Double neutron spin resonances and gap anisotropy in underdoped superconducting NaFe{}_{0.985}Co{}_{0.015}As

Double neutron spin resonances and gap anisotropy in underdoped superconducting NaFeCoAs

Chenglin Zhang Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Rong Yu Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA    Yixi Su Jülich Centre for Neutron Science, Forschungszentrum Jülich GmbH, Outstation at FRM II, Lichtenbergstrasse 1, D-85747 Garching, Germany    Yu Song Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Miaoyin Wang Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Guotai Tan Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Physics department, Beijing Normal University, Beijing 100875, China    Takeshi Egami Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA    J. A. Fernandez-Baca Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Enrico Faulhaber Gemeinsame Forschergruppe HZB - TU Dresden, Helmholtz-Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany Forschungsneutronenquelle Heinz Maier-Leibnitz (FRM-II), TU München, D-85747 Garching, Germany    Qimiao Si Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA    Pengcheng Dai pdai@rice.edu Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
Abstract

We use inelastic neutron scattering to show that superconductivity in electron-underdoped NaFeCoAs induces a dispersive sharp resonance near meV and a broad dispersionless mode at meV. However, similar measurements on overdoped superconducting NaFeCoAs find only a single sharp resonance at meV. We connect these results with the observations of angle-resolved photoemission spectroscopy that the superconducting gaps in the electron Fermi pockets are anisotropic in the underdoped material but become isotropic in the overdoped case. Our analysis indicates that both the double neutron spin resonances and gap anisotropy originate from the orbital dependence of the superconducting pairing in the iron pnictides. Our discovery also shows the importance of the inelastic neutron scattering in detecting the multiorbital superconducting gap structures of iron pnictides.

pacs:
74.25.Ha, 74.70.-b, 78.70.Nx

High-transition temperature (high-) superconductivity in copper oxides and iron pnictdies can be derived from electron or hole doping to their antiferromagnetic (AF) parent compounds jmtranquada (); dai (). Since magnetism may be a common thread for the electron pairing in high- superconductors scalapino (), it is important to determine how magnetic excitations can probe the superconducting (SC) electron pairing interactions. For single band copper oxide superconductors, the neutron spin resonance, a sharp collective magnetic excitation at the AF ordering wave vector below , has been the subject of twenty years’ study and provided strong evidence for the sign changing nature of the -wave superconducting gap in these materials Eschrig (). In the case of multiband iron pnictide superconductors kamihara (); cwchu (), band structure calculations indicate that the Fermi surfaces consist of hole pockets near the zone center and electron pockets near the zone corner Singh (); kuroki (); Mazin (); hirschfeld (); chubukov (). Although the sign change of the quasipartice excitations (nesting) between the hole and electron pockets also necessitates a resonance at an energy below the sum of the electron and hole SC gap energies Korshunov (); Maier (), the multiple 3 Fe orbital nature of the iron pnictides Yi09 (); Yi13 () means that the SC gaps can be anisotropic on different Fermi surfaces Maier09 (); Goswami (). Therefore, if the resonance is a direct probe of the quasiparticle excitations between the hole and electron Fermi pockets, it should be sensitive to the SC gap energy anisotropy. In spite of intensive inelastic neutron scattering (INS) work on hole christianson (); chenglinzhang (); castellan () and electron-doped lumsden (); schi09 (); dsinosov09 (); steffens () BaFeAs family of iron pnictides, only a broad resonance consistent with the sign change of the SC pairing has been observed.

For the NaFeCoAs family of iron pnictides [Fig. 1(a)] slli09 (); Parker (), the London penetration depth measurements suggest that the SC gap is highly anisotropic even at optimal doping cho (). Moreover, angle-resolved photoemission (ARPES) experiments indicate the presence of large SC gap anisotropy in the electron Fermi pockets of the underdoped regime near , which is absent in the hole Fermi pockets; the gap anisotropy disappears upon increasing to 0.045 [Figs. 1(c),1(d)] qqge (); Liu_arpes (); thirupathaiah (). A likely origin RYu_theory () of this gap anisotropy is the angular variation of the relative orbital weight among the and the degenerate orbitals along the electron Fermi pockets, which is absent along the hole Fermi pockets. As such, this material offers the opportunity to study the role of orbital dependence in SC pairing via INS.

In this Letter, we present INS study of spin excitations in underdoped SC NaFeCoAs coexisting with static AF order ( K, K) and its comparison with overdoped SC NaFeCoAs ( K) [Fig. 1(a)] clzhang13 (). Our INS experiments reveal that superconductivity induces two distinct neutron spin resonances at the commensurate AF wave vector in NaFeCoAs [Figs. 2(a-c)]; this is an entirely new behavior which has never been observed in either the iron-based or copper-based superconductors. While the first resonance occuring at meV is sharp in energy and becomes dispersive along the -axis, there is also a broad dispersionless resonance at meV [Figs. 2(e-g)]. For electron-overdoped SC NaFeCoAs, the double resonances changes back to a single resonance [Fig. 1(f)] clzhang13 (). Our analysis indicates that both the SC gap anisotropy and the double resonances arise from the orbital dependent pairing strength, and reveals the important role that INS can play in probing of the multiorbital structure of superconductivity in the iron-based superconductors.

Figure 1: (a) The electronic phase diagram of NaFeCoAs, where the arrows indicate the Co-doping levels of our samples. The temperature dependence of the bulk susceptibility in the inset shows K. (b) The schematics of the -axis dispersion of the double resonances. (c,d) The schematics of Fermi surfaces and SC gaps in underdoped and overdoped samples near and points qqge (). (e) Double resonances obtained by taking temperature difference plots (4 K28 K) of constant- scans at in NaFeCoAs. (f) Similar data in NaFeCoAs showing only a single resonance. The horizontal bars in (e) and (f) indicate instrumental energy resolution.

We prepared 5 g single crystals of NaFeCoAs by self-flux method clzhang13 (). Susceptibility [inset in Fig. 1(a)], heat capacity gttan (), and nuclear magnetic resonance swoh () measurements showed that the sample is a homogeneous bulk superconductor ( K) microscopically coexisting with static AF order. Our neutron scattering experiments were carried out on the thermal (HB-3) and cold (PANDA) triple-axis spectrometers at High Flux Isotope Reactor, Oak Ridge National Laboratory and the FRM-II, TU Müchen, Germany schi09 (), respectively. At HB-3, we fixed final neutron energies at meV with Pyrolytic graphite (PG) monochromator and analyzer. At PANDA, We used focusing PG monochromator and analyzer with a fixed final neutron energy of meV. The wave vector at (,,) in Å is defined as (H,K,L) = (,,) reciprocal lattice unit (rlu) using the tetragonal unit cell (space group , Å and Å at 3 K). In this notation, the AF Bragg peaks occur at the positions with slli09 (). The samples are coaligned in the scattering zones with a mosaic less than 2. Figure 4(a) shows the temperature dependence of the elastic scattering at , which reveals a clear reduction at the onset of and dramatic increase below K [Fig. 4(a)]. These results suggest that NaFeCoAs is a homogeneous electron underdoped superconductor similar to underdoped SC BaFeAs (Co, Ni) [Fig. 1(a)] pratt09 (); Christianson09 (). From earlier ARPES measurements qqge (); Liu_arpes (); thirupathaiah (), we know that the SC gaps in the electron and hole pockets are quite isotropic for electron overdoped NaFeCoAs [Fig. 1(d)], but the SC gap becomes highly anisotropic for NaFeCoAs [Fig. 1(c)].

Figure 2: (a-c) at with L = 0, 0.25 and 0.5, respectively, at 3, 18, 28 and 40 K. (d-f) The difference of L-modulations above and below at , 3.25, 4.5 and 6 meV, respectively.
Figure 3: (a-c) scans along the direction at meV, meV, and meV, respectively, with . (d-f) scans along the direction at meV, = 3.25 meV, and = 6 meV, respectively, for SC NaFeCoAs. The horizontal bars indicate instrumental resolution. The solid lines are fits to Gaussians.

In previous INS work on overdoped NaFeCoAs ( K), a dispersionless sharp resonance was found at meV below [Fig. 1(f)] clzhang13 (). To explore what happens in the underdoped regime where superconductivity coexists with AF static order swoh (), we carried out constant-Q scans at wave vectors with , and rlu at , , and on NaFeCoAs. Figures 2(a)-2(c) show the at K, obtained by subtracting the background scattering of Q-scans in Fig. 3 and correcting for the Bose population factor using , where is the magnetic scattering function. At K ( K), the paramagnetic scattering at all three wave vectors probed are relaxational and can be fitted with as shown in solid lines in Figs. 2(a)-2(c). On cooling to K ( K), the overall lineshape of the scattering remain unchanged. On further cooling to K ( K), while the scattering at wave vectors with still have Lorentzian lineshape (relaxational) [blue symbols in Figs. 2(a) and 2(b)], a spin anisotropy gap of 1.5 meV opens at [blue symbols in Fig. 2(c)]. Finally, upon entering into the SC state at K ( K), we see that a sharp resonance and a broad resonance develop at and meV, respectively, at [Fig. 2(c)]. In addition, the normal state spin gap of 1.5 meV increases to 3 meV below [Fig. 2(c)]. The temperature difference plot between 4 K and 11 K shown in Fig. 1(e) confirms the presence of superconductivity-induced double resonance. On changing wave vectors to and , we see that a clear increase in energy of the sharp resonance while the broad mode remains at meV [Figs. 2(b) and 2(a)]. However, the low-temperature spin gaps are similar at all wave vectors.

To probe the -axis modulations of the low-energy spin excitations and superconductivity-induced effect, we carried out constant-energy scans along the direction at different energies above and below . Since there is a low-temperature spin gap below 3 meV, the -dependence of the normal state magnetic scattering at meV can be obtained by subtracting the data at K from those at 18 K. The magnetic scattering at meV and 18 K shows a broad peak at with rlu [Fig. 2(d)]. At the first resonance energy ( meV), superconductivity induces well-defined peaks centered at with [Fig. 2(e)]. The energy of the first resonance moves to meV at with , as illustrated in Fig. 2(f). Figure 2(g) shows that the second resonance at meV is indeed dispersionless with superconductivity-induced enhancement below decreases monotonically with increasing , following the Fe magnetic form factor.

To confirm the low-temperature spin gap and determine the wave vector dependence of the resonances, we carried out constant-energy scans at diferent energies above and below , and above . Figures 3(a-c) and 3(d-f) show along the and directions, respectively. At meV, a well-defined Gaussian peak in the normal state disappears below , confirming the presence of the low-temperature spin gap [Figs. 3(a) and 3(d)]. Comparing meV with [Fig. 3(b)] and meV with [Fig. 3(e)], we see that the intensity gain of the resonances below is larger at . At the second resonance energy meV [Figs. 3e and 3(f)], superconductivity-induced intensity gain decreases with increasing . By Fourier transforming the fitted Guassian peaks, we find that the spin-spin correlation lengths above are Å at . At 4 K and , spin correlation lengths increase to and Å at and meV, respectively. At 4 K and , they are and Å at 3.25 and 6 meV, respectively.

Figures 4(a-f) summarize the temperature dependence of the scattering at different energies and wave vectors. At the elastic AF Bragg position, we see clear effect of and [Fig. 4(a)]. For meV, spin excitations show a kink at signaling the static AF order, and decrease on cooling below [Figs. 4(b) and 4(c)]. From Figs. 4(d-f), we see that while the intensity at resonance energies show kinks at , they increase dramatically below . These results provide conclusive evidence of the presene of double resonance in underdoped NaFeCoAs.

Figure 4: (a) The temperature dependence of AF peak intensity at with vertical dashed line indicating K and K. (b) and (c) Temperature dependence of the scattering at meV at and , respectively. Temperature dependence of the scattering at (d) meV and , (e) meV and , and (f) meV and .

In iron pnictides, the Fermi surface is composed of multiple orbitals. In electron doped NaFeCoAs, the dominant orbital character of the electron pockets would be either or , depending on the direction in the Brillouin zone [Figs. 1(c) and 1(d)] qqge (); Liu_arpes (); thirupathaiah (). Recent theories and experiments find that the strength of electron correlations can be very different between the and orbitals Yu_multi11 (); YinKotliar11 (); Yu13b (); Yi13 (). This may induce orbital-selective SC pairing strengths, which naturally give anisotropic SC gaps along the electron pockets. The neutron resonance in the SC state is a bound state at energies just below the particle-hole excitation energy Eschrig (). If the anisotropic SC gap in the electron pocket is large, as in the underdoped NaFeCoAs, there are two characteristic gaps (respectively associated with and orbitals). Two resonance peaks are expected as a result of this separation of energy scales. As the electron doping is increased to the overdoped regime, the orbital selectivity of the correlations is reduced Yu13b (), which would give rise to a smaller SC gap anisotropy with . Therefore, only one resonance peak would be resolved.

Figure 5: The imaginary part of the dynamical susceptibility, at in the SC phase obtained from a five-orbital t-- model. For the case of sufficiently large gap anisotropy shown here, two resonance peaks are obtained.

The above picture RYu_theory () is supported by our theoretical calculation of the dynamical spin susceptibility in the SC state of a multiorbital model Goswami (); Yu11 (). The Hamiltonian reads . Here, contains a five-orbital tight-binding model adapted from Ref. Graser10 (). We have modified some tight-binding parameters such that the bandstructure better fits to the density function theory results on NaFeAs. The interaction part includes matrix couplings. Figure 5 shows the calculated imaginary part of the susceptibility, . Indeed we find two resonance peaks when the gap anisotropy is large, which turn into one sharp peak when the gap anisotropy is reduced.

We now turn to several remarks. First, in the underdoped regime where the SC and AF states coexist, a reconstruction of Fermi surface in the AF state may in principle cause a SC gap anisotropy. However, this mechanism is unlikely because ARPES observes neither the Fermi surface reconstruction nor any gap anisotropy on the hole Fermi pocket in the underdoped NaFeCoAs qqge (). Second, one may in principle consider the double spin resonances as originating from the quasiparticle excitations between two different hole and electron Fermi pockets with different SC gaps. However, such an effect would lead to spin resonances at different wave vectors due to mismatched Fermi surfaces tdas11 (). This is unlike our observation here that both resonances appear at the same commensurate wave vector. Third, we have emphasized the orbital selectivity in understanding the data. Through a spin-orbit coupling, this orbital-dependent effect may also lead to a spin anisotropy in the fluctuation spectrum.

In conclusion, we use INS to find two resonances at the same commensurate AF wave vector for the underdoped NaFeCoAs, but only one resonance for the overdoped SC NaFeCoAs. This is different from the -axis dispersion of the resonance in electron-doped BaFeNiAs schi09 () and hole-doped copper oxide superconductor YBaCuO pailhes (). The doping evolution of the spin resonance coincides with that of the SC gap anisotropy in ARPES experiments. Our experimental discoveries, together with our theoretical analysis, suggest that both properties arise from the orbital dependence of the SC pairing. This provides evidence that the orbital selectivity plays an important role in understanding the SC pairing of the multiorbital electrons in the iron pnictides. Because the multiplicity of electron orbitals is a distinct feature of the iron-based superconductors and likely makes a major contribution to their superconducting pairing, our results will be important to the eventual understanding of superconductivity in these and related materials.

We thank C. Redding and Scott Carr for their help in sample making process. The work at Rice/UTK was supported by the US DOE, BES, through contract DE-FG02-05ER46202 (P.D.). Work at Rice University was supported by the NSF Grant No. DMR-1006985 and the Robert A. Welch Foundation Grant No. C-1411 (Q.S.). C.L.Z and T.E are partially supported by the US DOE BES through the EPSCoR grant, DE-FG02-08ER46528. The work at the High Flux Isotope Reactor was partially supported by the Division of Scientific User Facilities, US DOE, BES.

References

  • (1) J. M. Tranquada, G. Xu, and I. A. Zaliznyak, arXiv: 1301.5888.
  • (2) P. C. Dai, J. P. Hu, and E. Dagotto, Nat. Phys. 8, 709 (2012).
  • (3) D. J. Scalapino, Rev. Mod. Phys. 84, 1383 (2012).
  • (4) M. Eschrig, Adv. Phys. 55, 47 (2006).
  • (5) Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296-3297 (2008).
  • (6) C. W. Chu, F. Chen, M. Gooch, A.M. Guloy, B. Lorenz, B. Lv, K. Sasmal, Z.J. Tang, J.H. Tapp, and Y.Y. Xue, Physica C 469, 326-331 (2009).
  • (7) D. J. Singh and M. H. Du, Phys. Rev. Lett. 100, 237003 (2008).
  • (8) K. Kuroki, S. Onari, R. Arita, H. Usui, Y. Tanaka, H. Kontani, and H. Aoki, Phys. Rev. Lett. 101, 087004 (2008).
  • (9) I. I. Mazin, D. J. Singh, M. D. Johannes, & M. H. Du, Phys. Rev. Lett. 101, 057003 (2008).
  • (10) P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Rep. Prog. Phys. 74, 124508 (2011).
  • (11) A. Chubukov, Annual Reviews in Condensed-Matter Physics 3, 57 (2012).
  • (12) M. M. Korshunov and I. Eremin, Phys. Rev. B 78, 140509(R) (2008).
  • (13) T. A. Maier, S. Graser, D. J. Scalapino, and P. Hirschfeld, Phys. Rev. B 79, 134520 (2009).
  • (14) M. Yi, D. H. Lu, J. G. Analytis, J.-H. Chu, S.-K. Mo, R.-H. He, R. G. Moore, X. J. Zhou, G. F. Chen, J. L. Luo, N. L. Wang, Z. Hussain, D. J. Singh, I. R. Fisher, and Z.-X. Shen, Phys. Rev. B 80, 024515 (2009).
  • (15) M. Yi, D. H. Lu, R. Yu, S. C. Riggs, J.-H. Chu, B. Lv, Z. K. Liu, M. Lu, Y.-T. Cui, M. Hashimoto, S.-K. Mo, Z. Hussain, C. W. Chu, I. R. Fisher, Q. Si, and Z.-X. Shen, Phys. Rev. Lett. 110, 067003 (2013).
  • (16) T. A. Maier, S. Graser, D. J. Scalapino and P. J. Hirschfeld, Phys. Rev. B 79, 224510 (2009).
  • (17) P. Goswami, P. Nikolic, and Q. Si, EuroPhys Lett. 91, 37006 (2010).
  • (18) A. D. Christianson, E. A. Goremychkin, R. Osborn, S. Rosenkranz, M. D. Lumsden, C. D. Malliakas, I. S. Todorov, H. Claus, D. Y. Chung, M. G. Kanatzidis, R. I. Bewley, and T. Guidi, Nature 456, 930 (2008).
  • (19) C. L. Zhang, M. Wang, H. Q. Luo, M. Y. Wang, M. S. Liu, J. Zhao, D. L. Abernathy, T. A. Maier, K. Marty, M. D. Lumsden, S. Chi, S. Chang, J. A. Rodriguez-Rivera, J. W. Lynn, T. Xiang, J. P. Hu, and P. C. Dai, Scientific Reports 1, 115 (2011).
  • (20) J.-P. Castellan, S. Rosenkranz, E. A. Goremychkin, D. Y. Chung, I. S. Todorov, M. G. Kanatzidis, I. Eremin, J. Knolle, A. V. Chubukov, S. Maiti, M. R. Norman, F. Weber, H. Claus, T. Guidi, R. I. Bewley, and R. Osborn, Phys. Rev. Lett. 107, 177003 (2011).
  • (21) M. D. Lumsden, A. D. Christianson, D. Parshall, M. B. Stone, S. E. Nagler, G. J. MacDougall, H. A. Mook, K. Lokshin, T. Egami, D. L. Abernathy, E. A. Goremychkin, R. Osborn, M. A. McGuire, A. S. Sefat, R. Jin, B. C. Sales, and D. Mandrus, Phys. Rev. Lett. 102, 107005 (2009).
  • (22) S. Chi, A. Schneidewind, J. Zhao, L. W. Harriger, L. J. Li, Y. K. Luo, G. H. Cao, Z. A. Xu, M. Loewenhaupt, J. P. Hu, and P. C. Dai, Phys. Rev. Lett. 102, 107006 (2009).
  • (23) D. S. Inosov, J. T. Park, P. Bourges, D. L. Sun, Y. Sidis, A. Schneidewind, K. Hradil, D. Haug, C. T. Lin, B. Keimer, and V. Hinkov, Nat. Phys. 6, 178 (2010).
  • (24) P. Steffens, C. H. Lee, N. Qureshi, K. Kihou, A. Iyo, H. Eisaki, and M. Braden, Phys. Rev. Lett. 110, 137001 (2013).
  • (25) S. L. Li, C. de la Cruz, Q. Huang, G. F. Chen, T.-L. Xia, J. L. Luo, N. L. Wang, and P. C. Dai, Phys. Rev. B 80, 020504(R) (2009).
  • (26) D. R. Parker, M. J. P. Smith, T. Lancaster, A. J. Steele, I. Franke, P. J. Baker, F. L. Pratt, M. J. Pitcher, S. J. Blundell, and S. J. Clarke, Phys. Rev. Lett. 104, 057007 (2010).
  • (27) K. Cho, M. A. Tanatar, N. Spyrison, H. Kim, Y. Song, P. C. Dai, C. L. Zhang, and R. Prozorov, Phys. Rev. B 86, 020508(R) (2012).
  • (28) Q. Q. Ge, Z. R. Ye, M. Xu, Y. Zhang, J. Jiang, B. P. Xie, Y. Song, C. L. Zhang, P. C. Dai, and D. L. Feng, Phys. Rev. X 3, 011020 (2013).
  • (29) Z.-H. Liu, P. Richard, K. Nakayama, G.-F. Chen, S. Dong, J.-B. He, D.-M. Wang, T .-L. Xia, K. Umezawa, T. Kawahara, S. Souma, T. Sato, T. Takahashi, T. Qian, Y. B. Huang, N. Xu, Y. B. Shi, H. Ding, and S.-C. Wang, Phys. Rev. B. 84, 064519 (2011).
  • (30) S. Thirupathaiah, D. V. Evtushinsky, J. Maletz, V. B. Zabolotnyy, A. A. Kordyuk, T. K. Kim, S. Wurmehl, M. Roslova, I. Morozov, B. Bchner, and S. V. Borisenko, Phys. Rev. B 86, 214508 (2012).
  • (31) R. Yu, J-X. Zhu and Q. Si, arXiv:1306.4184.
  • (32) C. L. Zhang et al., Phys. Rev. B 88, 064504 (2013).
  • (33) G. T. Tan, P. Zheng, X. C. Wang, Y. C. Chen, X. T. Zhang, J. L. Luo, T. Netherton, Y. Song, P. C. Dai, C. L. Zhang, and S. L. Li, Phys. Rev. B 87, 144512 (2013).
  • (34) S. W. Oh, A. M. Mounce, J. A. Lee, W. P. Halperin, C. L. Zhang, S. Carr, P. C. Dai, A. P. Reyes, P. L. Kuhn, arXiv: 1307.5366.
  • (35) D. K. Pratt, W. Tian, A. Kreyssig, J. L. Zarestky, S. Nandi, N. Ni, S. L. Bud¡¯ko, P. C. Canfield, and A. I. Goldman, Phys. Rev. Lett. 103, 087001 (2009).
  • (36) A. D. Christianson, M. D. Lumsden, S. E. Nagler, G. J. MacDougall, M. A. McGuire, A. S. Sefat, R. Jin, B. C. Sales, and D. Mandrus, Phys. Rev. Lett. 103, 087002 (2009).
  • (37) T. Das and A. V. Balatsky, Phys. Rev. Lett. 106, 157004 (2011).
  • (38) R. Yu and Q. Si, Phys. Rev. B 84, 235115 (2011); Phys. Rev. B 86, 085104 (2012).
  • (39) Z. P. Yin, K. Haule, and G. Kotliar, Nat. Mater. 10, 932 (2011).
  • (40) R. Yu and Q. Si, Phys. Rev. Lett. 110, 146402 (2013).
  • (41) R. Yu, P. Goswami, Q. Si, P. Nikolic, and J.-X. Zhu arXiv:1103.3259.
  • (42) S. Graser, A. F. Kemper, T. A. Maier, H.-P. Cheng, P. J. Hirschfeld, and D. J. Scalapino, Phys. Rev. B 81, 214503 (2010).
  • (43) S. Pailhs, Y. Sidis, P. Bourges, V. Hinkov, A. Ivanov, C. Ulrich, L. P. Regnault, and B. Keimer, Phys. Rev. Lett. 93, 167001 (2004).
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