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

## TL;DR

The paper shows how atomic-scale features in sub-nanometer gaps affect optical fields and tunneling, using quantum theory to guide nanoscale device design.

## Contribution

The study introduces quantum hydrodynamic theory to explain and predict optical behavior in sub-nanometer gaps with atomic-scale protrusions.

## Key findings

- Atomic protrusions reshape nanofocusing without altering far-field resonances.
- Quantum theory predicts a red-to-blue spectral crossover with field suppression in tunneling regimes.
- Protrusion geometry controls the onset and strength of optical crossovers.

## Abstract

What are the main findings?
Atomistic protrusions barely shift far-field resonances but strongly reshape hotspot nanofocusing.Near-field enhancement is set by the protrusion aspect ratio competing with the nonclassical charge response.QHT predicts a red-to-blue crossover with suppressed enhancement in the tunneling-relevant regime.Protrusion geometry tunes the onset and strength of the crossover and near-field suppression.

Atomistic protrusions barely shift far-field resonances but strongly reshape hotspot nanofocusing.

Near-field enhancement is set by the protrusion aspect ratio competing with the nonclassical charge response.

QHT predicts a red-to-blue crossover with suppressed enhancement in the tunneling-relevant regime.

Protrusion geometry tunes the onset and strength of the crossover and near-field suppression.

What are the implications of the main findings?
Far-field spectra can be misleading proxies for nanoscale field confinement below 1 nm gaps.Atomic-scale morphology becomes a practical design knob for quantum plasmonic field control.It provides QHT-based rules to engineer stable, extreme hotspots in sub-nanometer nanogaps.

Far-field spectra can be misleading proxies for nanoscale field confinement below 1 nm gaps.

Atomic-scale morphology becomes a practical design knob for quantum plasmonic field control.

It provides QHT-based rules to engineer stable, extreme hotspots in sub-nanometer nanogaps.

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.