# Highly excited electronic image states of metallic nanorings

## TL;DR

This paper investigates the existence of Rydberg-like electronic image states around metallic nanorings, revealing how geometry influences their formation and providing analytical and numerical insights into these quantum states.

## Contribution

It introduces a model for electronic image states around metallic nanorings, deriving the potential analytically and computing the states numerically, which was not previously done.

## Key findings

- Detached image states exist around nanorings.
- The aspect ratio of the torus determines the support for such states.
- Analytical potential and numerical solutions confirm the states' existence.

## Abstract

We study electronic image states around a metallic nanoring and show that the interplay between the attractive polarization force and a repulsive centrifugal force gives rise to Rydberg-like image states trapped several nanometers away from the surface. The nanoring is modeled as a perfectly conducting isolated torus whose electrostatic image potential is derived analytically. The image states are computed via a two-dimensional finite-difference scheme as solutions of the effective Schr\"odinger equation describing the outer electron subject to this image potential. These findings demonstrate not only the existence of detached image states around nanorings but allow us also to provide general criteria on the ring geometry, i.e. the aspect ratio of the torus, that need to be fulfilled in order to support such states.