Fig. 1: A 2D kagome MOF on an atomically thin insulator: DCA₃Cu₂ on single-layer hBN on Cu(111).

a STM image of MOF (with organic DCA-only regions; V_b = −1 V, I_t = 10 pA). 'P' and 'W' indicate pore (dashed white circle) and wire regions of hBN/Cu(111) moiré pattern. Lower inset: Fourier transform of STM image; sharp spots correspond to MOF hexagonal periodicity (scale bar: 0.25 nm⁻¹). Upper inset: STM image of bare hBN/Cu(111) moiré pattern (V_b = 4 V, I_t = 100 pA, scale bar: 4 nm). Red arrows: examples of crack, vacancy, and Cu cluster defects within MOF domain. b Top-view of MOF model overlaid upon small-scale STM image of region within red box in a (V_b = −1 V, I_t = 10 pA). MOF unit cell indicated in light blue. Blue dashed lines and solid circles: kagome pattern formed by DCA molecules, with inter-site electron hopping, t, and on-site Coulomb repulsion, U. c Model of MOF/hBN/Cu(111) (side view). Hydrogen: white; carbon: grey; boron: pink; nitrogen: blue; copper: orange. d Electronic band structure calculated by DFT (with U = 0)³⁶. Blue circles: projections onto MOF states. Grey curves: Cu(111) states (hBN states do not contribute within the shown energy range). Hybridisation between MOF and Cu(111) is hindered by the hBN monolayer; the MOF band structure retains its kagome character. Chemical potential E_F (blue dashed line) is close to half-filling of kagome bands. e Density of states, DOS(E) (tight-binding model with thermal broadening, U = 0, blue), and spectral function, A(E) (DMFT, U = 0.65 eV, orange), of freestanding MOF. Local Coulomb interaction opens a significant Mott energy gap E_g between lower (LHB) and upper Hubbard bands (UHB).