Two-dimensional (2D) materials hold immense promise for next-generation electronic devices due to their unique physical properties. However, a significant challenge hindering their practical application is the susceptibility of their band edge states to environmental perturbations. These perturbations occur through two primary mechanisms: local chemical interactions and nonlocal dielectric screening. While nonlocal screening effects can be engineered through substrate selection or layer thickness, local chemical coupling (from surface adsorption or interfacial interactions) is difficult to control and predict. Even weak van der Waals interactions at typical distances can significantly alter the band edge states, impacting device performance. Therefore, an ideal 2D material would exhibit band edge states robust against these local chemical coupling effects. This study investigates MoSi₂N₄, a recently synthesized material, as a potential candidate. MoSi₂N₄, belonging to the MSi₂N₄ family (M = transition metal), exhibits excellent ambient stability and predicted properties such as piezoelectricity, high thermal conductivity, and spin-valley coupling. This work uses density functional theory (DFT) and many-body perturbation theory to explore how MoSi₂N₄'s band edge states are protected from chemical coupling, while its quasiparticle and excitonic properties can be tuned via nonlocal dielectric screening.

The introduction extensively reviews existing literature on 2D materials, highlighting the challenges posed by environmental perturbations. It cites numerous publications focusing on interlayer coupling effects to tune 2D material properties (refs 3-9), and specifically addresses the issue of environmental sensitivity of band edge states. Several works on the tunability of quasiparticle and optical properties through nonlocal dielectric screening are reviewed (refs 10-13). Previous research on MoSi₂N₄ is also summarized, citing its synthesis (ref 14), predicted properties (refs 15-17), and the need for further investigation into its electronic structure.

The study employs a combination of density functional theory (DFT) and many-body perturbation theory calculations. Structural optimizations of monolayer, bilayer, and bulk MoSi₂N₄ with various stacking patterns were performed using the Vienna ab initio simulation package (VASP) with the Perdew-Burke-Ernzerhof (PBE) functional and the DFT-D3 correction for van der Waals interactions. Layer-dependent quasiparticle and optical properties were calculated using the BerkeleyGW package, employing the GW approximation and solving the Bethe-Salpeter equation (BSE). Norm-conserving pseudopotentials were used, with semicore states of Mo included as valence electrons. The Hybertsen-Louie generalized plasmon-pole model was used to extend the static dielectric function to finite frequencies. Accelerated methods were employed to improve the efficiency of GW calculations for 2D systems, addressing limitations in conventional approaches. Convergence tests were conducted regarding k-point sampling, vacuum layer thickness, and the number of valence and conduction bands in the excitonic wave function expansion.

DFT calculations revealed that the band gap of MoSi₂N₄ shows negligible layer dependence, remaining nearly constant from monolayer to bulk. Analysis of Kohn-Sham wave functions showed that band edge states primarily originate from interior atomic orbitals (Mo and interior N atoms), shielding them from interfacial chemical coupling. GW calculations demonstrated that while the DFT band gap shows minimal layer dependence, the quasiparticle band gap exhibits a more substantial layer dependence, varying from 2.82 eV (monolayer) to 2.41 eV (bulk). However, this layer dependence remains significantly weaker than in other well-known 2D materials. GW-BSE calculations revealed layer-dependent electron-hole excitations and optical properties. Three prominent low-energy absorption peaks were identified, with exciton binding energies decreasing with increasing layer thickness due to stronger dielectric screening and weakened electron-hole interaction. Interestingly, the optical band gap remained relatively stable with respect to layer thickness, likely due to the protection of band edge states from interlayer coupling. The study found a partial cancellation between quasiparticle self-energy correction and exciton binding energy, contributing to the stable optical gap.

The findings address the research question by demonstrating that MoSi₂N₄ possesses robust band edge states largely unaffected by surface or interfacial chemical interactions. This robustness contrasts sharply with other 2D materials where interlayer coupling significantly modifies the band gap. The ability to tune the quasiparticle and excitonic properties solely through nonlocal dielectric screening (controllable by substrate and layer thickness) makes MoSi₂N₄ a unique material. The moderate band gap, stability, and tunability offer significant advantages for various applications. The stable optical gap, even with increasing layers, is particularly noteworthy.

This research demonstrates the unique properties of MoSi₂N₄ as a 2D material with robust, chemically protected band edge states and tunable quasiparticle and excitonic properties via dielectric screening. This combination of stability and tunability makes MoSi₂N₄ a promising material for diverse applications in energy, 2D electronics, and optoelectronics. Future research could explore the material's behavior in different environments, investigating its interaction with various substrates and the impact on device performance.

The accuracy of the calculations relies on the approximations inherent in DFT and many-body perturbation theory. The study does not account for temperature effects or other factors that could influence the optical properties in real-world applications. While convergence tests were done, the computational cost limited the resolution in some calculations. Additional experimental verification would strengthen the conclusions.