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Efficient band structure unfolding with atom-centered orbitals: General theory and application

Jingkai Quan1,2, Nikita Rybin1, Matthias Scheffler1, and Christian Carbogno1,*

  • *Contact author: carbogno@fhi-berlin.mpg.de
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Phys. Rev. B 113, 085112 – Published 9 February, 2026

DOI: https://doi.org/10.1103/7xym-7388

Abstract

Band structure unfolding is a key technique for analyzing and simplifying the electronic band structure of large, internally distorted supercells that break the primitive cell's translational symmetry. In this work, we present an efficient band unfolding method for atomic orbital (AO) basis sets that explicitly accounts for both the nonorthogonality of atomic orbitals and their atom-centered nature. Unlike existing approaches that typically rely on a plane-wave representation of the (semi)valence states, we here derive analytical expressions that recast the primitive cell translational operator and the associated Bloch functions in the supercell AO basis. In turn, this enables the accurate and efficient unfolding of conduction, valence, and core states in all-electron codes, as demonstrated by our implementation in the all-electron ab initio simulation package fhi-aims, which employs numeric atom-centered orbitals. We explicitly demonstrate the capability of running large-scale unfolding calculations for systems with thousands of atoms and showcase the importance of this technique for computing temperature-dependent spectral functions in strongly anharmonic materials using CuI as example.

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Phys. Rev. B 113, 085112– Published 9 February, 2026
  • Received 26 June 2025
  • Revised 11 October 2025
  • Accepted 5 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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