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Transport calculation method for supercell

Accurate prediction of electronic transport properties is essential for the rational design of thermoelectric materials, particularly in complex systems where alloying, doping, and disorder strongly modify the electronic structure. While conventional transport calculations are often limited to pristine unit cells or rely on approximations that neglect local chemical environments, realistic materials frequently require a supercell-based description to capture these effects. To address this challenge, we have developed Electra, an in-house electronic transport code capable of directly calculating transport coefficients from first-principles supercell electronic structures. By explicitly incorporating the band structure modifications arising from alloying, doping, defects, and chemical disorder, Electra enables a more realistic description of carrier transport in complex materials. This approach bridges the gap between atomistic structural models and experimentally measurable transport properties, providing a powerful framework for understanding and optimizing thermoelectric performance in compositionally engineered materials.

The transport properties should be same irrespective of chosen symmetry if the atomic arrangement is same. Therefore, with supercell structure where fermi surface is folded onto smaller Brillouin Zone, transport properties should remain same. Figure in right show our developed code which produces same Power factor for primitive and 2 supercell with different symmetry.

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Fundamental Challenge:

One of most fundamental challenge in the supercell calculation is at the Density Functional Theory (DFT) level. The electronic structure (fermi surface) of supercell calculated using any DFT code leads to mixing of Fermi surface when folded onto a same high symmetry point. A result of such mixing leads to altered q = |k -k'|, i.e initial and final momentum of scattered carrier leading to incorrect scattering. So far there is not method to overcome this problem as it is at the fundamental level of DFT calculation.

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