A simple derivation of the shell polarizability formula and investigation of the plasmonic behavior of aluminum nanoshells with the Mie theory.

In this paper, we found that the formula of shell polarizability in existing popular monographs is not uniform, which may lead to misuse of this expression in research. To avoid potential misuse, a detailed derivation has been supplemented in this work to clarify this formula. Using the attained correct shell polarizability, we questioned the conclusion of the surface plasmon resonances of aluminum metal nanoshells that could be tuned into the near-infrared region in previous research. More importantly, the new reliable parameters are successfully searched to achieve controllable surface plasmon resonances of aluminum nanoshells, such as tuning into the near-infrared regime, based on the Mie theory.