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Multi-orbital Analysis on the Superconductivity in Na x CoO 2 yH 2 O

Multi-orbital Analysis on the Superconductivity in Na x CoO 2 yH 2 O. Youichi YANASE, Masahito MOCHIZUKI and Masao OGATA J. Phys. Soc. Jpn. 74 (2005) 430. 2006/1/30 Suzuki-Kusakabe group Fumiya Kanetake. Contents.

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Multi-orbital Analysis on the Superconductivity in Na x CoO 2 yH 2 O

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  1. Multi-orbital Analysis on the Superconductivity in NaxCoO2 yH2O Youichi YANASE, Masahito MOCHIZUKI and Masao OGATA J. Phys. Soc. Jpn. 74 (2005) 430 2006/1/30 Suzuki-Kusakabe group Fumiya Kanetake

  2. Contents • Introduction- NaxCoO2yH2O vs. High-Tc cuprates - Gap function (order parameter) • Theory- Multi-orbital Hubbard model- 2nd order perturbation Green’s function method • Calculation Result • Summary

  3. NaxCoO2yH2O vs. High-Tc cuprates(La2-xSrxCuO4) G. Baskaran Phys.Rev.Lett.91(2003)097003 超伝導 黒木和彦・青木秀夫 K. Takada et al , Nature 422 (2003) 53 3

  4. NaxCoO2yH2O vs. La2-xSrxCuO4 eg NaxCoO2 yH2O…NaxCoO2 →(Na1+)xCo(4-x)+(O2-)2 →3d5+xmain conduction band: t2g(dxy,dyz,dzx) ( (5+x)/6 electron ) La2-xSrxCuO4 …La2-xSrxCuO4→(La3+)2-x(Sr2+)xCu(2+x)+(O2-)4→3d9-xmain conduction band: dx2-y2 ( (1+x)/2 hole ) 3d t2g x2-y2 eg 3d 3z2-r2 t2g xy yz,zx Na1/3CoO2 K.-W. Lee et al,Phys.Rev.B.70(2004)045104 La2CuO4 L.F.Mattheiss Phys.Rev.Lett.58(1987)1028 4

  5. dx2-y2-wave + -- -- - - + ++ Gap function (order parameter) Gap function indicates Energy gap, Symmetry of superconductivity. s-wave, p-wave, d-wave, f-wave…(from symmetry of lattice)BCS S.C. … s-wave.The others …not s-wave. Gap equation f1-wave s-wave π/a p-wave + - - ++ -- - ky + + + - -π/a -π/a kx π/a 5

  6. Motivation • They want to decide gap function of NaxCoO2 yH2O because it has not been decided in experiment and theory. • It is necessary to consider 3-orbital that is not considered in theory up to now. 6

  7. Single-orbital Hubbard model It suites Electron localized system. ( f.e. d-orbital, f-orbital)parameters・Hopping energy (kinetic energy) t (t1,t2,t3…)・On site coulomb energy (potential energy) U t2 t1 t3 7

  8. Multi-orbital Hubbard model NaxCoO2yH2O…main conduction band: t2g (dxy, dyz, dzx)3-orbital⇒3-orbital Hubbard model Hopping energy tij fits LDA band structure. ky εk kx tayz,zy taxy,xy Fitting - + + - - + - + - - + + - - + + K.-W. Lee et al, Phys.Rev.B.70(2004)045104 8 a=0.8

  9. 2nd order perturbation Green’s function method This method considers only 1st and 2nd order Feynman diagrams. V(k,k’) 2nd 3rd 1st k k’ + + = + + + + -k -k’ + + + + more + + + + +… 2nd order perturbation 3rd order perturbation 9

  10. Method of decision of gap function • Setting of Parameters (‘a’, U, U’, ne)‘a’: hopping energy scale, U: on-site intra-orbital coulomb energy, U’: on-site inter-orbital coulomb energy, ne: hole density • Calculation of Green’s function • Solving gap equation 10

  11. Calculation Result (U’=U/2) Hopping energy scale • p-wave and f1-wave is dominant. (a little difference) • There is no method of decision of ‘a’. Eigen value 11 (a=0.8) hole density

  12. Calculation Result (U’=U/2,a=0.8) 3-orbital effective 2-orbital • The rank doesn’t change. • Absolute value of λe changes. 12

  13. Calculation Result (ne=0.35, a=0.6, U’=U/3) • There is no reversal of p-wave and f1-wave. • There is no method of decision of U,U’. → Kusakabe theory (cond-mat/0505703). 13

  14. Summary • The calculation results indicates that p-wave or f1-wave gap function is stable. (little difference) • There is no method of decision of ‘a’ and U,U’ in this paper. 14

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