Self-Assembled H2NC Molecular Lattices as a Platform for Substrate-Tunable Quantum Superlattices

Abstract

Compared to van der Waals moiré systems, molecular assembly has emerged as an exciting alternative platform for superlattice engineering via heterointegration. The electronic properties of the self-assembled square lattice monolayer molecular crystal of metal-free naphthalocyanine (H2Nc), in particular the electronic band dispersion and their tunability by metal substrates, remain less explored. Using density functional theory, supported by angle-resolved photoemission and scanning tunneling microscopy, we compare the electronic structure of a free-standing H2Nc monolayer with that of H2Nc lattice assembled on noble metal substrates. In the freestanding film, we identify both nearly flat, molecule-localized states and more dispersive bands, and we show that each can be compactly described by an anisotropic tight-binding Hamiltonian that yields band-resolved hopping anisotropies. We further reveal wide tunability in the Coulomb interaction and inter-site hopping based on different molecular orbitals. Adsorption on Ag(100) drives strong orbital hybridization, charge transfer, and C2 symmetry breaking, producing partially filled, substrate-mediated dispersive states that metallize the molecular lattice. Orbital analysis identifies C2-even and C2-odd components and maps the spatial pattern of charge redistribution tied to symmetry breaking. Complementary ARPES on H2Nc/Au(111) qualitatively corroborates the predicted dispersion and partial filling. These results clarify how metal substrates convert H2Nc from isolated molecules into a tunable 2D lattice and highlight molecular superlattices as a versatile platform to simulate anisotropic lattice models.

Figures (5)

• Figure 1: (a) Top view of the relaxed H$_2$Nc thin film and high-symmetry line through the first Brillouin zone of the anisotropic square lattice. (b) Low-energy band structure; labels i-iii mark the most dispersive low-energy bands. (c,d) HOMO and LUMO bands, respectively. (e,f) Real parts of the $\Gamma$-point Bloch orbitals for the thin film (e) and an isolated molecule (f). orbitals were prepared using vaspkitvaspkit and visualized using VESTAVESTA.
• Figure 2: (a) Maximally-localized Wannier orbital for HOMO in the free-standing H$_2$Nc monolayer. $U$ represents the on-site Coulomb interaction. Sites labeled $V_{1,0}$ and $V_{1,1}$ indicate the nearest- and next-nearest-neighbor vectors used to extract short-range Coulomb interactions $V_{ij}$. (b) Schematic of the model geometry and parameters entering the screening kernel (see text and Eqn. (5)). (c) Tight-binding parameters $\varepsilon_n$, $t_{x,n}$, and $t_{y,n}$, for the free-standing 2D thin film, for all bands in an energy window around $E_F$ (shaded/open markers distinguish positive/negative hoppings). (d) Computed on-site $U$ and short-range intersite $V_{ij}$ for several choices of the effective dielectric $\varepsilon$ and screening length $\xi$.
• Figure 3: (a) Projected band structure and density of states (DOS) of the free-standing H$_2$Nc monolayer and (b) the monolayer adsorbed on Ag(100). A Gaussian smearing of 20 meV has been applied to all DOS curves. The reference DOS for the bare Ag(100) slab is also shown. (c,e) Top and side views of the relaxed H$_2$Nc/Ag(100) geometry. Further structure characterization can be found in the supplementary material. (d,f) Top and side views of the bonding charge density difference, with isosurfaces shown at $3\times10^{-4}$ e$^-$/Å$^3$. Orange represents electron accumulation and green shows depletion.
• Figure 4: Electronic structure of H$_2$Nc self-assembly on Au(111). (a) Comparison of UPS spectra of pristine Au(111) surface and H$_2$Nc monolayer. Inset shows high-resolution zoom-in view of the low-energy electronic states. Red arrow denotes the HOMO band, and blue arrow denotes the Shockley surface state band bottom. Energy-momentum cuts through $\Gamma$ on (b) sub-monolayer H$_2$Nc/Au(111) and (c) pristine Au(111) surface. Yellow dashed lines denote the Shockley surface state of Au(111). (d) Fitted dispersion of the HOMO band. (e) Topographic image of local patches of self-assembled H$_2$Nc on Au(111).
• Figure 5: Different molecular configurations studied by density functional theory. We refer to them as (a): $(0,0)$, (b): $(\pi,\pi)$, (c): $(\pi,0)$, (d): $(0,\pi)$ orders. Red circles over the macrocycles with inscribed lines emphasize hydrogen atom orientations. The $(0,0)$ order was found to be lowest in energy by about 25 meV/molecule.