雙軌道重整化平均場論探討簡化鐵基超導體模型

Renormalized Mean Field Theory for a Simpli.ed Two-Orbital Model of Iron-Based Superconductors

黃信銘(Shin-Ming Huang)

指導教授 ： 李定國

國立清華大學/理學院/物理學系/博士(2010年)

https://doi.org/10.6843/NTHU.2010.00331

摘要

As more and more experimental results indicate that the iron-based superconductors are intermediately correlated systems close to the Mott insulator, a starting point from the strong coupling side as we believe would be more appropriate. In the thesis, we use the localized spin model—two-orbital t-J1-J2 model—to study the superconducting state. First, we study the model without considering on-site correlation effect. By group theory, the superconducting order parameters are written down for the s-wave (A_1g) and the d-wave (B_1g). The phase diagram of the superconducting state shows that these two symmetry states are competitive with very close energies. The d-wave state is favorable for large J1, while the s-wave state for large J2.
Next, we examine the correlation in the model, including the intra- and inter-orbital Hubbard interactions and also the Hund’s coupling. We use the Gutzwiller wavefunction to deal with the correlation effect. The Gutzwiller wavefunction combines both the itinerant and the localized electronic natures, which would be a good way to study the intermediately correlated system. The Gutzwiller projector can be replaced by renormalization factors after using Gutzwiller approximation. By Gutzwiller approximation, the Hamiltonian is renormalized to give a renormalized bandwidth and spin coupling constants. With the on-site interaction increased, the bandwidth will be reduced but the spin couplings will be increased. Moreover, the Gutzwiller projector will mix the intra- and inter-orbital spin couplings together and consequently enhance the inter-orbital pairing. Because of symmetry, only the s-wave state allows the inter-orbital pairing. Therefore, the on-site interaction will make the s-wave state more stable against the d-wave one. When the inter-orbital pairing becomes stronger, the SC gaps on the electron pockets will be more anisotropic with a hump along the (π,0)-(0,π) directions.

關鍵字

鐵基超導體 ； 局域自旋 ； 超導 ； 重整化平均場論

並列摘要

隨著越來越多的實驗顯示，鐵基超導體系統有著中等程度的交互作用，靠近於Mott絕緣體邊界，因此我們認為從強相關系統模型出發是個合適的出發點，於是我們採用局域電子自旋模型—雙軌道t-J_1-J_2模型—來研究鐵機超導體的超導態，並且去探討局域交互作用的影響。
首先，我們忽略電子局域的關聯性，利用群論，寫下超導的序參量，由平均場論得出超導的相位圖。我們發現超導相位圖裡，ｓ波(A_1g)與ｄ波(B_1g)兩態互相競爭，J_2幫助ｓ波，而J_1幫助ｄ波。
接下來，我們考慮電子局域關聯，引入同、異軌道Hubbard交互作用以及Hund偶合，我們使用Gutzwiller波函數來表示此交互作用的影響。Gutzwiller波函數描述一個既有流動又有局域特性的電子系統，因此我們認為這是一個好的方法來研究這中等程度交互作用的系統。利用Gutzwiller近似，將局域關聯的效果表現在重整化能帶以及重整化自旋偶合常數上，而得到的重整化漢密頓量將描述超導準粒子的運動。隨著局域交互作用的增加，能帶寬度會減小而自旋偶合會增強。此外，Gutzwiller投射運算子會混雜同軌道與異軌道自旋偶合，因而增加異軌道電子配對。由於對稱性的關係，只有ｓ波允許異軌道電子配對，因此局域交互作用可以讓ｓ波變得比ｄ波更穩定。而當異軌道電子配對增強時，費米面上的超導能隙會變得越各向異性，在(π,0)-(0,π) 方向造成隆起。

並列關鍵字

iron-based superconductor ； spin model ； Gutzwiller approximation ； superconductivity ； renormalized mean field theory

參考文獻

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