[Paper Review] Many-Body effects beyond excitons in second-harmonic generation of monolayer MoS$_{2}$

Peio Garcia-Goiricelaya, Julen Ibañez-Azpiroz|arXiv (Cornell University)|Feb 25, 2026

2D Materials and Applications0 citations

TL;DR

The paper develops an ab initio framework combining MBPT with time-dependent current-density functional theory to quantify second-harmonic generation in monolayer MoS2, showing three-particle (trionic) correlations are needed for quantitative agreement with experiment.

ABSTRACT

We present a quantitative study of many-body effects including the three-particle level on second-harmonic generation in monolayer MoS$_{2}$. Our approach combines many-body perturbation theory with time-dependent current-density-functional theory within an extit{ab initio} framework in the optical limit. Inclusion of two-particle excitonic effects extit{via} a dynamical long-range linear exchange-correlation kernel reproduces the qualitative features of the second-harmonic response, but underestimates the experimentally reported magnitudes by nearly a factor of two. By incorporating three-particle (trionic) correlations through a static long-range quadratic exchange-correlation kernel, we achieve significantly improved quantitative agreement with experiment. These findings highlight the role of many-body interactions beyond the excitonic level in accurately describing second-order optical responses in two-dimensional semiconductors.

Motivation & Objective

• Motivate the need to understand nonlinear optical responses in 2D semiconductors beyond excitons.
• Quantify how two- and three-particle many-body effects influence SHG in monolayer MoS2.
• Develop and apply an ab initio framework integrating MBPT with TDCDFT to capture linear and quadratic responses.
• Assess the quantitative impact of trionic (three-particle) correlations on SHG spectra.

Proposed method

• Compute quasiparticle corrections with G0W0 and excitonic effects via the Bethe-Salpeter equation to obtain accurate linear optical response.
• Extract and use the long-range linear exchange–correlation kernel from the dielectric function to reproduce excitonic effects in TD-DFT/TDCDFT.
• Incorporate three-particle correlations through a static long-range quadratic exchange–correlation kernel to model trions in SHG.
• Employ Wannier interpolation and an effective thickness L_eff to compute the macroscopic SHG susceptibility within the TDCDFT framework.
• Derive and use a Dyson-like equation for the SHG tensor that includes both two-body (α_LRC) and three-body (β_LRC) contributions.
• Compare calculated SHG spectra with experimental data to tune the β_LRC parameter for best agreement.

Experimental results

Research questions

• RQ1 How do two-particle (excitonic) and three-particle (trionic) many-body interactions affect second-harmonic generation in monolayer MoS2?
• RQ2 Can a TDDFT/TDCDFT-based approach, combined with MBPT inputs, quantitatively reproduce SHG spectra observed experimentally?
• RQ3 What is the role of the long-range exchange–correlation kernels in capturing nonlinear optical responses beyond excitons?
• RQ4 To what extent does incorporating a quadratic (three-body) kernel improve agreement with measured SHG magnitudes and peak positions?

Key findings

• Including two-particle excitonic effects via a dynamical long-range linear kernel reproduces qualitative SHG features but underestimates magnitudes by about a factor of two.
• Incorporating three-particle (trionic) correlations via a static long-range quadratic kernel significantly improves quantitative agreement with experiment.
• The SHG peak near 1.4–1.5 eV is well captured in position and shape when β_LRC is tuned to match experimental intensity.
• A physically grounded effective thickness L_eff used in the macroscopic dielectric calculation yields better quantitative SHG results than conventional choices.
• The study demonstrates the importance of three-body interactions for accurate second-order optical responses in 2D semiconductors.