As far as I know, the refractive index of a specific material is its intrinsic properties but all materials have other unique properties if their size reduce down to nanoscale. I am not quite if this RI property will alter as their dimension change.
The refractive index of a material is known to decrease with band gap. On the other hand, the size dependency of the band gap is a well-known and widely studied quantum confinement effect. So, for example in quantum dots, whose band gap is size-dependent, it is expected that the refractive index and size will have certain correlation. See for example the attached reference where the RI of spherical CdTe QDs is calculated using 5 different models, showing for all models a RI that decreases quickly as the size is reduced. However, measuring the RI of nanoparticles is not an easy task, and due to the lack of experimental values, it is commonly assumed that the RI matches the bulk value. I do research on this topic if interested.
Article Pseudopotential Study of CdTe Quantum Dots: Electronic and O...
Adding to what Raul Montes already stated: The refractive index (or more general) the dielectric properties of a material, depend on their energy states. This can already be seen in a semiclassical Lorentz oscillator model of the dielectric function. If you plug in a different resonance frequency (e.g. different band gap), the dielectric function will shift, hence the (complex) refractive index will change at given frequencies. The closer to the resonance, the more drastic this effect will become. In more complex models, for example extracting a meaningful dielectric function from density functional theory, you exactly plug in all energy states (i.e. your calculated band structure for both, excited and ground states) to obtain the dielectric function. So, if the energy landscape changes, so will the dielectric function.
I agree with Raul Montes meaningful changes to the energy landscape, i.e. quantum confinement, often require very small structures, which simply have also a very small volume to probe during a measurement. This is particular true for the real part of the index; the complex part (i.e. absorption) is usually very strong close to resonances atleast. So, in a sense, you are probing a refractive index, when doing spectroscopy of a nanomaterials.
Michael
https://scholar.google.ru/citations?view_op=view_citation&hl=en&user=FCw46vEAAAAJ&cstart=100&pagesize=100&citation_for_view=FCw46vEAAAAJ:o9ULDYDKYbIC (this artickle is in my Research Gate list also)
Brewster laser refractometry of some type film glasses at thickness 100-200nm has not discovered any changes of Index refraction. Supposed that surface contribution has to appear on more thinner samples.
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