Fermi surface, spin fluctuation and pairing symmetry in the two-dimensional Hubbard model

Abstract

The numerical studies of pairing correlation for the two simensional Hubbard model have been conducted to resolve the discrepancy between the numerically negative result for superconductivity and the results by the analytic calculations with diagrammatical techniques, which have supported the spin fluctuation mediated pairing in the model. Through the numerical studies, a possibility of the link between the shape of the Fermi surface and the spin correlation/pairing correlation among various systems has been explored. The two dimensional Hubbard model with nearest neighbor (nn, t), next nearest neighbor (nnn, t'), and third neighbor (t'') hoppings have been considered in order to take account of various scattering processes. The Quantum Monte Carlo (QMC) has first been conducted on the simplest case of nn hoppings taking 46 electrons in 8 x 8 = 64 sites. The QMC result for the d(sub (x(exp 2)-y(exp 2))) pairing correlation was shown in figures, and it was found that the result was consistent with the spin fluctuation mediated pairing picture. The pairing symmetry affected by the shape of the Fermi surface has been studied for the cases of both hole and electron doped high T(sub c) copper oxides. From the QMC result for the hole doped case, it was found that the d(sub (x(exp 2)-y(exp 2))) pairing agreed with the expectation from the spin fluctuation mediated pairing picture. The QMC result for the case of electron doping has shown an enhancement of the d(sub (x(exp 2)-y(exp 2))) correlation, although the enhancement was smaller than in the hole-doped case. And this result for the electron doping suggested the coexistence of the d(sub (x(exp 2)-y(exp 2))) and the (square root of 2) x (square root of 2)d(sub xy) pairing. The link between the Fermi surface and the spin fluctuation/pairing symmetry in organic superconductors has been investigated. The numerical results by QMC method supported the possibility of anisotropic pairing superconductivity in the Hubbard model on lattices representing copper oxide and organic superconductors.

2次元ハバード模型において、スピンゆらぎ媒介型の対形成を裏付けるダイアグラム手法を用いた解析計算結果と、超伝導性に対して否定的な数値計算結果の間の不一致を解明するために、対形成相関の数値的研究を行った。数値研究を通して、様々な系におけるフェルミ面の形状とスピン相関/対形成相関間のつながりの可能性を調べた。種々の散乱過程を考慮に入れるため最隣接(nn, t)、第2最隣接(nnn, t')および3次隣接(t'')ホッピングの2次元ハバード模型を考案した。8×8=64サイトに46個の電子をとる最も単純なnnホッピングの場合について、量子モンテカルロ(QMC)法を適用した。d(sub (x(exp 2)-y(exp 2)))対形成相関についてのQMC結果を図示した。QMC法による結果はスピンゆらぎ媒介対形成図と一致することが分かった。正孔ドープおよび電子ドープ高臨界温度銅酸化物の両方について、フェルミ面形状が影響する対形成対称性を研究した。正孔ドープの場合のQMC結果から、d(sub (x(exp 2)-y(exp 2)))対形成はスピンゆらぎ媒介型対形成図に基づく予測と一致することが分かった。電子ドープの場合のQMC結果は、d(sub (x(exp 2)-y(exp 2)))相関の増大を示したが、その増大の度合いは正孔ドープの場合よりも小さかった。電子ドープに対する結果は、d(sub (x(exp 2)-y(exp 2)))対形成と√2×√2d(sub xy)対形成が共存することを示唆した。有機超伝導体におけるフェルミ面とスピンゆらぎ/対形成対称性間のつながりを検討した。QMC法による数値計算結果は、銅酸化物および有機超伝導体を表す格子に対するハバード模型では、異方的対形成超伝導性である可能性を裏付けた。