phys. Rev. Lett. 103, 267001 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.267001
14. S. Onari and H. Kontani, Phys. Rev. Lett. 109, 137001 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.137001
15. H. Kontani, Y. Inoue, T. Saito, Y. Yamakawa, and S. Onari, Solid State Commun. 152, 718 (2012). SSCOA4 0038-1098 10.1016/j.ssc.2012.01.012
16. R.M. Fernandes and A.J. Millis, Phys. Rev. Lett. 111, 127001 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.127001
17. Y. Ohno, M. Tsuchiizu, S. Onari, and H. Kontani, J. Phys. Soc. Jpn. 82, 013707 (2013). JUPSAU 0031-9015 10.7566/JPSJ.82.013707
18. M. Tsuchiizu, Y. Ohno, S. Onari, and H. Kontani, Phys. Rev. Lett. 111, 057003 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.057003
19. M. Yi, D.H. Lu, J.-H. Chu, J.G. Analytis, A.P. Sorini, A.F. Kemper, B. Moritz, S.-K. Mo, R.G. Moore, M. Hashimoto, W.-S. Lee, Z. Hussain, T.P. Devereaux, I.R. Fisher, and Z.-X. Shen, Proc. Natl. Acad. Sci. U.S.A. 108, 6878 (2011). PNASA6 0027-8424 10.1073/pnas.1015572108
20. H. Miao, L.-M. Wang, P. Richard, S.-F. Wu, J. Ma, T. Qian, L.-Y. Xing, X.-C. Wang, C.-Q. Jin, C.-P. Chou, Z. Wang, W. Ku, and H. Ding, Phys. Rev. B 89, 220503(R) (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.220503
21. Y. Gallais, R.M. Fernandes, I. Paul, L. Chauviere, Y.-X. Yang, M.-A. Measson, M. Cazayous, A. Sacuto, D. Colson, and A. Forget, Phys. Rev. Lett. 111, 267001 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.267001
22. Y.-X. Yang, Y. Gallais, R.M Fernandes, I. Paul, L. Chauviere, M.-A. Measson, M. Cazayous, A. Sacuto, D. Colson, and A. Forget, arXiv:1310.0934.
23. K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H. Aoki, Phys. Rev. Lett. 101, 087004 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett. 101.087004
24. P.J. Hirschfeld, M.M. Korshunov, and I.I. Mazin, Rep. Prog. Phys. 74, 124508 (2011). RPPHAG 0034-4885 10.1088/0034-4885/74/12/124508
25. A.V. Chubukov, D.V. Efremov, and I. Eremin, Phys. Rev. B 78, 134512 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.134512
26. H. Kontani and S. Onari, Phys. Rev. Lett. 104, 157001 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.157001
27. S. Onari, Y. Yamakawa, and H. Kontani, Phys. Rev. Lett. 112, 187001 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.187001
28. T. Saito, S. Onari, and H. Kontani, Phys. Rev. B 88, 045115 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.045115
29. S. Onari and H. Kontani, Phys. Rev. Lett. 103, 177001 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.177001
30. Y. Yamakawa, S. Onari, and H. Kontani, Phys. Rev. B 87 195121 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.195121
31. S. Onari, H. Kontani, and M. Sato, Phys. Rev. B 81, 060504(R) (2010). PRBMDO 1098-0121 10.1103/PhysRevB.81.060504
32. S. Onari and H. Kontani, Phys. Rev. B 84, 144518 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.144518
33. S. Kasahara, H.J. Shi, K. Hashimoto, S. Tonegawa, Y. Mizukami, T. Shibauchi, K. Sugimoto, T. Fukuda, T. Terashima, A.H. Nevidomskyy, and Y. Matsuda, Nature (London) 486, 382 (2012). NATUAS 0028-0836 10.1038/nature11178
34. Y.K. Kim, W.S. Jung, G.R. Han, K.-Y. Choi, C.-C. Chen, T.P. Devereaux, A. Chainani, J. Miyawaki, Y. Takata, Y. Tanaka, M. Oura, S. Shin, A.P. Singh, H.G. Lee, J.-Y. Kim, and C. Kim, Phys. Rev. Lett. 111, 217001 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.217001
35. H. Kontani, T. Saito, and S. Onari, Phys. Rev. B 84, 024528 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.024528
36. P. Nozieres, Theory of Interacting Fermi Systems (Benjamin, New York, 1964);
37. A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975);
38. A.J. Leggett, Phys. Rev. 140, A1869 (1965). PHRVAO 0031-899X 10.1103/PhysRev.140.A1869
39. H. Kontani and K. Yamada, J. Phys. Soc. Jpn. 65, 172 (1996); JUPSAU 0031-9015 10.1143/JPSJ.65.172
40. H. Kontani and K. Yamada, J. Phys. Soc. Jpn. 66, 2232 (1997). JUPSAU 0031-9015 10.1143/JPSJ.66.2232
41. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.113.047001 for detailed discussion of the influence of the finite quasiparticle lifetime due to the impurity scattering.
42. A.-J. Millis, H. Monien, and D. Pines, Phys. Rev. B 42, 167 (1990); PRBMDO 0163-1829 10.1103/PhysRevB.42.167
43. P. Monthoux and D. Pines, Phys. Rev. B 47, 6069 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.47.6069
44. P. Steffens, C.H. Lee, N. Qureshi, K. Kihou, A. Iyo, H. Eisaki, and M. Braden, Phys. Rev. Lett. 110, 137001 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.137001
45. The analytic expression of (Equation presented) is given as Λ qω-lim = ?α,β,γα≠β ? k { 1 ε kβ-ε kα (f kβ ε kβ-ε k- qγ-f kα ε kα-ε k- qγ) + f k- qγ (ε k- qγ-ε kα) (ε k- qγ-ε kβ) } z kα z kβ z k- qγ + ?α,γ ? k f k- qγ-f kα (ε kα-ε k- qγ)2 { z kα }2 z k- qγ.
46. T. Miyake, K. Nakamura, R. Arita, and M. Imada, J. Phys. Soc. Jpn. 79, 044705 (2010). JUPSAU 0031-9015 10.1143/JPSJ.79.044705
47. M. Hirano, Y. Yamada, T. Saito, R. Nagashima, T. Konishi, T. Toriyama, Y. Ohta, H. Fukazawa, Y. Kohori, Y. Furukawa, K. Kihou, C.-H. Lee, A. Iyo, and H. Eisaki, J. Phys. Soc. Jpn. 81, 054704 (2012). JUPSAU 0031-9015 10.1143/JPSJ.81.054704