Surface distortion splits surface plasmons asymmetrically in energy with a net lowering of zero-point energy. We contrast this with the symmetrical distortion of electronic energy levels. We use conformal mapping to demonstrate this splitting and find that surface corrugation always leads to a decrease in the zero-point energy of a metallic surface, but the decrease is not strong enough to drive a surface reconstruction on its own. A second metallic surface in proximity to the first gives a more significant lowering of energy, sufficient to drive the instability of a mercury thin film. This mechanism provides a fundamental length scale limit to planar nanostructures.

• Received 24 January 2020
• Accepted 8 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.046802