Linear scaling coefficient between exciton binding energy and quasiparticle bandgap in two-dimensional tetragonal crystals

Exciton binding energy (Eb) and lifetime of the two-dimensional (2D) materials have attracted giant attention due to their abundant multi-body physical properties. There is a robust linear scaling law between the exciton binding energy and its quasiparticle bandgap (EQP) in 2D hexagonal crystals, namely, Eb/EQP = 1/4. However, the relationship between Eb and EQP in 2D tetragonal crystals is still lacking so far. Here, based on the k·p perturbation theory and the screened hydrogen model, we verified the linear scaling law in 2D tetragonal crystals, i.e., Eb/EQP≈ 3/8, which is different from that in 2D hexagonal crystals. Moreover, we have systemically verified the relationship of Eb and EQP in different 2D tetragonal crystals by utilizing G0W0 and Bethe–Salpeter equation calculations, which are in good agreement with the previously theoretical results. Importantly, the exciton lifetime of most KAgSe-like monolayers (up to 1.76 ps) is significantly higher than that of 2D transition metal sulfides at 0 K, which usually depends on the larger Eb. Overall, our work not only enriches the exciton properties of 2D crystals but also provides a feasible way to explore 2D crystal materials with extended exciton lifetime and high luminous efficiency.