Unveiling the landscape of Mottness and its proximity to superconductivity in 4Hb-TaS$_2$

Mott physics is at the root of a plethora of many-body quantum phenomena in quantum materials. Recently, the stacked or twisted structures of van der Waals (vdW) materials have emerged as a unique platform for realizing exotic correlated states in the vicinity of the Mott transition. However, the definitive feature of Mottness and how it rules the low-energy electronic state remain elusive and experimentally inaccessible in many interesting regimes. Here, we quantitatively describe a filling-controlled Mott state and its interplay with superconductivity by scanning tunnelling spectroscopy in a vdW bulk heterostructure, 4Hb-TaS$_2$, that interleaves strongly correlated 1T-TaS$_2$ layers with superconducting 1H-Ta$_2$ layers. The fine tunability of electron doping induced by interlayer charge transfer allows us to continuously track the spectral function with unsurpassed energy resolution from a depleted narrow band (0.2 electrons per site) toward a Mott transition at half filling. The gradually emerging Mott-Hubbard bands, followed by the sharpening and vanishing of the central quasiparticle peak as predicted in the Brinkman-Rice scenario, unambiguously demonstrate the Mott physics at play. Importantly, the renormalization of the low-energy electrons acts destructively on the superconducting pairing potential, leaving behind nonsuperconducting, paramagnetic puddles at the nanoscale. Our results reveal a seminal system near the border of the Mott criterion that enables us to illustrate the predictive power of the Hubbard model, and set such heterostructures as promising ground for realizing new correlated states in the heavily doped Mott regime.