发表机构
Norwegian University of Life Sciences（挪威生命科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出协变重整化方案，通过缩放厄米动量矩阵本征值谱，提升 k$\u00c2\u00b7p 模型的收敛性和精度，并生成紧凑或全区域模型，用于能带结构和输运性质计算。
AI 中文摘要
k$\u00c2\u00b7p 方法可以直接应用于第一性原理能量和动量矩阵元，但所得模型随能带数收敛缓慢，并且在底层哈密顿量非局域的任何地方都不精确。我们表明，通过对厄米动量矩阵的本征值谱进行重整化，可以很大程度上消除这两个限制。这些谱是规范不变的，并且对于对称相关的笛卡尔分量是相同的，因此对重复出现的量级进行缩放提供了一组适中的参数，这些参数保持简并性和晶体对称性，而无需构造对称适配基。我们选择参考从高对称点出发的射线上的本征值和能带速度来重整化模型。对于 GaP，一个 15 能带模型可以在近带隙参考区域内以几 meV 的精度重现能带结构。对于闪锌矿和纤锌矿 AlN，类似的精度需要 30 或 66 能带模型，对于闪锌矿，这归因于 [110] 方向的强翘曲。该方案很容易推广到岩盐 PbTe，它包含自旋轨道耦合，并且具有 L 中心的价带和导带极值。此外，我们针对 GaP 展示了如何通过在同一重整化方案内进行向下折叠来获得紧凑的四能带哈密顿量。此外，通过将拟合区域改为覆盖整个布里渊区，该方案可用于生成能重现态密度的全区域模型。实际效用通过 GaP 的 59 能带 k.p 模型得以说明，该模型可以在比参考计算密集得多的网格上进行评估，进而既可用于解析态密度中的精细特征，也可用于计算低温下的空穴电导率。
英文摘要
The k$\cdot$p method can be applied directly to first-principles energies and momentum matrix elements, but the resulting models converge slowly with the number of bands and are inexact wherever the underlying Hamiltonian is nonlocal. We show that both limitations can be largely removed by renormalizing the eigenvalue spectra of the Hermitian momentum matrices. These spectra are gauge invariant, and are identical for symmetry-related Cartesian components, hence scaling the recurring magnitudes provides a modest set of parameters that preserves degeneracies and crystal symmetry without needing to construct a symmetry-adapted basis. We choose to renormalize the models against reference eigenvalues and band velocities on rays out of a high-symmetry point. For GaP, a 15-band model can reproduce the band structure in the near-gap reference regions within a few meV. For zincblende and wurtzite AlN, similar accuracy requires 30- or 66-band models, which in the case of zincblende is traced to the strong warping in the [110] direction. The scheme readily generalizes to rocksalt PbTe, which includes spin-orbit coupling, and has L-centered valence and conduction band extrema. Further, we demonstrate, for GaP, how compact four-band Hamiltonians can be obtained by downfolding within the same renormalization scheme. Moreover, by changing the fitting regime to encompass the entire Brillouin zone, the scheme can be used to generate full-zone models that reproduce the density of states. The practical utility is illustrated with a 59-band k.p model for GaP, which can be evaluated on meshes far denser than the reference calculation, that in turn can be used both to resolve fine features in the density of states and to compute the hole conductivity at low temperature.
Comments9 pages, 10 figures, 1 table
