Automated construction of symmetrized Wannier-like tight-binding models from ab initio calculations

Wannier tight-binding models are effective models constructed from first-principles calculations. As such, they bridge a gap between the accuracy of first-principles calculations and the computational simplicity of effective models. In this work, we extend the existing methodology of creating Wannier tight-binding models from first-principles calculations by introducing the symmetrization post-processing step, which enables the production of Wannier-like models that respect the symmetries of the considered crystal. Furthermore, we implement automatic workflows, which allow for producing a large number of tight-binding models for large classes of chemically and structurally similar compounds or materials subject to external influence such as strain. As a particular illustration, these workflows are applied to strained III-V semiconductor materials. These results can be used for further study of topological phase transitions in III-V quantum wells.

Figure 1

Comparison of the initial (blue) and symmetrized (orange) band structure for a tight-binding model of silicon with atom-centered $s{p}^3$ orbitals. (a) In the $\mathrm{eV}$ scale, there are no visible differences between the two models. (b) A zoom in around the $X$ point on the $\mathrm{meV}$ scale reveals a slight lifting of the band degeneracies in the initial model. This incorrectness is resolved in the symmetrized model. For comparison, a symmetrized band structure taking into account only symmorphic symmetries (green) is also shown.

Figure 2

Comparison between the reference first-principles band structure (blue) and band structures calculated from tight-binding models (orange) for InSb. The tight-binding model in (a) was calculated with the initial energy window, whereas (b) shows the model using the optimized energy window as detailed in Table 2. The model in (c) was calculated without the disentanglement procedure, using the exclude_bands parameter.

Figure 3

Schematic of the AiiDA workflow for creating tight-binding models with energy window optimization. Workflows are shown in blue and calculations in purple. Orange arrows show calls from parent to child workflows (or calculations). Dashed green arrows show the implicit data dependency between workflows of the same level. In calculation names, the suffix Calculation is omitted for brevity.

Figure 4

Average (blue, left axis) and total (orange, right axis) weights of the hopping parameters for the unstrained InSb tight-binding model, as a function of distance.

Figure 5

Sketch of the workflow for constructing strained tight-binding models. The color scheme is the same as in Fig. 3.

Figure 6

Sketch of the FirstPrinciplesRunBase subclass used for calculating the Wannier90 input and reference bands with VASP and hybrid functionals.

Figure 7

Comparison between the InSb band structure obtained directly from the tight-binding model with $2\%$ biaxial (001) strain (blue) and from the linear interpolation (orange) between models with $1\%$ and $3\%$ strain. The energy scale is fixed by setting the top of the valence bands at $\mathrm{\Gamma }$ to zero. (a) At the electron-volt scale, the only visible difference is in the upper bands along the $\mathrm{\Gamma }\text{−}K$ line. (b) Closeup of the bands around $\mathrm{\Gamma }$. The bands for $1\%$ (purple) and $3\%$ strain (green) are also shown.

Figure 8

Strain dependence of band energies. The two highest valence bands and the lowest conduction band are shown at the $\mathrm{\Gamma }$ (blue), $X$ (orange), and $L$ (green) points, where each band is doubly degenerate. Energy values are shifted such that the valence band maximum at $\mathrm{\Gamma }$ is zero. The line represents values calculated from the tight-binding models with linear interpolation [Eq. (8)] in steps of $0.1\%$. For comparison, the points show values calculated from first principles. We find a good agreement between the tight-binding and first-principles values, except for the conduction band value at the $L$ point at $-4\%$ biaxial (111) strain.