Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Maximally-localized Wannier functions (MLWFs) are a powerful and broadly used tool to characterize the electronic structure of materials, from chemical bonding to dielectric response to topological properties. Most generally, one can construct MLWFs that describe isolated band manifolds, e.g. for the valence bands of insulators, or entangled band manifolds, e.g. in metals or describing both the valence and the conduction manifolds in insulators. Obtaining MLWFs that describe a target manifold accurately and with the most compact representation often requires chemical intuition and trial and error, a challenging step even for experienced researchers and a roadblock for automated high-throughput calculations. Here, we present a very natural and powerful approach that provides automatically MLWFs spanning the occupied bands and their natural complement for the empty states, resulting in WÎannier Hamiltonian models that provide a tight-binding picture of optimized atomic orbitals in crystals. Key to the success of the algorithm is the introduction of a projectability measure for each Bloch state onto atomic orbitals (here, chosen from the pseudopotential projectors) that determines if that state should be kept identically, discarded, or mixed into a disentangling algorithm. We showcase the accuracy of our method by comparing a reference test set of 200 materials against the selected-columns-of-the-density-matrix (SCDM) algorithm, and its reliability by Wannierizing 21 737 materials from the Materials Cloud.

最大化局域化瓦尼尔函数（Maximally-localized Wannier functions, MLWFs）是一类功能强大且应用广泛的工具，可用于表征材料的电子结构，研究范畴涵盖化学键合、介电响应乃至拓扑性质。最一般地，人们可以构建MLWFs以描述孤立能带流形，例如绝缘体的价带，或是纠缠能带流形，例如金属中的能带结构，或同时描述绝缘体的价带与导带流形。精准且以最紧凑的表征形式获取对应目标流形的MLWFs，往往需要借助化学直觉并反复试错；即便对于经验丰富的研究者而言，这一步也颇具挑战性，同时也是自动化高通量计算的一大障碍。本文提出一种自然且高效的方法，可自动生成覆盖占据态能带及其空态自然补集的MLWFs，最终得到瓦尼尔哈密顿量模型（Wannier Hamiltonian models），该模型可呈现晶体中优化原子轨道的紧束缚图像。该算法成功的关键在于，为每个布洛赫态（Bloch state）引入了一种投影性度量，将其投影到原子轨道（本文中选自赝势投影子（pseudopotential projectors））上，以此判定该态是应当保留不变、直接舍弃，还是需混入解纠缠算法（disentangling algorithm）中。我们通过将200种材料的参考测试集与密度矩阵选列法（selected-columns-of-the-density-matrix, SCDM）的计算结果进行对比，验证了本方法的准确性；同时通过对材料云（Materials Cloud）中的21737种材料进行瓦尼尔化处理，证明了其可靠性。