# Acoustic plasmons at the crossover between the collisionless and hydrodynamic regimes in two-dimensional electron liquids

## TL;DR

This paper theoretically investigates acoustic plasmon modes in two-dimensional electron liquids, identifying signatures of the transition between collisionless and hydrodynamic regimes using near-field optical microscopy.

## Contribution

It introduces a comprehensive non-local conductivity model that includes various collision effects and many-body interactions to analyze plasmon dispersion and damping.

## Key findings

- Identification of key experimental signatures of the collisionless-hydrodynamic crossover.
- Derivation of dispersion relations for acoustic plasmons including damping effects.
- Analysis of coupling between plasmons and near-field probes in different regimes.

## Abstract

Hydrodynamic flow in two-dimensional electron systems has so far been probed only by dc transport and scanning gate microscopy measurements. In this work we discuss theoretically signatures of the hydrodynamic regime in near-field optical microscopy. We analyze the dispersion of acoustic plasmon modes in two-dimensional electron liquids using a non-local conductivity that takes into account the effects of (momentum-conserving) electron-electron collisions, (momentum-relaxing) electron-phonon and electron-impurity collisions, and many-body interactions beyond the celebrated Random Phase Approximation. We derive the dispersion and, most importantly, the damping of acoustic plasmon modes and their coupling to a near-field probe, identifying key experimental signatures of the crossover between collisionless and hydrodynamic regimes.