鉄系超伝導体,強相関物質の放射光ARPES 吉田鉄平京都大学大学院人間・環境学研究科 2014年1月30日山形大学研究科紹介京都大学大学院人間・環境学研究科自然と人間の共生共生人間学専攻共生文明学専攻総合人間学部人間・環境学研究科相関環境学専攻自然科学系（物理系、化学系、地学系、生物系）大学院入試年２回（９月、２月） Outline 鉄系超伝導体 • 元素置換はキャリアドープになっているか？ • 超伝導ギャップの異方性：ノードの存在クーパー対の引力起源は？強相関物質 • SrVO3の自己エネルギー解析鉄系超伝導体の元素置換効果 Ba(Fe1-xTx)2As2 T= Co, Ni, Cu S. Ideta, T. Y. et al., Phys. Rev. Lett. 110, 107007 (2013). T= Zn S. Ideta, T. Y. et al., Phys. Rev. B 87, 201110(R) (2013). T= Mn H. Suzuki, T. Y. et al., Phys. Rev. B 88, 100501(R) (2013). Collaborators Photoemission, XAS S. Ideta, H. Suzuki, I. Nishi, G. Shibata, K. Ishigami, T. Kadono, A. Fujimori, T. Shimojima, K. Ishizaka, University of Tokyo W. Malaeb, S. Shin* (ISSP) M. Hashimoto, D. H. Lu, Z.-X. Shen, Stanford University E. Sakai, Y. Kotani, H. Kumigashira, K. Ono KEK-PF H. Anzai, Y. Nakashima, M. Arita, A. Ino*, H. Namatame, M. Taniguchi Hiroshima U, HiSOR Samples S. Kasahara, T. Shibauchi, T. Terashima, Y. Matsuda Kyoto U M. Nakajima, S. Uchida University of Tokyo H. Eisaki, K. Kihou, A. Iyo, T. Ito, C. H. Lee, Y. Tomioka AIST Y. Nakashima, S. Yamaichi, M. Matsuo, T. Sasagawa Tokyo Institute of Technology Theory R. Arita (University of Tokyo) H. Ikeda (Kyoto U) 銅酸化物と鉄系超伝導体 CuO2面 FeAs面 CuO2面 E. Pavarini et al., PRL (2001). FeAs面 C. H. Lee et al., JPSJ (2008). CuO2面 K. Kuroki et al., PRB (2009). 銅酸化物鉄系超伝導体モット絶縁体（反強磁性）擬ギャップ金属金属（反強磁性）超伝導電子量ホール量金属金属超伝導電子量超伝導ホール量鉄系超伝導体の相図不純物効果？電子ドープ Ba(Fe1-xCox)2As2 ホールドープ Ba1-xKxFe2As2 等原子価置換 BaFe2(As1-xPx)2 ノードのある超伝導？鉄系超伝導体の不純物効果銅酸化物鉄系超伝導体 Fukuzumi et al. PRL 96’ Nakajima et al., arXiv 13 不純物に強い超伝導？銅酸化物と鉄系超伝導体：バンド分散、フェルミ面 K. Kuroki et al., PRL ‘08 Cuprates electron hole H. Shishido et al, PRL ’10. Multi band H. Sakakibara et al., PRL ‘09 Single band スピン揺らぎを媒介とした超伝導 Theoretical prediction of line-node in SC gap electron hole hole electron hole electron hole electron Re (q) I. Mazin et al., PRL ‘08 electron 秩序パラメータの符号反転 Pn electron Kuroki et al., PRB ’09. Z 不純物置換に弱い超伝導 Fe Pnictogen height Z Transition metal substitution in BaFe2As2 Hole doping Electron doping Ba(Fe1-xTx)2As2 (T = Co, Ni, Cu, Zn) Fe Extra electrons per Fe/TM site Co ex Fe Ni 2e2x Fe Cu Fe 3e3x Zn 4e4x Are doped electrons working as carriers ? Experimental condition of ARPES PF BL-28A Photon Factory (PF) BL-28A •Photon energy h = 33-50 eV •Measuring temperature T= 9, 35 K •Scienta analyzer SES-2002 •Energy resolution ~7-10 meV •Angular resolution ~0.2º HiSOR BL-9A HiSOR BL-9A •Photon energy h = 10-34 eV •Measuring temperature T= 9, 35 K •Scienta analyzer SES-R4000 •Energy resolution ~6-9 meV •Angular resolution ~0.2º Tc and TN of T-Ba122 Ba(Fe1-xTx)2As2 (T = Co, Ni, Cu) Canfield et al., PRB ‘09. Ni et al., PRB ‘10. Are doped electrons working as carriers ? Band structure calculation (Supercell) H. Wadati et al., PRL ’10. Doped electrons are localized ? S. Konbu et al., JPSJ ’11. Rigid-band model ? Valence band spectra of Ni-122 and Cu-122 S. Ideta, T. Y. et al., PRL ‘13. Fermi surface of Ba(Fe1-xTx)2As2 T= Ni T= Cu electron hole S. Ideta, T. Y. et al., PRL ‘13. Carrier number estimated from FS volume nh: hole carrier nel: electron carrier Part of the doped electrons do not contribute to the formation of FSs. S. Ideta, T. Y. et al., PRL ‘13. Tc and TN plotted as a function of nel -nh Phase diagrams for different transition metal substitution accord with each other. S. Ideta, T. Y. et al., PRL ‘13. Valence‐band spectra of Zn‐Ba122 Ba(Fe1-xZnx)2As2 TN~140 K H. Wadati et al., PRL ‘11. Zn 3d level ~ 10 eV below EF S. Ideta, T. Y. et al., PRB ‘13. Fermi surface and band dispersions of Zn‐Ba122 Folded FSs and band dispersions have been observed. S. Ideta, T. Y. et al., PRB ‘13. Fermi surface in the k//‐kz plane x=0.08 x=0.25 Shapes of the FSs for different doping level are nearly the same. S. Ideta, T. Y. et al., PRB ‘13. Density of states for T‐Ba122 10 10 10x Total electron number 6 10(1-x) 6+x 6+4x S. Ideta, T. Y. et al., PRB ‘13. Phase diagram of Mn-122 Ba(Fe1-xMnx)2As2 x<0.74 x>0.74 A. Thaler et al. PRB 84 144528 (2011) M.G. Kim et al. PRB 83 054514 (2011) Intensity (arb. units) Partial Density of States of Mn3d orbitals Mn PDOS is distributed around EB=2~12eV H. Suzuki, T. Y. et al., PRB ‘13. Partial density of states Emergence of local magnetic moments due to on-site Coulomb potential U and Hund coupling J H. Suzuki, T. Y. et al., PRB ‘13. Outline 鉄系超伝導体 • 元素置換はキャリアドープになっているか？ • 超伝導ギャップの異方性：ノードの存在クーパー対の引力起源は？強相関物質 • SrVO3の自己エネルギー解析鉄系超伝導体の超伝導ギャップ、ペアリング対称性 T. Yoshida et al., arXiv:1301.4818. s-波的超伝導ギャップ Ba1-xKxFe2As2 x=0.4 s-wave-like full gap superconductivity? s++ ? s+- ? H. Ding et al., EPL ‘08 Superconducting gap in iron pnictide superconductors s-wave-like full gap (Ba,K)Fe2As2 Octed line node Tc~ 4K Tc~ 37K H. Ding et al.,EPL ’08 KFe2As2 K. Okazaki et al., Science ’12 等原子価置換 BaFe2（As1-xPx）2 Phase diagram of BaFe2(As1-xPx)2 BaFe2As2 BaFe2P2 H. Shishido et al, PRL ’10. S.Kasahara et al., PRB ‘10. •Number of Fe 3d electron is constant. •Pnictogen height hPn decreases. T. Yoshida et al., PRL ‘11 BaFe2(As1-xPx)2 鉄系超伝導体の超伝導ギャップ超伝導秩序変数  水平ノード＠ホールフェルミ面ホール面電子面 K. Suzuki et al., JPSJ ‘11 ループノード＠電子面ノードほとんどの物質ではs-波 BaFe2(As,P)2などはノード（節）の存在が示唆されている。運動量空間のどこにノードが存在する？ I. Mazin et al., PRB ‘10 SC gap of BaFe2(As1-xPx)2 in the hole FSs Laser ARPES Horizontal node is unlikely ? T. Shimojima et al., Science `11. SC gap of BaFe2(As1-xPx)2 x= 0.30 Horizontal node ? K. Suzuki et al., JPSJ ‘11 Isotropic gap in the electron FSs Y. Zhang et al.,Nature Physics `12. Superconducting gap for hole FSs around the Z point Intensity (arb. units) h= 35eV Clear gap at low T x= 0.30, Tc=30 K Pseudogap (cf. S. Kasahara et al., Nature ‘12.) Inplane anisotropy for hole FS Superconducting peak Gap anisotropy Intensity (arb. units) Symmetrized EDCs Isotropic SC gap coexists with pseudogap x= 0.30, Tc=30 K h= 35eV kz dependence of the SC gaps for the hole FSs Outer FS Middle FS Inner FS x= 0.30, Tc=30 K SC gap in the electron FSs of BaFe2(As1-xPx)2 x= 0.30, Tc=30 K h=40 eV SC gap in the electron FSs of BaFe2(As1-xPx)2 x= 0.35, Tc=28 K h=22 eV Summary of the observed SC gap Electron FSs Hole FSs outer hole FS kz dependence Spin fluctuation mechanism Theoretical prediction of line-node in SC gap Spin fluctuation mechanism Absence of xy FS Node in SC gap Kuroki et al., PRB ’09. Three hole FSs are observed. Orbital fluctuations SC order parameter determined by ARPES Loop node in the electron FS   Electron FSs Hole FSs Saito, Onari, Kontani et al., PRB 13 Summary (Iron-based superconductor) We have performed an ARPES study of the iron pnictide superconductors. • Impurity effects in Ba(Fe1-xTx)2As2 Deviation from rigid-band model • Nodal superconductivity in BaFe2(As1-xPx)2 Loop-like node in the electron FS ? Orbital fluctuation is required to explain the observed gap anisotropy. Outline 鉄系超伝導体 • 元素置換はキャリアドープになっているか？ • 超伝導ギャップの異方性：ノードの存在クーパー対の引力起源は？強相関物質 • SrVO3の自己エネルギー強相関電子系SrVO3の自己エネルギー S. Aizaki et al., Phys. Rev. Lett. 109, 056401 (2012). 共同研究者相崎真一，滝沢優, 出田真一郎，藤森淳吉松公平，蓑原誠人，堀場弘司*，尾嶋正治* K. Gupta, P. Mahadevan 組頭広志* 東大理東大工 S. N. Bose研究所高エネ研PF Electronic structure of SrVO3 dxy dHvA ARPES Bulk SVO Thin film SVO kz ky dyz kx dzx I. H. Inoue et al., PRL ‘02. SrVO3 ( d1) Incoherent Coherent T. Yoshida et al., PRB ’10. Energy relative to EF (eV) T. Yoshida et al., PRB ’10. M. Takizawa et al., PRB ’09. Self-energy of strongly correlated system ARPES Phenomenological model of self-energy DMFT M. Takizawa et al., PRB ’09. Extraction of the self-energy from experimental data. 「強相関電子論の基礎」藤森淳 Sample and Experimental conditions Photon Factory BL-28A Sample : Synchrotro n radiation Laser MBE Chamber SrVO3 / SrTiO3 (001) Analyzer : SCIENTA SES-2002 Photon Energy : h = 50-110 eV Temperature : T ~ 15 K Resolution : Eres ~ 15 meV Pressure : better than 10-10 Torr Photoemission Chamber Preparation Chamber Sample Entry K. Horiba et al., Rev. Sci. Instrum. 74, 3406 (2003). ARPES spectra of SrVO3 thin film Band dispersion Coherent Incoherent Fermi surface Band dispersions and self-energies near EF QP band dispersion Re Self-energy Kink ~ 60meV Electron-phonon coupling cf. High-Tc cuprates One can not determine the self-energy in the high-energy region. Self-energy deduced from the ARPES spectra start ARPES spectra A(k,) = - ImG(k, )/ Kramers-Kronig (KK) relation ReG(k, ) Initial data of A(k,) G (k ,  )  •k=kF A(k,)=I()+I(-) 1    k  ( k ,  )  k  Re (k ,  )  i Im (k ,  )    •k<kF A(k,)=I() () =0 () new ( k ,  ) 1 G (k ,  ) Electron-hole symmetry Im (k ,  )  Im (k , ) Re (k ,  )   Re (k , ) Self-energy deduced from the ARPES spectra Self energy (average) A(k,) Re k=kF k=0 Im LDA+DMFT k=kF k=0 Nekrasov et al., PRB ’06. Simulation of the spectral weight A(k,w)of SrVO3 Simulation of A(k,)  1   G ( k , 0 )    k  Re  k Bare dispersion k has been obtained. ARPES data The QP dispersions and the incoherent part are successfully reproduced by the simulation. Pole and zero surfaces of the Green function Energy scale of Green function Self energy from ARPES k=0 ReG(k,)   1 1  ( )   an     i    i      n n n n n   zero 2D Hubbard model pole pole Pole (QP) Zero (ReG=0) S. Sakai, Y. Motome, M. Imada, PRL ‘09. まとめ (SrVO3) 薄膜SrVO3のin-situ ARPESを行い、インコヒーレント部分も含む自己エネルギーを決定した。 • 低エネルギーキンク ~60 meV 銅酸化物と同様のエネルギーペロブスカイト型酸化物sに特徴的なフォノン • クラマース・クロニッヒ関係を使って、ARPESスペクトルから自己エネルギーの広いエネルギー領域で求めることができた。 • 電子-電子相互作用のエネルギースケール ~0.7 eV インコヒーレントピーク ~1.5 eVを形成 zero surface ~0.7 eV