RAPID COMMUNICATIONS PHYSICAL REVIEW B 82, 140504共R兲 共2010兲 Pairing symmetry of the multiorbital pnictide superconductor BaFe1.84Co0.16As2 from Raman scattering S. Sugai,1,2,3 Y. Mizuno,1,3 K. Kiho,3,4 M. Nakajima,3,5 C. H. Lee,3,4 A. Iyo,3,4 H. Eisaki,3,4 and S. Uchida3,5 1 Department of Physics, Faculty of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan 2 Venture Business Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan 3TRIP, Japan Science and Technology Agency (JST), Chiyoda, Tokyo 102-0075, Japan 4National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan 5 Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan 共Received 23 March 2010; published 18 October 2010兲 The pairing symmetry of BaFe2−xCoxAs2 was investigated by Raman scattering. The gap structure appears only in the B2g symmetry inconsistent with Muschler et al. 关Phys. Rev. B 80, 180510共R兲 共2009兲兴. They concluded that the gap symmetry is the extended s with the argument that the B2g spectra probe the electron pocket. Our calculation using the realistic band parameter, however, shows that the B2g spectra are derived from mainly the hole pocket. The calculated intensity is much stronger in A1g than in B2g but the observed A1g spectra have no gap structure. This inconsistency is removed, if the orbital combination is introduced in the pairing symmetry. That is, the symmetry of orbital combination is B2g and that of momentum space is A1g. The energy of the gap peak is smaller than the gap energy of the hole pocket, indicating the observed peak is the resonant peak created in the gap of the s⫾ superconductor. DOI: 10.1103/PhysRevB.82.140504 PACS number共s兲: 74.70.Xa, 74.25.nd, 74.20.Rp, 74.25.Ha Symmetry of the superconducting gap is a key of the superconductivity mechanism. Spin-fluctuation-mediated pairing mechanism arising from the nesting between the hole pocket at the ⌫ point and the electron pocket at the M point was proposed because the superconducting phase of the iron pnictide is adjacent to the spin-density wave phase. The s⫾ pairing model in which the gap changes the sign between hole and electron pockets but has no node on Fermi surfaces 共FSs兲 was proposed.1–3 With increasing electron density the extended s 共nodal s⫾: nodes in the electron pocket兲 or d 共nodes in the hole pocket兲 pairing becomes stable. Functional renormalization study presented the extended s pairing with the nearly isotropic gap in the hole pocket and anisotropic gap in the electron pocket.4,5 A time-reversal symmetry breaking s + id pairing model was proposed.6 A s++ pairing model was also proposed to explain the robust superconductivity to impurities.7 Angle-resolved photoemission spectroscopy 共ARPES兲 disclosed that the gap energies are nearly isotropic in each of the hole and electron pockets and the gap energy changes from the ⌫ to M point consistent with the s⫾ symmetry.8–11 Maier and Scalapino12 proposed that the imaginary part of the dynamical spin susceptibility has a resonant peak below the gap 2⌬, if the gap symmetry is s⫾. Neutron scattering disclosed the magnetic resonant peaks.13–15 Recently Chubukov et al.16 proposed that the s⫾ gap can be distinguished from the pure s, extended s, and d wave gaps by using Raman scattering because a resonant peak develops inside the gap only in the s⫾ pairing. In other symmetry a pair-breaking peak develops at the gap energy. Very recently Muschler et al.17 reported that the gap structure in the Raman spectra of BaFe2−xCoxAs2 can be understood by the extended s symmetry18 on the assignment that the gap structure in the B2g spectra are derived from the electron pocket. Our calculation, however, shows that the hole pocket always gives the dominant intensity in all polarization con1098-0121/2010/82共14兲/140504共4兲 figurations. The calculated A1g intensity is much larger than the B2g spectra even if the screening effect is introduced but the A1g spectra have no gap structure. The inconsistency is removed by introducing the symmetry of the orbital combination which is the characteristic property of the multiorbital superconductor.19,20 Single crystals of BaFe1.84Co0.16As2 were synthesized by a self-flux method. The superconducting transition temperature is 25 K. Raman spectra were obtained on the fresh cleaved surface in the quasi-back-scattering configuration using 5145 Å Ar-ion laser. The polarization configuration c共ab兲c̄ denotes that the polarized light with the electric field parallel to the a axis is illuminated along the c axis and the backward scattered light with the electric field parallel to the b axis is measured, where a, b, and c are the crystallographic axes of the tetragonal structure. The a and b axes are parallel to the Fe-As-Fe directions. The bisecting directions of the a and b axes are named x and y. The A1g and B1g modes are allowed in the 共aa兲 spectra, B2g in 共ab兲, A1g and B2g in 共xx兲, and B1g in 共xy兲. The Raman system was calibrated so that the 2 ⳵ S intensity is proportional to ⳵␻⳵ ⍀. Figure 1共a兲 shows the polarized Raman spectra in the superconducting state at 5 K and the normal state at 25 K. All the spectra are plotted in the same intensity scale with the common zero level. Any background subtraction was not done to determine the zero level. The intensity around 75 cm−1 is largest in the 共aa兲 spectra and then 共xx兲, 共ab兲 and to 共xy兲 in decreasing order. The 75 cm−1 peaks in the 共ab兲 and 共xx兲 spectra at 5 K are the superconducting gap peaks. The gap symmetry is B2g in the same way as Muschler et al.17 In the 共aa兲 and 共xy兲 spectra the low-energy intensity below 100 cm−1 decreases as temperature decreases from 25 to 5 K but the superconducting peak does not emerge. The sharp peak at 214 cm−1 is the B1g phonon peak and the broad peak at 184 cm−1 is the A1g phonon peak which broadens below 100 K as discussed later. 140504-1 ©2010 The American Physical Society RAPID COMMUNICATIONS PHYSICAL REVIEW B 82, 140504共R兲 共2010兲 SUGAI et al. (b) (arb. units) (a) β γ Fe ky As α δ b y a kb ka x kx (c) FIG. 1. 共Color online兲 共a兲 Polarized Raman spectra below and at Tc. The intensity scales and the zero levels are the same for all four spectra. 共b兲 Differential Raman spectra between 5 and 25 K and the resonant peak observed by neutron scattering 共Refs. 14 and 15兲. The Raman peak energy is shown by the red or leftmost solid line. The solid black lines are gap energies of electron and hole pockets obtained by ARPES 共Ref. 11兲. The dashed line is the gap energy obtained by tunnel spectroscopy 共Ref. 21兲. The differential Raman spectra between the superconducting phase and the normal phase are plotted in Fig. 1共b兲 together with the resonant peaks observed in neutron scattering. The top two spectra are the differential neutronscattering spectra between 10 and 30 K in BaFe1.84Co0.16As2 by Lumsden et al.14 and the differential spectra between 4 and 60 K at 共1/2, 1/2, 1兲 in BaFe1.85Co0.15As2 by Inosov et al.15 The average gap energies of the hole pocket 共2⌬ = 13.2 meV兲 and the electron pocket 共10.0 meV兲 obtained by ARPES 共Ref. 11兲 are shown by solid lines. The observed anisotropy is small. The gap energy obtained by tunnel spectroscopy is also shown.21 The A1g Raman spectra were obtained from 关I共aa兲 + I共xx兲 − I共ab兲 − I共xy兲兴 / 2. The peak energies in the A1g, B2g, and 共xx兲 spectra are the same 75 cm−1 共red or leftmost solid line兲 as the resonant peak energies in neutron scattering. The energy is close to the gap energy of the electron pocket but smaller than that of the hole pocket. If the Raman peak is produced from the hole pocket, it is the resonant peak of the s⫾ pairing but if the peak is produced from the electron pocket, it is the pair-breaking peak. Individual charge fluctuation is screened by the longrange Coulomb interaction, if the charge fluctuation averaged on the Fermi surface is nonzero.22–24 The screened Raman efficiency without the final-state interaction is given by23 冋 2 具␮−1F典FS ⳵ 2S បe4 = 4 Im 具␮−2F典FS − ⳵␻ ⳵ ⍀ c 具F典FS 册 ⳵ 2⑀ 1 e 兺 S,i ⳵ ki ⳵ k j eL,j , ប2 i,j F is the Tsuneto function whose imaginary part is (kaka) (kakb) (kakb) ka (kxkx) (kxkx) (kxky) (kxky) ky kx 0 1 FIG. 2. 共Color online兲 共a兲 The structure of an FeAs layer. As atoms with 共without兲 black edge are above 共below兲 the Fe atomic sheet. 共b兲 Hole FSs ␣ and ␤ and the electron FSs ␥ and ␦. The ac and bc orbitals are shown by red and green, respectively. The dotted square is the folded Brillouin zone. 共c兲 兩⳵2⑀ / ⳵ki ⳵ k j兩2 of the hole and electron bands in the two-orbital model. The intensity on the FS gives the Raman intensity. 共1兲 Im F共␻,k兲 = ␲NF 共2兲 Electron band (kaka) kb at zero temperature, where ␮ is the mass tensor, ␮−1 = Hole band 4兩⌬k兩2 ␻冑␻2 − 4兩⌬k兩2 , 共3兲 具 典FS represents the average along the Fermi surface, eL and eS are the polarizations of the laser and scattered light, NF is the density of states at the Fermi level, and ⌬共k兲 is the gap energy. The first and the second terms of Eq. 共1兲 represent 140504-2 RAPID COMMUNICATIONS PAIRING SYMMETRY OF THE MULTIORBITAL PNICTIDE… PHYSICAL REVIEW B 82, 140504共R兲 共2010兲 TABLE I. Raman intensity from the hole pocket ␤ at 共␲ , ␲兲 and the sum of the electron pockets ␥ + ␦ at 共0 , ␲兲 and 共␲ , 0兲. tron pocket and vice versa. The maximum screening is ob2 tained by calculating 具␮−1典FS within each pocket. The maxi2 is listed in Table I. mally screened intensity 具␮−2典FS − 具␮−1典FS The largest screened intensity comes from the ␤ hole pocket in the 共aa兲 spectra. The intensity from the electron pocket is small. The decreasing order of scattering intensity from 共aa兲 : A1g + B1g and 共xx兲 : A1g + B2g, 共ab兲 : B2g to 共xy兲 : B1g is consistent with the experimental result. In the cuprate with a single a2 − b2 orbital the strength of the gap peak in the superconducting state is proportional to the intensity in the normal state. In contrast, in the iron pnictide the 共aa兲 spectra of Fig. 1共a兲 do not show the gap structure in spite of the large intensity. Instead the 共ab兲 共B2g兲 spectra have strong gap structure. Raman scattering in multiorbital electronic states is little different from single-orbital states in the normal phase because the electronic transition is mainly to the neighboring intraorbital state across the FS by the momentum conservation with light. On the other hand in the superconducting phase the paired states are composed of two orbitals ac and bc.19,20 The orbital combination is expressed by ␾†␶␾, where ␾ = 共ac , bc兲, and ␶0, ␶1 − ␶3 are the unit and Pauli matrices. ␾†␶0␾ = a2c2 + b2c2, ␾†␶1␾ = 2acbc, and ␾†␶3␾ = a2c2 − b2c2 transform as a2 + b2 共A1g兲, ab 共B2g兲, a2 − b2 共B1g兲 in the D4h point group, respectively. If the symmetry of the orbital combination is B2g, the observed gap symmetry B2g is derived from the A1g pairing symmetry in the momentum space because B2g = A1g 丢 B2g. The hole pocket gives the dominant part of the A1g intensity in the momentum space. The Raman peak energy of the gap structure is smaller than the gap energy of the hole pocket observed in ARPES as shown in Fig. 1共b兲. The A1g symmetry does not change under the final-state interaction.16 Therefore the observed peak is the resonant peak of the s⫾ gap which has the A1g symmetry. Precursor phenomena are observed above the superconducting transition. Figure 3 shows the temperature dependence of the low-energy Raman spectra. The intensity below 60 cm−1 increases in the 共xx兲 and 共ab兲 spectra as tempera- 共aa兲 Hole Electron 共xx兲 Bare Screened Bare Screened 100 18 28 1 100 16 11 5 共ab兲 共xy兲 9 3 7 3 (arb. units) the bare and the screening intensities, respectively. This screening term is finite for the A1g mode but zero for other modes because of the cancellation of the plus and minus mass along the FS. Equation 共2兲 gives the polarization dependence and Eq. 共3兲 does the pair-breaking peak at 2⌬. Figure 2共a兲 shows the FeAs layer viewed from the c axis. Figure 2共b兲 is the FS of hole pockets ␣ and ␤ and electron pockets ␥ and ␦ in the two-orbital tight-binding model of BaFe2As2.25 The ac and bc orbitals are shown by red and green, respectively.26 The dotted lines show the folded Brillouin zone 共BZ兲 for the crystallographic unit cell including two iron atoms. We use the symmetry of the folded Brillouin zone. The hole pocket ␤ is folded into ⌫ in the folded BZ. Figure 2共c兲 shows the contour maps of 兩⳵2⑀ / ⳵ki ⳵ k j兩2 for the electron band and the hole band in the two-orbital model. A set of ki and k j is denoted by 共kik j兲, which gives the scattering intensity in the 共ij兲 polarization configuration. In the electron-doped Ba2Fe1.85Co0.15As2 the ␣ hole pocket disappears11 and the ␤ and ␥共␦兲 pockets are in the good nesting condition. In the 共aa兲 and 共xx兲 polarization configurations the 兩⳵2⑀ / ⳵ki ⳵ k j兩2 has large intensity near the ␣ and ␤ hole FSs while small near the ␥ and ␦ electron FSs. In the 共ab兲 polarization configuration the intensity of 兩⳵2⑀ / ⳵ki ⳵ k j兩2 is small near the ␣ and ␤ hole FSs and much smaller near the ␥ and ␦ electron FSs. In the 共xy兲 polarization configuration the 兩⳵2⑀ / ⳵ki ⳵ k j兩2 is small both in hole pockets and electron pockets. For the hole pocket the screening is reduced by the elec- FIG. 3. 共Color online兲 Temperature dependence of polarized Raman spectra. The 20 K spectra are superimposed on the 5 K spectra. 140504-3 RAPID COMMUNICATIONS PHYSICAL REVIEW B 82, 140504共R兲 共2010兲 ture decreases below 70 K while the change is not observed in the 共aa兲 and 共xy兲 spectra. The change is induced by the increase in the electronic states near the Fermi energy. The polarization configurations with the precursor phenomena are the same as those of the resonant peaks. The 182 cm−1 共at 300 K兲 A1g phonon is active in the 共aa兲 and 共xx兲 spectra and the 207 cm−1 共at 300 K兲 B1g phonon is active in the 共aa兲 and 共xy兲 spectra.27,28 The sharp A1g phonon peak heavily broadens from the width 8 cm−1 at 300 K to 20 cm−1 at 5 K in the 共aa兲 spectra and from 8 cm−1 at 300 K to 32 cm−1 at 5 K in the 共xx兲 spectra. The broadening is related to the superconductivity because the broadening is not observed in BaFe2As2. This mode is the vibration of As atoms along the c direction. It is known that the height of the As atom from the Fe layer is sensitive to the pairing symmetry.29 In order to ensure the presence of spin excitations, the high-energy spin excitation spectra are shown in Fig. 4. The spectra are almost the same as those in the normal state of BaFe2As2.30 The energy range of large scattering intensity extends far above the two-magnon peak energy 2200 cm−1 in the spin-density wave phase of BaFe2As2. The present high-energy spectra indicate that the short-range magnetic correlation remains in the superconducting state. In conclusion, the present Raman scattering disclosed that the pairing symmetry of the multiorbital BaFe1.84Co0.16As2 is expressed by A1g in the momentum space and B2g in orbitals. The 75 cm−1 superconducting peak is the resonant peak of 1 I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett. 101, 057003 共2008兲. 2 K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H. Aoki, Phys. Rev. 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Lumsden et al., Phys. Rev. Lett. 102, 107005 共2009兲. 15 D. S. Inosov et al., Nat. Phys. 6, 178 共2010兲. 16 A. V. Chubukov, I. Eremin, and M. M. Korshunov, Phys. Rev. B (arb. units) SUGAI et al. FIG. 4. 共Color online兲 Wide-energy Raman spectra presenting magnetic excitations. The normal phase spectra of BaFe2As2 共Ref. 30兲 are also shown. The scale is on the right side. the hole pocket created inside the gap of the s⫾ superconductor. The existence of the high-energy spin excitations as in the cuprate superconductors suggests the spin-fluctuationmediated superconductivity This work was supported by Transformative Research Project on Iron Pnictides 共TRIP兲, Japan Science and Technology Agency 共JST兲. 79, 220501共R兲 共2009兲. Muschler, W. Prestel, R. Hackl, T. P. Devereaux, J. G. Analytis, J. H. Chu, and I. R. Fisher, Phys. Rev. B 80, 180510共R兲 共2009兲. 18 G. R. Boyd, T. P. Devereaux, P. J. Hirschfeld, V. Mishra, and D. J. Scalapino, Phys. Rev. B 79, 174521 共2009兲. Their B2g is the present B1g. 19 Y. Wan and Q.-H. Wang, EPL 85, 57007 共2009兲. 20 A. Moreo, M. Daghofer, J. A. Riera, and E. Dagotto, Phys. Rev. B 79, 134502 共2009兲. 21 Y. Yin, M. Zech, T. L. Williams, X. F. Wang, G. Wu, X. H. Chen, and J. E. Hoffman, Phys. Rev. Lett. 102, 097002 共2009兲. 22 M. V. Klein and S. B. Dierker, Phys. Rev. B 29, 4976 共1984兲. 23 M. Cardona, Physica C 317-318, 30 共1999兲. 24 T. P. Devereaux and R. Hackl, Rev. Mod. Phys. 79, 175 共2007兲. 25 S. Raghu, X.-L. Qi, C.-X. Liu, D. J. Scalapino, and S.-C. Zhang, Phys. Rev. B 77, 220503共R兲 共2008兲. 26 S. Graser, T. A. Maier, P. J. Hirschfeld, and D. J. Scalapino, New J. Phys. 11, 025016 共2009兲. 27 A. P. Litvinchuk, V. G. Hadjiev, M. N. Iliev, B. Lv, A. M. Guloy, and C. W. Chu, Phys. Rev. B 78, 060503共R兲 共2008兲. 28 M. Rahlenbeck, G. L. Sun, D. L. Sun, C. T. Lin, B. Keimer, and C. Ulrich, Phys. Rev. B 80, 064509 共2009兲. 29 K. Kuroki, H. Usui, S. Onari, R. Arita, and H. Aoki, Phys. Rev. B 79, 224511 共2009兲. 30 S. Sugai, Y. Mizuno, R. Watanabe, K. Takenaka, H. Ikuta, Y. Takayanagi, N. Hayamizu, and Y. Sone 共unpublished兲. 17 B. 140504-4