超导是一种具有零电阻特性和完全抗磁性的宏观量子现象，自从它在1911年被发现以来，人们一直致力寻找新的超导体，尤其是具有高超导临界转变温度（T_c）的材料。超导研究发展至今，已经有许多高温超导材料被发现，如铜酸盐、铁基超导材料以及高压氢化物超导体等。
铁基超导材料在2008年被发现，现已迅速发展成为仅次于铜氧化物超导体的第二大高温超导家族，对这类材料的探究有助于深入了解高温超导机理。近些年，一种新的1144型铁基超导材料CaKFe₄As₄由于具有相对较高的晶体对称性、很高的临界电流密度以及上临界磁场，并且能被合成高质量的单晶样品，而受到广泛的关注。这一材料可以看作是完美掺杂的体系，其母体材料本身已表现出35 K的超导性。此外，实验发现它在离子掺杂时存在一种独特的非共线的“刺猬”型自旋涡旋相（hedgehog-SVC），并与超导态共存。本文基于密度泛函理论计算方法，从系统总能量和Fe-As四面体结构两个维度来确定反铁磁基态，并给出了其在不同自旋密度波相下的电子结构性质。弛豫计算表明，条纹自旋密度波（SSDW）相中Fe-As四面体的结构变化更小，并且其键角和阴离子高度更有利于CaKFe₄As₄材料中As介导Fe局域磁矩间的反铁磁超交换相互作用的实现，从而达到更高的T_c。此外，较于hedgehog-SVC相，SSDW相在能量上是更有利的。由于理论计算和实验测量的局域磁矩在大小上存在差异，因此通过调节不同的磁矩约束值，来探究Fe磁矩大小对材料电子结构和磁性质的影响。结果表明Fe磁矩与Fe-As相互作用和磁涨落存在着较强的耦合，表现在随着Fe磁矩的减弱，同一个四面体层中上下两个As-As之间的垂直距离h _As-As随之减小，两种自旋密度波相的系统能量差减小。此外，文章中还分别探究了该母体材料在hedgehog-SVC和SSDW两种相的电子结构性质。基于费米能级附近的态密度分析，在磁对称性的影响下，hedgehog-SVC相中简并的Fe-3d_xz和3d_yz轨道，在SSDW中变为非简并轨道。随着Fe磁矩的降低，洪德耦合作用的减弱使得Fe-3d原子轨道的劈裂减小，SSDW相中3d_xz和3d_yz轨道也变得近简并。两种自旋密度波相的费米面结构非常相似，均表现出三维特征。但是，在Fe磁矩约束到0.2 µB的实验值时，两者的电子型口袋均消失，并且沿高对称路径X-M和R-A的能带出现近简并。
非常遗憾的是，目前仍没有明确的统一理论可以用来指引这些超导体走向“室温超导”。近些年，高压氢化物超导体的发现又一次推起了高超导临界转变温度的研究热潮，它们和简单金属一样都符合 BCS 超导理论，在极高的压力下可以达到近室温的超导转变温度。例如，具有高度对称笼状结构的LaH₁₀在170~200GPa下其转变温度可以达到250 K，YH₉在201 GPa的高压下具有243 K的转变温度。然而，实现这些材料的超导态所需的极高压力为样品制备和实际应用带来很多困难。因此，寻找更低压力下具有高T_c的氢化物超导材料是目前超导领域的重要研究方向之一。本文预测了一种新型三元超导化合物Mg₃InH，它在环境压力下具有 36 K 的超导转变温度。该材料是在金属钙钛矿框架的体心位置引入H原子，通过Mg-H和In-H离子键合帮助构成稳定结构。研究表明，Mg₃InH是一种典型的声子介导的超导材料，其高T_c可归因于H的振动产生的高频声子与金属离子提供的传导电子之间存在的较强的电子-声子耦合，其电子-声子耦合强度高达0.97。这一发现为寻找环境压力下的新型三元氢化物高温超导材料提供了新的策略。此外，电子局域函数显示了In和Mg原子间隙处有较大的局域化的间隙电子，这些电子来自于Mg原子贡献的剩余电子积累并围绕In原子呈笼状分布。间隙电子在费米能级处具有较高的态密度，表明Mg₃InH可能是一种新型的电子氢化物超导材料。

Superconductivity is a macroscopic quantum phenomenon with zero resistance and perfect diamagnetism. Ever since its discovery in 1911, people have been searching for new superconductors, especially the materials with high superconducting critical transition temperatures (T_c). So far, a lot of high-temperature superconductors have been discovered, such as cuprates, iron-based superconductors, and high-pressure hydride superconductors.

Iron-based superconductors were discovered in 2008, which have rapidly developed into the second largest family of high-temperature superconducting materials after cuprates. The study of these materials will help to deepen the understanding about the mechanism of high-temperature superconductivity. In recent years, a newly synthesized 1144-type iron-based superconductor, CaKFe₄As₄, has received extensive attention due to its high degree of crystal symmetry, high critical current density and upper critical magnetic field, and can be synthesized as high-quality single crystal samples. The material can be regarded as a perfect doped system, and its parent compound itself can exhibit superconductivity of 35 K. In addition, it was found that the system also has an unique non-collinear "hedgehog" type spin vortex phase (SVC) when doped, which can coexist with the superconducting states. Based on the density functional theory, the antiferromagnetic ground state of CaKFe₄As₄ is determined from the two respects of total energy and the structure of Fe-As tetrahedra, and its electronic structure properties in different phases are given. After relaxation, the Fe-As tetrahedra in the striped spin density wave (SSDW) phase are less structurally variable, and their bond angles and anion heights are more favorable for realizing the As-bridged antiferromagnetic superexchange interactions between the local magnetic moments of Fe, leading to higher T_c. Compared with the SVC phase, SSDW phase is more favorable in energy. Since there is a significant difference in the magnitude of the local magnetic moment between the theoretical calculations and experimental measurements, we further investigate the effect of the amount of magnetic moments on the electronic structure and magnetic properties of the material by adjusting the constraint values of the magnetic moments. The results reveal that there exists a strong coupling among the Fe magnetic moment, the Fe-As interaction, and the magnetic fluctuations, as manifested by the fact that the perpendicular distance h _As-As between the upper and lower As in the same tetrahedra  decreases with the weakening of the Fe magnetic moment, and the energy difference between the two spin-density-wave phases decreases. 

In addition, the electronic structural properties of the parent material under the SVC and SSDW phases are studied. Based on the density of states analysis near the Fermi level, the degenerated Fe-3d_xz and Fe-3d_yz orbitals in the SVC phase become non-degenerate orbitals in the SSDW phase due to the restriction of the symmetry. With the decrease of Fe magnetic moment, the splittings of Fe-3d orbitals are reduced because of the weak Hund's couplings, and the 3d_xz and 3d_yz orbitals in the SSDW phase become nearly degenerate. The Fermi surface structure of the two spin density waves phases are very similar, both exhibiting three-dimensional characteristics. However, when the Fe magnetic moment is constrained to the experimental value of 0.2 µB, the electron-type pockets in the two phases disappear, while the bands along X-M and R-A nearly degenerate.

Unfortunately, there is still no theory that can be used to guide the search of superconductors to room temperature superconductivity. In recent years, the discovery of high-pressure hydride superconductors has once again promoted the research interest of superconductors with high T_c. Similar to simple metals, the superconductivity of hydrides can be explained with BCS theory, and their superconducting transition temperature could be close to room temperature under extremely high pressure. For example, $\text{LaH}_{10}$ with a high symmetric cage structure can reach a transition temperature of 250 K under 170GPa, and YH₉ has a transition temperature of 243 K at a high pressure of 201 GPa. However, the extremely high pressure required to achieve superconductivity of these materials also pose great difficulties for sample preparation and practical application. The search for hydride superconductors with high T_c at lower pressures is one of the important topic in the field of superconductivity. In this paper, a new type of ternary superconducting compound, Mg₃InH, with a T_c of 36 K under ambient pressure is predicted. This material is formed by introducing H atoms at the body center of the metal perovskite framework, achieving the structural stability through the bonding of Mg-H and In-H. It is shown that Mg₃InH is a typical phonon-mediated superconducting material, whose high T_c can be attributed to the strong electron-phonon coupling between the high-frequency phonons generated by the vibration of H and the conduction electrons provided by the metal ions. The electron-phonon coupling strength is as high as 0.97. This discovery provides a new strategy for the search of novel ternary hydride high-temperature superconducting materials under ambient pressure. In addition, the electron localization function shows that there are large interstitial electrons localized in the space between the In and Mg atoms, which are accumulated from the excess electrons contributed by the Mg atoms and distributed in a shell around the In atoms. The interstitial electrons have a large density of states at the Fermi level, which indicates that Mg₃InH may be a new type of electride superconductor hydrides.