New Directions of Superconducting Nanostructures Nagoya 9 4

New Directions of Superconducting Nanostructures, Nagoya, 9. 4 -5, 2009 Unconventional superconductivity from multiple spin fluctuation modes in the iron pnictide superconductors University of Electro-Communications, JST, TRIP Kazuhiko Kuroki Collaborators： Hidetomo Usui (Univ. Electro-Comm. ) 　 Seiichiro Onari (Nagoya Univ. , JST, TRIP)　　　　　 Ryotaro Arita（Univ. of Tokyo, JST, TRIP） Yukio Tanaka (Nagoya Univ. , JST, TRIP) Hiroshi Kontani (Nagoya Univ. , JST, TRIP) Hideo Aoki (Univ. of Tokyo, JST, TRIP)　　　　　　　　　　　　　　 references: Phys. Rev. Lett. 101, 087004 (2008), ibid 102, 109902(E)(2009), Phys. Rev. B 79, 224511 (2009)

Discovery of SC in La. Fe. As. O

La. Fe. PO Tc～ 4 to 7 K P As and F doping gives 26 K

High Tc up to 55 K by La->Sm, Nd iron-base tional nven co cs Tc (K) oxid liq N La. Fe. As. OF organi liq 4 He d es room T 2008 year

Theoretical study from the early stage First principles band calculation : Lebegue, Singh, Ishibashi et al. , Yildirim, Cao et al, Dong et al. . Electron phonon interaction : Boeri et al. Strong correlation effects : Haule et al. , … Spin fluctuation mediated pairing : Mazin, Kuroki, Wang, Eremin, Nomura, Raghu, Ikeda, Graser… Pairing by polarization : Sawatzky et al.

Lattice structure and parameters La. Fe. As. O=“La 1111” unit cell tetrahedral coodination of As top view of the Fe. As layer z. La=0. 14154, z. As=0. 6512

Band Calculation Comparison with PES Fe 3 d G X M G plane-wave basis set (Quantum-ESPRESSO) exchange correlation: Perdew-Burke-Wang cutoff energy: 40 Ry 1000 k-point meshes, Maleeb et al, JPSJ 2008

Maximally Localized Wannier functions Maximally localized Wannier orbitals : Marzari and Vanderbilt, PRB 56, 12847 (1997) Z 2 La 4 f XZ Fe 3 d YZ x 2 -y 2 O 2 p As 4 p Y XY Uses the code developed by Mostofi et al. X As 4 p are effectively included

Unfolding the Brillouin Zone: 5 band model unfolded Fe As reduced ed ld fo l a in ig or original(folded) BZ unfolded BZ

Character of the bands and Fermi surface mainly XZ, YZ XY hole Z 2 g mainly X 2 -Y 2= xy heavily entangled ! electron

Effective Hamiltonian i, j: site、m, n: orbitals intraorbital U, interorbital U’, Hunds coupling J, pair hopping J’ as parameters assume U, U’, J, J’ independent of the orbitals, U=U’+J+J’ evaluation from first principles: K. Nakamura et al, JPSJ 77 (2008) 093711 V. Anisimov et al, 0810. 2629 T. Miyake et al, JPSJ 77 (2008) Suppl. C 99 non-doped system d 6 band filling n (number of eletron /site)= 6, doped system n=6+x (x: F content), mainly 10% doping, n=6. 1

Multiorbital RPA Green’s function: Cf. Wang, Ikeda, Nomura…. . dispersion: irreducible susceptibility: li : orbital indices spin susceptibility: charge (orbital) susceptibility: 3 dimensional calculation 32 x 4 k-point meshes, 512 Matsubara frequencies

Linearized Eliashberg equation effective interaction for singlet: effective interaction for triplet: linearized Eliashberg eq. : l=1 at T=Tc, l can used as a measure for the strength of SC instability Dl, m (orbital representation) Db (band representation) by unitary transf.

Linearized Eliashberg equation l Tc T l=1 at T=Tc Dl, m (orbital representation) Db (band representation) by unitary transf.

Linearized Eliashberg equation l case B case A T l at a fixed T can used as a measure for the strength of SC instability Dl, m (orbital representation) Db (band representation) by unitary transf.

Spin fluctuation mediated SC Example : square lattice antiferromagnetic spin fluctuations possibility of d-wave superconductivity at q ～Q V(q)>0 d-wave gap nodes in the gap are “necessary evil” in the spin fluctuation medaited pairing

HTC due to Disconnected Fermi surfaces Kuroki&Arita, 2001, 2002 spin fluctuation (repulsive interaction) sign change of the gap necessary disconnected Fermi surface: sign change without nodes of the gap intersecting the Fermi surface

RPA result: spin susceptibility n=6. 1 (10% dope), Nx=32, Ny=32, Nw=1024, T=0. 02, U=1. 2, U’=0. 9, J=J’=0. 15(e. V) eigenvalue of the spin suceptibility matrix (p, 0) unfolded= (p, p) folded neutron scattering C. de la Cruz Nature 453, 899 (2008) also from first principles calculations: I. I. Mazin et al Phys. Rev. Lett. 101, 057003 (2008) J. Dong et al. , Europhys. Lett. 83 27006 (2008) S. Ishibashi et al　J. Phys. Soc. Jpn. 77 (2008) 053709 T. Yildirim, Phys. Rev. Lett. 101 (2008) 057010

“Orbital dependent” nesting b-g nesting dominating Mazin, Nomura, Ikeda, Wang, KK, Chubukov, Ji, Daghofer…. Graser et al. Mishra et al. KK et al. b 1 -b 2 nesting dominating KK et al. , Graser et al, Yanagi…. .

For La. Fe. As. O (with experimentally determined lattice structure) U=1. 2, U’=0. 9, J=J’=0. 15 n=6. 1 (10% dope) T=0. 02 (e. V) gap in the band representation Erratum : PRL 102, 109902 (2009) a 1 a 2 b 1 fully gapped sign rev. s-wave dominates

Sign rev. s-wave : consistencies/inconsistencies with experiments NMR relaxation rate : Ikeda, Graser et al, Nagai et al, Kariyado&Ogata, Dolgov et al… Superfluid density, penetration depth : Nagai et al, Dolgov et al. , Bang… Resonance peak at (p, 0) : Maier&Scalapino…. Impurity effect : Parker et al, Chubukov et al, Mishra et al, Onari&Kontani… Tunnelling spectroscopy, point contact junction : Onari&Tanaka, Golubov et al, Linder et al… Doping dependence of Tc : Ikeda, Fuseya et al… …. . …… full gap for arsenides, but sign change still controversial

Material dependence of Tc regular tetrahedron Nd Tb La La. Fe. PO C. -H. Lee et al, JPSJ 77 (2008) 083704 K. Miyazawa et al, 0812. 4599 also by J. Zhao, Nat. Mat. 7, 953 (2008)

Material dependence of SC gap While a number of experiments suggest fully open gap (with multiple gaps or anisotropy) for the arsenides, for La. Fe. PO, recent experiments show presence of line nodes in the SC gap penetration depth Fletcher et al, PRL 102, 147001 (2009) also Hicks et al. , ar. Xiv: 0903. 5260 thermal conductivity M. Yamashita et al. , ar. Xiv: 0906. 0622

Presence/Absence of nodes n n Mishra et al. , PRB 79, 094512 (2009) impurity effect Parker et al. ar. Xiv 0904. 4832, coexistence of SDW Chubukov et al. ar. Xiv 0903. 5547, doping dependence Thomale et al. ar. Xiv 0906. 4475, doping dependence

Pnictogen “height” La. Fe. PO h P = 1. 14 Å La. Fe. As. O h As = 1. 32 Å Nd. Fe. As. O h. As = 1. 38 Å

“high” “low” also by Singh&Du, Vildosola et al, others ＞＞ b-g nesting dominates b 1 -b 2 nesting dominates ～ ＝ KK et al. , PRB 79 (2009) 224511

“Height” as a switch between high Tc nodeless and low Tc nodal pairings U=1. 2, U’=0. 9, J=J’=0. 15 n=6. 1 (10% dope) T=0. 02 (e. V) low Tc nodal high Tc nodeless

“Frustration” in momentum space small h. Pn frustrated nodal low Tc SC unfolded BZ large h. Pn nonfrustrated full gap high Tc SC on disconncted FS

HTC due to Disconnected Fermi surfaces Kuroki&Arita, 2001, 2002 spin fluctuation (repulsive interaction) sign change of the gap necessary disconnected Fermi surface: sign change without nodes of the gap intersecting the Fermi surface

Lattice constant dependence smaller a larger hopping for XZ, YZ, but X 2 -Y 2 nearly unchanged unfavorable for SC smaller c larger hopping for X 2 -Y 2 but XZ, YZ nearly unchanged unfavorable for SC

Schematic “Phase diagram” 22426 P 0. 37 the numbers are the eigenvalue of the Eliashberg equation for T=0. 02 e. V, n=6. 1 Nd Dy La h Pn P As-Fe-As angle　a small lattice constants a, c small

Summary n 5 band model from first principles calculation n Pnictogen height can act as a switch between high Tc nodeless and low Tc nodal pairings n All five Fermi surfaces are fully gapped in the high Tc state despite the sign change due to the disconnectivity of the Fermi surface n Lattice const. also are the factors controlling Tc　 height × lattice const = Lee et al’s experiment n Strong possibility of gapless pairing (either nodal s-wave or d-wave ) in La. Fe. PO, as observed experimentally