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arXiv · 2506.23652

Precise quantum-geometric electronic properties from first principles

José Luís Martins·Carlos Loia Reis·Ivo Souza
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Abstract

The calculation of quantum-geometric properties of Bloch electrons -- Berry curvature, quantum metric, orbital magnetic moment and effective mass -- was implemented in a pseudopotential plane-wave code. The starting point was the first derivative of the periodic part of the wavefunction psi_k with respect to the wavevector k. This was evaluated with perturbation theory by solving a Sternheimer equation. Comparison of effective masses obtained from perturbation theory for silicon and gallium arsenide with carefully-converged numerical second derivatives of band energies confirms the high precision of the method. Calculations of quantum-geometric quantities for gapped graphene were performed by adding a bespoke symmetry-breaking potential to first-principles graphene. As the two bands near the opened gap are reasonably isolated, the results could be compared with those obtained from an analytical two-band model, allowing to assess the strengths and limitations of such widely-used models. The final application was trigonal tellurium, where quantum-geometric quantities flip sign with chirality.

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José Luís Martins, Carlos Loia Reis, Ivo Souza. 2025-06-30. Precise quantum-geometric electronic properties from first principles. https://doi.org/10.21468/scipostphys.19.4.109

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