Abstract
Bulk FeSe is a special iron-based material in which superconductivity emerges inside a well-developed nematic phase. We present a microscopic model for this nematic superconducting state, which takes into account the mixing between s-wave and d-wave pairing channels and the changes in the orbital spectral weight promoted by the sign-changing nematic order parameter. We show that nematicity only weakly affects Tc, but gives rise to cos2θ variation of the pairing gap on the hole pocket, whose magnitude and size agrees with angle resolved photoemission spectroscopy and STM data. We further show that nematicity increases the weight of the dxz orbital on the hole pocket, and increases (reduces) the weight of the dxy orbital on the Y (X) electron pocket.
Original language | English (US) |
---|---|
Article number | 267001 |
Journal | Physical review letters |
Volume | 120 |
Issue number | 26 |
DOIs | |
State | Published - Jun 26 2018 |
Bibliographical note
Funding Information:In this Letter we argued that the experimentally observed anisotropy of the superconducting gap in bulk FeSe can be explained within the low-energy model for nematic order, without adding phenomenologically different quasiparticle weights for the d x z / d y z orbitals. Our key result is that T c is not strongly affected by the nematic order, but nematicity mixes s -wave and d -wave pairing channels and gives rise to a cos 2 θ h gap anisotropy on the hole pocket The sign of the cos 2 θ h term is determined by the interplay between the nematic order parameters on hole and electron pockets, which are of different sign, and the relative strength of s -wave and d -wave components of the pairing interaction. On the Z pocket, we found a sizable cos 2 θ h gap anisotropy with the gap maximum along the X direction, in agreement with the data. In our calculations the gap on the Γ pocket is smaller and less anisotropic. On the peanutlike X pocket, the gap is found to be maximal along the minor axis, which is also in agreement with the data. We also argued that nematicity decreases the weight of the d x y orbital on the X pocket and increases it on the Y pocket. This may potentially explain why the Y pocket is less visible in STM and in some ARPES data. We are thankful to B. Andersen, L. Bascones, L. Benfatto, S. Borisenko, A. Coldea, M. Eschrig, P. Hirschfield, A. Kreisel, C. Meingast, L. Rhodes, J. C. Séamus Davis, O. Vafek, M. Watson, and Y. Y. Zhao for useful discussions. J. K. was supported by the National High Magnetic Field Laboratory through NSF Grant No. DMR-1157490 and the State of Florida. R. M. F. and A. V. C. were supported by the Office of Basic Energy Sciences, U.S. Department of Energy, under Awards No. DE-SC0012336 (R. M. F.) and No. DE-SC0014402 (A. V. C.). J. K. thanks FTPI at the University of Minnesota for hospitality during the completion of this work. The authors are thankful to KITP at UCSB, where part of the work has been done. K. I. T. P. is supported by NSF Grant No. PHY 17-48958. [1] 1 See, e.g., A. Böhmer and A. Kreisel , J. Phys. Condens. Matter 30 , 023001 ( 2018 ), and references therein. JCOMEL 0953-8984 10.1088/1361-648X/aa9caa [2] 2 R. M. Fernandes and A. J. Millis , Phys. Rev. Lett. 111 , 127001 ( 2013 ). PRLTAO 0031-9007 10.1103/PhysRevLett.111.127001 [3] 3 J. Kang , A. F. Kemper , and R. M. Fernandes , Phys. Rev. Lett. 113 , 217001 ( 2014 ). PRLTAO 0031-9007 10.1103/PhysRevLett.113.217001 [4] 4 G. Livanas , A. Aperis , P. Kotetes , and G. Varelogiannis , Phys. Rev. B 91 , 104502 ( 2015 ). PRBMDO 1098-0121 10.1103/PhysRevB.91.104502 [5] 5 H. C. Xu , X. H. Niu , D. F. Xu , J. Jiang , Q. Yao , Q. Y. Chen , Q. Song , M. Abdel-Hafiez , D. A. Chareev , A. N. Vasiliev , Q. S. Wang , H. L. Wo , J. Zhao , R. Peng , and D. L. Feng , Phys. Rev. Lett. 117 , 157003 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.157003 [6] 6 T. Hashimoto , Y. Ota , H. Q. Yamamoto , Y. Suzuki , T. Shimojima , S. Watanabe , C. Chen , S. Kasahara , Y. Matsuda , T. Shibauchi , K. Okazaki , and S. Shin , Nat. Commun. 9 , 282 ( 2018 ). NCAOBW 2041-1723 10.1038/s41467-017-02739-y [7] 7 Y. S. Kushnirenko , A. V. Fedorov , E. Haubold , S. Thirupathaiah , T. Wolf , S. Aswartham , I. Morozov , T. K. Kim , B. Büchner , and S. V. Borisenko , Phys. Rev. B 97 , 180501 ( 2018 ). PRBMDO 2469-9950 10.1103/PhysRevB.97.180501 [8] 8 D. Liu , arXiv:1802.02940 . The authors measure the gap on the Γ pocket, but the size of their pocket is larger than in other ARPES studies and is consistent with what other groups found for the Z pocket. [9] 9 L. C. Rhodes , M. D. Watson , A. A. Haghighirad , D. V. Evtushinsky , M. Eschrig , and T. K. Kim , arXiv:1804.01436 . [10] 10a P. O. Sprau , A. Kostin , A. Kreisel , A. E. Böhmer , V. Taufour , P. C. Canfield , S. Mukherjee , P. J. Hirschfeld , B. M. Andersen , and J. C. Sèamus Davis , Science 357 , 75 ( 2017 ); SCIEAS 0036-8075 10.1126/science.aal1575 10b see also A. Kostin , P. O. Sprau , A. Kreisel , Y.-X. Chong , A. E. Böhmer , P. C. Canfield , P. J. Hirschfeld , B. M. Andersen , and J. C. Séamus Davis , arXiv:1802.02266 . [11] 11 L. Jiao , C.-L. Huang , S. Rößler , C. Koz , U. K. Rößler , U. Schwarz , and S. Wirth , Sci. Rep. 7 , 44024 ( 2017 ). SRCEC3 2045-2322 10.1038/srep44024 [12] 12 A. Kreisel , B. M. Andersen , P. O. Sprau , A. Kostin , J. C. Séamus Davis , and P. J. Hirschfeld , Phys. Rev. B 95 , 174504 ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.95.174504 [13] 13 A. V. Chubukov , M. Khodas , and R. M. Fernandes , Phys. Rev. X 6 , 041045 ( 2016 ). PRXHAE 2160-3308 10.1103/PhysRevX.6.041045 [14] 14a R.-Q. Xing , L. Classen , M. Khodas , and A. V. Chubukov , Phys. Rev. B 95 , 085108 ( 2017 ); PRBMDO 2469-9950 10.1103/PhysRevB.95.085108 14b L. Classen , R.-Q. Xing , M. Khodas , and A. V. Chubukov , Phys. Rev. Lett. 118 , 037001 ( 2017 ). PRLTAO 0031-9007 10.1103/PhysRevLett.118.037001 [15] 15a F. Wang , H. Zhai , Y. Ran , A. Vishwanath , and D.-H. Lee , Phys. Rev. Lett. 102 , 047005 ( 2009 ); PRLTAO 0031-9007 10.1103/PhysRevLett.102.047005 15b C. Platt , W. Hanke , and R. Thomale , Adv. Phys. 62 , 453 ( 2013 ). ADPHAH 0001-8732 10.1080/00018732.2013.862020 [16] 16 A. I. Coldea and M. D. Watson , Annu. Rev. Condens. Matter Phys. 9 , 125 ( 2018 ). ARCMCX 1947-5454 10.1146/annurev-conmatphys-033117-054137 [17] 17 A. Fedorov , A. Yaresko , T. K. Kim , Y. Kushnirenko , E. Haubold , T. Wolf , M. Hoesch , A. Grüneis , B. Büchner , and S. V. Borisenko , Sci. Rep. 6 , 36834 ( 2016 ). SRCEC3 2045-2322 10.1038/srep36834 [18] 18 V. Cvetkovic and O. Vafek , Phys. Rev. B 88 , 134510 ( 2013 ). PRBMDO 1098-0121 10.1103/PhysRevB.88.134510 [19] 19 Y. Suzuki , T. Shimojima , T. Sonobe , A. Nakamura , M. Sakano , H. Tsuji , J. Omachi , K. Yoshioka , M. Kuwata-Gonokami , T. Watashige , R. Kobayashi , S. Kasahara , T. Shibauchi , Y. Matsuda , Y. Yamakawa , H. Kontani , and K. Ishizaka , Phys. Rev. B 92 , 205117 ( 2015 ). PRBMDO 1098-0121 10.1103/PhysRevB.92.205117 [20] 20 S. Onari , Y. Yamakawa , and H. Kontani , Phys. Rev. Lett. 116 , 227001 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.227001 [21] 21 L. Fanfarillo , J. Mansart , P. Toulemonde , H. Cercellier , P. Le Fevre , F. Bertran , B. Valenzuela , L. Benfatto , and V. Brouet , Phys. Rev. B 94 , 155138 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.155138 [22] 22 L. Benfatto , B. Valenzuela , and L. Fanfarillo , arXiv:1804.05800 . [23] 23 S. Graser , T. A. Maier , P. J. Hirschfeld , and D. J. Scalapino , New J. Phys. 11 , 025016 ( 2009 ). NJOPFM 1367-2630 10.1088/1367-2630/11/2/025016 [24] 24 A. V. Chubukov , Annu. Rev. Condens. Matter Phys. 3 , 57 ( 2012 ). ARCMCX 1947-5454 10.1146/annurev-conmatphys-020911-125055 [25] We did not set the pairing interaction to be different for d x z and d y z orbitals due to nematic order. Such renormalization is rather weak if one introduces orbital order and directly compute the splitting of interactions on d x z and d y z orbitals [10,26]. The situation may be different if nematicity is due to composite Ising spin order [22]. [26] 26 L. Fanfarillo , G. Giovannetti , M. Capone , and E. Bascones , Phys. Rev. B 95 , 144511 ( 2017 ). PRBMDO 2469-9950 10.1103/PhysRevB.95.144511 [27] 27 P. Bourgeois-Hope , S. Chi , D. A. Bonn , R. Liang , W. N. Hardy , T. Wolf , C. Meingast , N. Doiron-Leyraud , and L. Taillefer , Phys. Rev. Lett. 117 , 097003 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.117.097003 [28] 28 L. Wang , F. Hardy , T. Wolf , P. Adelmann , R. Fromknecht , P. Schweiss , and C. Meingast , Phys. Status Solidi B 254 , 1600153 ( 2017 ). PSSBBD 0370-1972 10.1002/pssb.201600153 [29] 29 Y. Sato , S. Kasahara , T. Taniguchi , X. Z. Xing , Y. Kasahara , Y. Tokiwa , T. Shibauchi , and Y. Matsuda , Proc. Natl. Acad. Sci. U.S.A. 115 , 1227 ( 2018 ). PNASA6 0027-8424 10.1073/pnas.1717331115 [30] 30 T. Hanaguri , K. Iwaya , Y. Kohsaka , T. Machida , T. Watashige , S. Kasahara , T. Shibauchi , and Y. Matsuda , Sci. Adv. 4 , eaar6419 ( 2018 ). SACDAF 2375-2548 10.1126/sciadv.aar6419 [31] 31 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.120.267001 for the description of the dispersion and orbital weights of each band and the BCS equation to obtain the anisotropic gap. [32] Whether STM is probing the Z or the Γ pocket is difficult to determine because STM data are likely averaged over k z . [33] 33 M. D. Watson , T. K. Kim , A. A. Haghighirad , N. R. Davies , A. McCollam , A. Narayanan , S. F. Blake , Y. L. Chen , S. Ghannadzadeh , A. J. Schofield , M. Hoesch , C. Meingast , T. Wolf , and A. I. Coldea , Phys. Rev. B 91 , 155106 ( 2015 ). PRBMDO 1098-0121 10.1103/PhysRevB.91.155106 [34] 34 R. M. Fernandes and A. V. Chubukov , Rep. Prog. Phys. 80 , 014503 ( 2017 ). RPPHAG 0034-4885 10.1088/1361-6633/80/1/014503 [35] 35 R. M. Fernandes and O. Vafek , Phys. Rev. B 90 , 214514 ( 2014 ). PRBMDO 1098-0121 10.1103/PhysRevB.90.214514 [36] 36 M. D. Watson , T. K. Kim , L. C. Rhodes , M. Eschrig , M. Hoesch , A. A. Haghighirad , and A. I. Coldea , Phys. Rev. B 94 , 201107 ( 2016 ). PRBMDO 2469-9950 10.1103/PhysRevB.94.201107 [37] 37 A. I. Coldea (private communication). [38] 38 M. C. Rahn , R. A. Ewings , S. J. Sedlmaier , S. J. Clarke , and A. T. Boothroyd , Phys. Rev. B 91 , 180501 ( 2015 ). PRBMDO 1098-0121 10.1103/PhysRevB.91.180501 [39] 39 Q. Wang , Y. Shen , B. Pan , Y. Hao , M. Ma , F. Zhou , P. Steffens , K. Schmalzl , T. R. Forrest , M. Abdel-Hafiez , X. Chen , D. A. Chareev , A. N. Vasiliev , P. Bourges , Y. Sidis , H. Cao , and J. Zhao , Nat. Mater. 15 , 159 ( 2016 ). NMAACR 1476-1122 10.1038/nmat4492 [40] 40 Q. Wang , Y. Shen , B. Pan , X. Zhang , K. Ikeuchi , K. Iida , A. D. Christianson , H. C. Walker , D. T. Adroja , M. Abdel-Hafiez , X. Chen , D. A. Chareev , A. N. Vasiliev , and J. Zhao , Nat. Commun. 7 , 12182 ( 2016 ). NCAOBW 2041-1723 10.1038/ncomms12182 [41] 41 M. D. Watson , A. A. Haghighirad , L. C. Rhodes , M. Hoesch , and T. K. Kim , New J. Phys. 19 , 103021 ( 2017 ). NJOPFM 1367-2630 10.1088/1367-2630/aa8a04 [42] 42 N. Lanata , H. U. R. Strand , G. Giovannetti , B. Hellsing , L. de Medici , and M. Capone , Phys. Rev. B 87 , 045122 ( 2013 ). PRBMDO 1098-0121 10.1103/PhysRevB.87.045122 [43] 43 Z. P. Yin , K. Haule , and G. Kotliar , Nat. Mater. 10 , 932 ( 2011 ). NMAACR 1476-1122 10.1038/nmat3120 [44] 44 E. Bascones , B. Valenzuela , and M. J. Calderón , Phys. Rev. B 86 , 174508 ( 2012 ). PRBMDO 1098-0121 10.1103/PhysRevB.86.174508
Publisher Copyright:
© 2018 American Physical Society.