向列態在鐵基超導體中是較為奇特的態，其成因有許多種可能，仍尚無定論。目前普遍認為向列序的來源與自旋有密切的關係，而本研究所要探討的向列序則是種由兩個不同振幅的反鐵磁條紋相互正交穿插所形成的序。文中我們從正方形晶格上的雙軌道平均場哈密頓量出發，其包含了反鐵磁序與超導序的競爭。而後在不同的電子濃度的情形下，找到所對應的純超導態、自旋密度波態與向列態。在計算向列態的局域態密度時我們發現，當加入系統內的雜質沿著磁化強度較弱的方向排列並互相靠近時，雜質間的量子干涉效應會抑制反鐵磁序對局域磁矩的增強效應，使得雜質共振峰的位置向費米能量靠近。最後我們針對對角化大型矩陣的演算法，建立了關於中央處理器與顯示卡平行運算間的基準測試，且對於有限硬體設備提出了混合編成的有效解決方案。

The nematic state is an exotic state in the iron-based superconductors and the origin is still debated, but generally believed that the source of the nematic order is closely related to spin. In this thesis, we consider a nematic order which consists of two different amplitudes of antiferromagnetic stripes. The stripes are orthogonal and interpenetrating each other. We start from the two-orbit mean-field Hamiltonian on a square lattice which contains the competition between the antiferromagnetic order and the superconducting order. Then find the pure superconducting state, the spin density wave state, and the nematic state at the different electron doping levels. We found that when the impurities are aligned with the direction of weaker magnetization in the nematic state and get close to each other, the quantum interference effect between two impurities will suppress the enhancement effect of the local moments by the antiferromagnetic magnetization. The suppressed local moments will push the impurity resonance peak toward the Fermi energy. Finally, we benchmark the CPU and GPU parallel algorithm of diagonalizing large matrix and propose a mixture solution for the limited hardware equipment.

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