Screening and Many-Body Effects in Two-Dimensional Crystals: Monolayer MoS$_{2}$ (1605.08733v1)

Abstract: We present a systematic study of the variables affecting the electronic and optical properties of two-dimensional(2D) crystals within \textit{ab initio} GW and GW plus Bethe Salpeter Equation (GW-BSE) calculations. As a prototypical 2D transition metal dichalcogenide material, we focus our study on monolayer MoS${}_2$. We find that the reported variations in GW-BSE results in the literature for monolayer MoS${}_2$ and related systems arise from different treatments of the long-range Coulomb interaction in supercell calculations and convergence of k-grid sampling and cutoffs for various quantities such as the dielectric screening. In particular, the quasi-2D nature of the system gives rise to fast spatial variations in the screening environment, which are computationally challenging to resolve. We also show that common numerical treatments to remove the divergence in the Coulomb interaction can shift the exciton continuum leading to false convergence with respect to k-point sampling. Our findings apply to GW-BSE calculations on any low-dimensional semiconductors.

• The paper demonstrates that careful treatment of Coulomb truncation and k-point convergence is crucial for accurate quasiparticle gaps and excitonic predictions in monolayer MoS₂.
• The study employs ab initio GW-BSE calculations to reveal how rapid variations in screening, due to the quasi-2D nature of MoS₂, affect its optical and electronic properties.
• The findings provide actionable guidelines for selecting computational parameters, enhancing simulations of 2D semiconductors for optoelectronic applications.

Electron and Hole Interactions in Monolayer MoS$_2$: An Ab initio Study

This paper investigates the computational challenges of accurately predicting the electronic properties of two-dimensional (2D) crystals, focusing primarily on the transition metal dichalcogenide (TMD) monolayer MoS$_2$. The paper employs ab initio methods, specifically the GW approximation coupled with the Bethe Salpeter Equation (GW-BSE) approach, to analyze the many-body effects that influence electronic and optical properties. The insights gained from this work are particularly valuable for researchers in condensed matter physics, materials science, and related fields.

The authors address the significant variability seen in existing GW-BSE calculations for monolayer MoS$_2$ and related systems. This paper identifies that substantial discrepancies in reported quasiparticle (QP) gaps and exciton binding energies arise due to differences in how the long-range Coulomb interaction is treated, as well as the convergence criteria regarding k-point sampling and energy cutoffs. A pivotal finding is that the quasi-2D nature of MoS$_2$ results in rapid variations in the screening environment, making precise computational modeling challenging.

Key findings from the paper include:

1. Convergence Challenges: The paper emphasizes the computational difficulty in achieving convergence of QP gaps with respect to k-point sampling, the dielectric cutoff, and the number of bands considered. It highlights that the convergence is closely linked to the supercell size and the handling of the Coulomb interaction, underscoring the need for meticulous parameter selection in simulations of low-dimensional semiconductors.
2. Coulomb Truncation: Introducing Coulomb truncation in a supercell framework is shown to be critical for preventing the over-screening effects that arise from interaction between periodic images. The lack of convergence due to untruncated interactions has been identified as a primary source of discrepancies in the literature.
3. Excitonic Effects: The results reveal a complex excitonic spectrum where the exciton states deviate significantly from predictions based on simple hydrogenic models. Particularly, higher angular momentum states are more strongly bound than predicted due to non-uniform screening effects. Excitonic states are shown to be highly localized in momentum space, further complicating the computational modeling of their properties.
4. Optical Properties and Screening: The paper finds that traditional methods of averaging the screened Coulomb interaction for small q-vectors can lead to incorrect predictions of exciton binding energies by falsely implying convergence. It advocates for careful treatment of the zero q-limit to ensure accurate optical predictions.

The paper's implications extend beyond MoS$_2$, as the lessons in computational treatment of Coulomb interactions and k-point convergence have broad applications across various 2D materials. By systematically addressing factors that lead to divergent results in GW-BSE calculations, this work provides a more reliable framework for understanding and predicting the properties of low-dimensional systems.

In conclusion, this research elucidates the pressing computational challenges and provides methodological recommendations for accurate modeling of 2D semiconductors. The insights pave the way for refined simulations that can more accurately simulate real-world optical properties and electronic behaviors, crucial for material design and applications in optoelectronic devices. Future research may focus on extending these computational methodologies to other material systems and further exploring the rich physics of 2D excitonic states facilitated by advanced many-body perturbation techniques.