High-fidelity k·p representations of first-principles electronic band structures through covariant renormalization
Abstract
The k·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 along symmetry-related directions; 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 85-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. A practical use of the method 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.
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BibTeX
@misc{berland2026highfidelity,
title = {{High-fidelity k$\cdot$p representations of first-principles electronic band structures through covariant renormalization}},
author = {Kristian Berland},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.11861},
eprint = {2609.11861},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11861},
}
RIS
TY - UNPB
TI - High-fidelity k·p representations of first-principles electronic band structures through covariant renormalization
AU - Kristian Berland
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.11861
UR - https://arxiv.org/abs/2609.11861
AB - The k·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 along symmetry-related directions; 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 85-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. A practical use of the method 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.
ER -