Prediction of protected band edge states and dielectric tunable quasiparticle and excitonic properties of monolayer MoSi₂N₄

The study addresses the challenge that band edge states in 2D materials are highly susceptible to environmental perturbations, impacting device applications. Two coupling mechanisms are identified: (i) local chemical interactions (e.g., adsorption or interfacial hybridization) that are hard to predict/control, and (ii) nonlocal dielectric screening that can be engineered via substrates or layer thickness. The research investigates whether MoSi₂N₄ offers band edge states robust against local chemical coupling while remaining tunable via dielectric screening. The purpose is to elucidate the origin of such protection and quantify how quasiparticle and excitonic properties evolve with layer-dependent screening, establishing MoSi₂N₄ as a stable yet tunable 2D semiconductor.

Prior work has leveraged interlayer coupling and heterostructuring to tune properties of 2D materials, including band structure, optics, magnetism, and exotic states in twisted graphene. Environmental dielectric screening is known to renormalize band gaps and excitonic effects (e.g., in black phosphorus and TMDs), and methods like Coulomb/dielectric engineering have been proposed to control these properties. In contrast, local chemical coupling—even at vdW distances—can drastically alter band edges and is experimentally difficult to control. MoSi₂N₄, part of the MSi₂N₄ family, has been synthesized with excellent ambient stability and predicted to exhibit properties such as piezoelectricity, high thermal conductivity, and spin-valley coupling. This work positions MoSi₂N₄ within that context, focusing on protection of band edges from chemical coupling and tunability via screening.

- Structures: Monolayer, bilayer, and bulk MoSi₂N₄ with multiple stacking patterns optimized using VASP with PBE functional and DFT-D3 vdW correction; >20 Å vacuum for monolayer/bilayer to avoid image interactions. - DFT calculations: PBE for electronic structures; SOC assessed for monolayer. Interlayer separations and binding energies computed; comparison with other layered materials. - GW quasiparticle calculations: BerkeleyGW, norm-conserving pseudopotentials including Mo 4s/4p semicore. Plane-wave cutoff 125 Ry (wavefunctions), dielectric cutoff 50 Ry. Hybertsen-Louie GPP model for frequency dependence. Coulomb truncation for 2D systems. Accelerated methods (combined subsampling and analytical BZ integration; inclusion of all conduction bands) used to achieve full convergence; typical self-energy BZ integration with 6×6×1 k-grid and four subsampling points, converging band gaps within ~0.03 eV. Vacuum thickness convergence tested. - BSE excitonic calculations: GW inputs used; Tamm-Dancoff approximation. Coarse-to-fine k-grid interpolation: monolayer/bilayer 24×24×1 → 72×72×1; bulk 18×18×2 → 36×36×8. Gaussian smearing 25 meV for ε₂(ω). Convergence of k-point sampling and number of bands verified (results within ~50 meV). SOC not included in GW-BSE optical spectra discussed. - Analysis: Orbital-projected wavefunction character near band edges; isosurface charge densities for VBM/CBM; layer dependence of DFT and GW gaps; exciton binding energies from non-interacting e–h gap and rigorous BSE definition; comparison with literature values for other materials.

- Structural and interlayer metrics for MoSi₂N₄: optimized monolayer in-plane lattice constant 2.896 Å; Si–Si layer distance ~5.99 Å. Most stable bilayer interlayer separation d = 2.825 Å; bulk theoretical d = 2.807 Å. Interlayer binding energy E_bind = 43.8 meV/Ų, comparable to typical layered materials. - DFT-PBE electronic structure (indirect Γ→K): band gaps are weakly layer-dependent: monolayer 1.79 eV, bilayer 1.77 eV, bulk 1.70 eV (changes of −0.02 and −0.09 eV, respectively). Direct K-point DFT gaps: 2.03 eV (monolayer), 2.09 eV (bilayer), 2.10 eV (bulk). SOC splits the top valence band at K by ~130 meV; negligible effect on CBM at K and VBM at Γ. - Contrast with other layered materials: DFT gaps change strongly with thickness in MoS₂ (1.72→0.88 eV), WS₂, black phosphorus, C₃N, and C₃B, despite similar interlayer separations/binding energies. - Origin of robustness: Band-edge states are dominated by Mo d orbitals with minor contributions from Si and surface N; charge density of VBM/CBM localized inside the layer, reducing interlayer chemical hybridization. - GW quasiparticle gaps (indirect Γ→K): monolayer 2.82 eV, bilayer 2.67 eV, bulk 2.41 eV; corresponding GW corrections (relative to DFT indirect gap): +1.03, +0.90, +0.71 eV. Direct K-point GW gaps: 3.13, 2.94, 2.71 eV with corrections +1.10, +0.85, +0.61 eV. Layer dependence exists but is weaker than in MoS₂ and black phosphorus. - Optical properties (GW-BSE, ε₂(ω)) and excitons: Three prominent absorption peaks identified in monolayer: A at 2.50 eV, B at ~2.79 eV, C at ~2.97 eV; experimental first peak reported at 2.21 eV. Peak A arises from e–h pairs near K/K′; B from near Γ and K/K′; C from near Γ along Γ–M with minor K/K′ contributions. • A-exciton binding energies: monolayer ~0.63 eV (from Enon-int at K) and 0.78 eV (rigorous BSE definition); bilayer 0.40 eV; bulk 0.12 eV. • Optical gap E_opt (A peak): 2.50 eV (monolayer), 2.53 eV (bilayer), 2.59 eV (bulk). Net correction ΔΣ − E_bind ≈ 0.47, 0.45, 0.49 eV, nearly constant across thickness. - Stability vs tunability: DFT band edges and optical gap remain nearly invariant with thickness (beneficial for device stability), while quasiparticle gaps and exciton binding can be tuned via dielectric screening (substrate/layer control).

The findings directly address whether MoSi₂N₄ possesses band-edge states resistant to local chemical coupling. Orbital decomposition and charge-density isosurfaces demonstrate that VBM/CBM are primarily Mo d-derived and localized within the interior of the multi-atomic layer, minimizing interlayer hybridization. This explains the negligible change of the DFT band gap and dispersion from monolayer to bulk and suggests robustness against weak adsorption or substrate interactions lacking strong bonding. At the same time, GW and BSE results reveal that nonlocal dielectric screening significantly renormalizes the electron self-energy and electron–hole interactions: quasiparticle gaps decrease with increasing layer number while exciton binding energies are strongly reduced. The near cancellation between GW self-energy corrections and exciton binding maintains an almost constant optical gap across thicknesses. Consequently, MoSi₂N₄ offers a favorable combination of chemically protected band edges for stable device operation and dielectric-tunable quasiparticle/excitonic properties, enabling controlled engineering via substrate selection and layer thickness without compromising band-edge integrity.

This work establishes monolayer-to-bulk MoSi₂N₄ as a 2D semiconductor with band-edge states protected from interfacial chemical coupling due to their dominant interior Mo d-orbital character. Despite minimal DFT-level thickness dependence of the band gap, GW-BSE calculations show that quasiparticle gaps and exciton binding energies remain tunable through nonlocal dielectric screening, while the optical gap is largely thickness-insensitive. These combined properties, together with reported thermodynamic/mechanical stability and moderate band gap, position MoSi₂N₄ for applications in energy technologies, 2D electronics, and optoelectronics. The study highlights dielectric (Coulomb) engineering via substrate and layer control as a practical route to tailor electronic and optical responses while retaining robust band edges.

- GW-BSE calculations for 2D materials are challenging to converge; final optical results rely on coarse-to-fine k-grid interpolation with estimated convergence uncertainty ~50 meV. - SOC effects are not included in the presented GW-BSE spectra; SOC would split the first excitonic peak by ~130 meV and modestly affect higher peaks (~50 meV). - Differences between calculated and experimental optical peaks may arise from finite-temperature and SOC effects, as well as numerical convergence limits. - Some small shifts of optical features with thickness are within the numerical accuracy of the calculations. - Results depend on computational choices (GPP model, truncation schemes), though convergence tests were performed (GW gap convergence ~0.03 eV).