Precise quantum-geometric electronic properties from first principles, by José Luís Martins, Carlos Loia Reis, Ivo Souza

José Luís Martins, Carlos Loia Reis, Ivo Souza SciPost Phys. 19, 109 (2025) · published 24 October 2025 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 $\psi_{k}(r)$ with respect to 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 confirmed 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 some quantum-geometric quantities flip sign with chirality.External links to supplemental resources; opens in a new tab.