  Substrates have strong effects on optoelectronic properties of
two-dimensional (2D) materials, which have emerged as promising platforms for
exotic physical phenomena and outstanding applications. To reliably interpret
experimental results and predict such effects at 2D interfaces, theoretical
methods accurately describing electron correlation and electron-hole
interaction such as first-principles many-body perturbation theory are
necessary. In our previous work [Phys. Rev. B 102, 205113(2020)], we developed
the reciprocal-space linear interpolation method that can take into account the
effects of substrate screening for arbitrarily lattice-mismatched interfaces at
the GW level of approximation. In this work, we apply this method to examine
the substrate effect on excitonic excitation and recombination of 2D materials
by solving the Bethe-Salpeter equation. We predict the nonrigid shift of 1s and
2s excitonic peaks due to substrate screening, in excellent agreements with
experiments. We then reveal its underlying physical mechanism through 2D
hydrogen model and the linear relation between quasiparticle gaps and exciton
binding energies when varying the substrate screening. At the end, we calculate
the exciton radiative lifetime of monolayer hexagonal boron nitride with
various substrates at zero and room temperature, as well as the one of WS2
where we obtain good agreement with experimental lifetime. Our work answers
important questions of substrate effects on excitonic properties of 2D
interfaces.
