Systematic cRPA study of two-dimensional MA$_2$Z$_4$ materials: From unconventional screening to correlation-driven instabilities

Abstract

Understanding the interplay between screening, electronic correlations, and collective excitations is essential for the design of two-dimensional quantum materials. Here, we present a comprehensive first-principles study of more than 60 MA$_2$Z$_4$ monolayers, encompassing semiconducting, metallic, cold-metallic, magnetic, and topological phases. Using the constrained random phase approximation (cRPA), we compute material-specific effective Coulomb interaction parameters $U$, $U'$, and $J$, including their spatial dependence across distinct correlated subspaces defined by local coordination and crystal symmetry. In semiconducting compounds, long-range nonlocal interactions persist, revealing unconventional screening and suggesting strong excitonic effects beyond simple dielectric models. In cold-metallic systems, sizable long-range Coulomb interactions remain despite the presence of free carriers, highlighting their atypical metallic screening. Among 33-valence-electron compounds, we find $U_{\mathrm{eff}} > W$ in the $β_2$ phase, indicating proximity to charge-density-wave or Mott instabilities. Several V- and Nb-based systems exhibit intermediate-to-strong correlation strength, with $U/W > 1 $ in multiple cases. Using cRPA-derived Stoner parameters, we identify magnetic instabilities in various V-, Nb-, Cr-, and Mn-based compounds. Finally, selected cold-metallic systems display plasmon dispersions that deviate from the conventional $\sqrt{q}$ behavior, revealing nearly non-dispersive low-energy modes. These results position MA$_2$Z$_4$ monolayers as a versatile platform for investigating correlation-driven instabilities and emergent collective behavior in two dimensions.

Figures (5)

• Figure 1: Side and top views of the two-dimensional crystal structure of intercalated architecture MA$_2$Z$_4$ in (a) $\alpha_1$ structure, (b) $\alpha_2$ structure, (c) $\beta_1$ structure, (d) $\beta_2$ structure, (e) $\beta_5$ structure, and (f) Star-of-David (SOD) reconstructed $\beta_2$ crystal structure. Dark gray, white, and blue spheres denote M, A, and Z atoms, respectively.
• Figure 2: Electronic structure and maximally localized Wannier functions (MLWFs) for representative MA$_2$Z$_4$ compounds. Panels (a)--(f) show the projected DFT-PBE band structures of $\alpha_1$-TaSi$_2$N$_4$, $\alpha_1$-TaSi$_2$P$_4$, $\beta_2$-CrGe$_2$N$_4$, $\alpha_1$-MoSi$_2$N$_4$, $\beta_5$-MnBi$_2$Te$_4$, and $\beta_2$-HgGa$_2$Se$_4$. Panels (g)--(l) compare the original DFT-PBE bands (gray) with the Wannier-interpolated bands (cyan) for three different correlated subspaces. Panels (m)--(r) display the spatial distributions of selected MLWFs used in the construction of these subspaces. Left column: $d_{z^2}$-like MLWF (one-orbital model). Middle column: $d_{xy}$-like MLWF from a three-orbital subspace ($d_{z^2}$ + $d_{xy}$ + $d_{x^2-y^2}$). Right column: $d_{x^2-y^2}$-like MLWF from the full $d$-manifold. For the topological compound $\beta_2$-HgGa$_2$Te$_4$, the relevant subspaces consist of $p_x$+$p_y$, $s$ + $p_x$+$p_y$, and $s$ + $p$ orbitals.
• Figure 3: On-site intra-orbital Coulomb interaction parameters — bare interaction $V$, partially screened interaction $U$, and fully screened interaction $\tilde{U}$ — for 2D MA$_2$Z$_4$ compounds with 32, 33, 34, and 41 valence electrons. Results are shown for different correlated subspaces, enabling comparison of the strength and screening of electronic interactions across a wide range of chemical compositions and electronic configurations. The abbreviation VEC refers to valence electron count.
• Figure 4: Real-space decay of the intra-orbital Coulomb interaction for selected MA$_2$Z$_4$ compounds with 34 and 33 valence electrons. Shown are the bare interaction $V(r)$ (solid lines), the partially screened interaction $U(r)$, and the fully screened interaction $\tilde{U}(r)$ as functions of distance $r$, expressed in units of the in-plane lattice constant $a$. All results correspond to the $d_{z^2}$+$d_{xy}$+$d_{x^2-y^2}$ (or $d_{z^2}$+$e_g$) correlated subspace. Panels (a)--(d) present 34-valence-electron compounds: (a) displays $V(r)$, $U(r)$, and $\tilde{U}(r)$ for $\alpha_1$-MoSi$_2$N$_4$ up to $r = 6a$; (b) extends this analysis to $r = 20a$ and includes power-law fits, where $U(r) \sim r^{-\alpha}$ and $\tilde{U}(r) \sim r^{-\beta}$ with $\alpha = 0.6$ and $\beta = 0.55$, respectively; (c) shows the analogous decay for $\alpha_1$-WSi$_2$N$_4$ up to $r = 20a$, exhibiting a similar slow screening behavior without fitted exponents; (d) presents $\beta_2$-CrGe$_2$N$_4$ up to $r = 9a$, where the faster decay of $\tilde{U}(r)$ reflects stronger metallic screening. Panels (e)--(h) extend the analysis to 33-valence-electron compounds: (e) and (f) show the decay of $V(r)$, $U(r)$, and $\tilde{U}(r)$ up to $r=12a$ for $\alpha_1$- and $\beta_2$-NbGe$_2$N$_4$, respectively; (g) and (h) present the corresponding results for $\alpha_1$- and $\beta_2$-TaSi$_2$N$_4$ up to $r=12a$.
• Figure 5: Plasmonic properties of selected 33-valence-electron MA$_2$Z$_4$ cold metallic compounds. Panels (a) and (b) show the calculated electron energy loss spectra $L(\mathbf{q},\omega)$ for wavevectors along the $\Gamma$--M direction in (a) $\alpha_1$-TaSi$_2$N$_4$ and (b) $\beta_2$-TaSi$_2$N$_4$. Plasmon dispersion relations extracted from the peak positions in $L(\mathbf{q},\omega)$ are plotted in (c)--(f) for four representative materials: (c) $\alpha_1$-TaSi$_2$N$_4$, (d) $\alpha_1$-NbSi$_2$N$_4$, (e) $\alpha_1$-NbGe$_2$N$_4$, and (f) $\beta_2$-TaSi$_2$N$_4$. The results show pronounced deviations from conventional $\sqrt{q}$ plasmon dispersion, including linear and negative-slope regimes characteristic of cold-metal band structures.