Quantum Hydrodynamic Theory for Sub-Nanometer Gaps: Atomic Protrusions Govern Near-Field Enhancement and Tunneling Signatures

As nanofabrication advances toward atom-by-atom control of surface morphology, plasmonic electrodes and nanogap devices are being pushed into a regime where atomic-scale protrusions and sub-nanometer separations become accessible. In this extreme limit, classical electrodynamics becomes unreliable because it cannot capture quantum effects. To this end, we compute the optical response of metallic sub-nanometer nanogaps containing atomic-scale protrusions by employing quantum hydrodynamic theory (QHT), and benchmark the predictions against the classical local-response approximation (LRA). We revealed that atomic-scale variations in protrusion can leave the far-field scattering spectrum nearly unchanged while profoundly reshaping tnear-field nanofocusing. Upon a continuous decrease in the nanogap, QHT successfully predicts non-monotonic spectral evolution with a redshift-to-blueshift deflection point accompanied via a suppression of field enhancement, whereas LRA yields a continuous redshift and a monotonic increase in field enhancement. We further demonstrated that such an inflection point is tunable, as determined by the atomic morphology of the electrodes, which provide a theoretical foundation for the experimental observation of varied inflection points. These results provide a practical route to optically diagnose and engineer tunneling-enabled charge exchange and quantum-regulated nanofocusing in extreme plasmonic nanogaps, and offer design guidance for molecular-scale optoelectronic and nanophotonic devices.