A new fundamental scale suggested by nanoplasmonics

Plasmonics has grown in recent years into a well established area of research with a great potential. Our interest to this area roots in mechanisms involved in plasmonic resonance responses and implied pretty narrow spatial dimension range between 1nm and 25nm. We entertain an idea that the very existence of surface plasmons with sizes in that range suggest a possibility of a new fundamental scale such as the size 5nm of a free electron in our neoclassical theory. This theory features a new spatial scale - the size a_e of a free electron. This scale is special to our theory and does not appear in either classical EM theory nor in the quantum mechanics where electron is always a point-like object. Our current assessed value for this scale is a_e≈100a_B where a_B is the Bohr radius, and consequently a_e≈5 nm. In our theory any elementary charge is a distributed in space quantity. Its size is understood as the localization radius which can vary depending on the situation. For instance, if an electron is bound to a proton in the Hydrogen atom then its the size of is approximately 1 Bohr radius, that is a_B≈0.05 nm, and when the electron is free its size is

a_e≈100a_B≈5 nm.

Interestingly, the upper bound 25 nm is the skin depth and that implies that a nanosystem of size smaller than 25nm is transparent to the external field. The same transparency should hold for a nanostructured surface indicating such a surface is better for nearly ideal field electron emission. There is an experimental evidence showing that the highest current densities were obtained for nanotips with sizes ∼1nm yet another important fact supporting a possibility of a fundamental nonoscale.