1651个磁空间群有效模型的穷举构造
Exhaustive constructions of effective models in 1651 magnetic space groups
摘要：
$k\cdot p$有效哈密顿量已被广泛应用于预测凝聚态系统中的各种现象。目前，构造$k\cdot p$哈密顿量的方法是逐例的，这极大地限制了它的应用，特别是在磁系统中。本文首先明确列出了1651个磁空间群（包括16230个空间群）中所有特殊$k$点的所有单值和双值不可约表示（不可约表示）和余不可约表示的所有表示矩阵。然后通过群论分析，得到了4857832个初等$k\cdot p$矩阵块，直接利用这些矩阵块可以得到任意周期系统的任意$k\cdot p$哈密顿量。我们相信我们的工作将促进凝聚态物理各个领域的研究，如半导体，拓扑物理，自旋电子学等，我们也期望我们的详尽的结果$k\cdot p$模型将起到至关重要的作用，在连接其他领域与凝聚态物理和促进实现各种理论模型，具有奇异的性质，但缺乏实际材料。
英文摘要：
The $k\cdot p$ effective Hamiltonians have been widely applied to predict a large variety of phenomena in condensed matter systems. Currently, the popular way to construct a $k\cdot p$ Hamiltonian is in a case-by-case manner, which significantly limits its applications especially for magnetic systems. In this work, we first explicitly tabulate all the representation matrices for all single-valued and double-valued irreducible representations (irreps) and co-irreps for the little groups of all special $k$ points in 1651 magnetic space groups (including nonmagnetic 230 space groups). Then through group theory analysis, we obtain 4 857 832 elementary $k\cdot p$ matrix blocks, and directly using these matrix blocks given in this work one can obtain any $k\cdot p$ Hamiltonian for any periodic system, including bulk or boundary. We believe our work will accelerate the studies in various fields in condensed matter physics, such as semiconductors, topological physics, spintronics, etc. We also expect our exhaustive results on $k\cdot p$ models will play vital roles in connecting other fields with condensed matter physics and promote realizations of diverse theoretical models which possess exotic properties but lack practical materials.
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