Time-dependent Bethe-Salpeter equation

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Real-time electron dynamics studies based on approximate TDDFT exchange-correlation kernels come with several deficiencies. A prominent deficiency is, that the binding energy of an exciton is not included in the exciton formation process. This leads to wrong excitation frequencies of excitons. A way out is the use of the time-dependent Bethe-Salpeter equation (tdBSE) [1], which comes with considerably higher computational cost than TDDFT. In this project, a computationally efficient tdBSE algorithm will be developed. A starting point could be the low-scaling GW algorithm in CP2K [2]. Potential applications of the tdBSE algorithm include exciton formation dynamics in two-dimensional materials, in particular moiré structures, see sketch below, which recently have attracted enormous attention [3].

[1] See Attaccalite et al., Real-time approach to the optical properties of solids and nanostructures: Time-dependent Bethe-Salpeter equation, Phys. Rev. B 84, 245110 (2011) and X. Jiang et al., Real-time GW-BSE investigations on spin-valley exciton dynamics in monolayer transition metal dichalcogenide, Sci. Adv. 7, eabf3759 (2021)

[2]? J. Wilhelm, D. Golze, L. Talirz, J. Hutter, C. A. Pignedoli: Toward GW calculations on thousands of atoms, J. Phys. Chem. Lett. 9, 306-312 (2018) and J. Wilhelm, P. Seewald, D. Golze: Low-scaling GW with benchmark accuracy and application to phosphorene nanosheets, J. Chem. Theory Comput. 17, 1662 (2021).

[3] See Schmitt et al., Formation of moiré interlayer excitons in space and time, Nature 608, 499–503 (2022), Barré et al., Optical absorption of interlayer excitons in transition-metal dichalcogenide heterostructures, Science 376, 406-410 (2022), and Karni et al., Structure of the moiré exciton captured by imaging its electron and hole, Nature 603, 247-252 (2022).
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