# Temperature dependence of the surface plasmon resonance in small electron gas fragments, self consistent field approximation

## TL;DR

This paper investigates how temperature affects the surface plasmon resonance in small metal spheres using an electron gas model, revealing a possible blue shift at high temperatures relevant for ultrafast experiments.

## Contribution

It provides a detailed theoretical analysis of temperature effects on plasmon resonance in small spheres beyond simple approximations, considering quantum effects.

## Key findings

- Blue shift of plasmon resonance with increasing temperature
- Significant effects when temperature is a large fraction of Fermi energy
- Guides for ultrafast pump-probe experiments

## Abstract

The temperature dependence of the surface plasmon resonance in small metal spheres is calculated using an electron gas model within the Random Phase Approximation. The calculation is mainly devoted to the study of spheres with diameters up to at least 10 nm, where quantum effects can still be relevant and simple plasmon pole approximation for the dielectric function is no more appropriate. We find a possible blue shift of the plasmon resonance position when the temperature is increased while keeping the size of the sphere fixed. The blue shift is appreciable only when the temperature is a large fraction of the Fermi energy. These results provide a guide for pump and probe experiments with a high time resolution, and tailored to study the excited electron system before thermalisation with the lattice takes place.