Precise quantum-geometric electronic properties from first principles

TL;DR

This paper introduces a first-principles method to accurately compute quantum-geometric properties of Bloch electrons, such as Berry curvature and quantum metric, using perturbation theory and a Sternheimer equation, validated on various materials.

Contribution

It develops a high-precision computational approach for quantum-geometric properties from first principles, enabling detailed analysis of complex materials.

Findings

Effective mass calculations agree with numerical derivatives for silicon and gallium arsenide.

Quantum-geometric quantities for gapped graphene match analytical models.

Quantum properties in trigonal tellurium depend on chirality, flipping sign.

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.