Precise quantum-geometric electronic properties from first principles

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) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>ψ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> </mml:mrow> </mml:math> with respect to wavevector k <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>k</mml:mi> </mml:math> . 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.