Assessing electronic transport in solid materials via the fluctuation-dissipation theorem
For the first-principles evaluation of electronic heat and charge transport coefficients, the Kubo-Greenwood formalism represents an appealing alternative to perturbative approaches, since it naturally incorporates all orders of anharmonic and vibronic effects. In practice, however, Kubo-Greenwood calculations often come with prohibitive computational costs, since crystalline materials typically require both dense reciprocal-space 𝐤-grids for the electronic degrees of freedom and large real-space supercells for the vibrational ones. This is especially challenging for the charge transport coefficient of intrinsic semiconductors with dispersive electronic structures, because the free carriers are very localised in 𝐤-space, which demands an extremely fine 𝐤-grid. In this work, we implement and investigate the application of the Fourier interpolation that can facilitate access to the extremely fine 𝐤-grids necessary to establish convergence. This enables the use of very dense 𝐤-grids for the evaluation of the Kubo-Greenwood formula, while 𝐤-grids used during the self-consistency cycle must only be dense enough to converge the total energy, which can typically be accomplished with substantially coarser 𝐤-grids. As demonstrated for silicon, this enables us to achieve 𝐤-grid convergence of the electrical conductivity spectrum with reduced computational resources. In other words, we can obtain 𝐤-grid convergence for systems, for which this was impossible before. This constitutes an important step towards affordable, fully anharmonic predictions of electronic heat and charge transport coefficients for all crystalline materials.
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