Possible Instability of the Fermi sea of metals against surface plasma oscillations

TL;DR

This paper demonstrates that in collision-less metals, the Fermi sea is inherently unstable against surface plasma oscillations due to surface-induced symmetry breaking, revealing a new self-amplification mechanism that challenges traditional damping assumptions.

Contribution

The authors develop a formalism showing an intrinsic instability of the Fermi sea against surface plasma oscillations, highlighting a novel energy conversion process caused by surface effects.

Findings

Instability of the Fermi sea against surface plasma oscillations in collision-less metals.

Analytical evaluation of the amplification rate based on energy conservation.

Landau damping is overcompensated, reducing its impact in sub-wavelength plasmonics.

Abstract

We derive a generic formalism for studying the energy conversion processes in bounded metals. Using this formalism we show that in the collision-less limit the Fermi sea of metals should experience an instability against surface plasma oscillations, which opens for the latter an intrinsic self-ampli cation channel. The origin of the instability is clari ed as arising from novel effects resulting from the translation symetry breaking due to the very presence of surface. The ampli cation rate of this channel is analytically evaluated on the basis of energy conservation and the effects of losses are discussed. In particular, the unique role played by the surface in energy conversion is unveiled. In contrast with common wisdom and in line with observations, Landau damping is shown as always overcompensated and therefore poses no serious issues in sub-wavelength plasmonics.