Wannier interpolation of reciprocal-space periodic and non-periodic matrix elements in the optimally smooth subspace

TL;DR

This paper introduces a multidimensional Wannier interpolation method for both periodic and non-periodic matrix elements in reciprocal space, enabling accurate and efficient calculation of optical properties on ultradense momentum grids.

Contribution

It presents a novel direct interpolation approach in the optimally smooth subspace that handles non-periodic quantities without relying on Wannier center positions.

Findings

Comparable accuracy to Fourier interpolation at lower cost

Enables interpolation and extrapolation of non-periodic observables

Applicable to tensors of any order without Wannier center information

Abstract

Maximally localized Wannier functions use the gauge freedom of Bloch wavefunctions to define the optimally smooth subspace with matrix elements that depend smoothly on crystal momentum. The associated Wannier functions are real-space localized, a feature often used to Fourier interpolate periodic observables in reciprocal space on ultradense momentum grids. However, Fourier interpolation cannot handle non-periodic quantities in reciprocal space, such as the oscillator strength matrix elements, which are crucial for the evaluation of optical properties. We show that a direct multidimensional interpolation in the optimally smooth subspace yields comparable accuracy with respect to Fourier interpolation at a similar or lower computational cost. This approach can also interpolate and extrapolate non-periodic observables, enabling the calculation of optical properties on ultradense momentum grids. Finally, we underline that direct interpolation in the optimally smooth subspace can be employed for periodic and non-periodic tensors of any order without any information on the position of the Wannier centers in real space.