Wigner-Seitz Truncated TDDFT Approach for the Calculation of Exciton Binding Energies in Solids

Time-Dependent Density Functional Theory (TDDFT) is a computationally efficient alternative to the Many-Body Perturbation Theory (MBPT) for calculating the optical properties of solids. However, the family of exchange-correlation kernels, known as long-range-corrected (LRC) kernels, which accurately capture excitonic features, still face some challenges that need to be addressed¹. In this work, we study the role of the Coulomb interaction in the calculations concerning excitonic effects within the TDDFT². We conduct a meticulous investigation of the impact of the long-range Coulomb term in both pure-TDDFT and hybrid approaches using a Wigner-Seitz truncated kernel. 

On the one hand, in the LRC-TDDFT framework, we find that the numerical method that is used throughout the literature to overcome the singularities of the Coulomb kernel often misses the effect of a surface term C_ck,vk that must be considered in periodic systems³. On the other hand, we propose a hybrid Wigner-Seitz Truncated kernel that regularizes the Coulomb kernel by employing a real space truncation in a Wigner-Seitz supercell of the crystal. We observe that while this kernel underestimates exciton binding energies of wide gap insulators, it yields exciton binding energies in good agreement with the BSE for small gap semiconductors^2,4. 

[1] Y. M. Byun et al., Phys. Rev. B 95, 205136 (2017)

[2] M. Arruabarrena et al., arXiv:2303.13389 (2023)

[3] B. Gu et al., Phys. Rev. B 87, 125301 (2013)

[4] J. Sun et al., Phys. Rev. Res. 2, 013091 (2020)