# Nonlocal optical responses of ultrapure metals in the hydrodynamic regime

## TL;DR

This paper develops a theoretical framework for understanding the optical responses of ultrapure metals in the hydrodynamic regime, highlighting the role of viscosity and proposing optical methods to measure hydrodynamic effects.

## Contribution

It introduces a hydrodynamic theory-based model for optical responses in ultrapure metals, extending beyond the traditional Drude theory.

## Key findings

- Identification of a hydrodynamic mode due to viscosity
- Calculation of reflectance and transmittance in electron fluids
- Proposals for optical probing of hydrodynamic effects

## Abstract

Our conventional understanding of optical responses in metals has been based on the Drude theory. In recent years, however, it has become possible to prepare ultrapure metallic samples where the electron-electron scattering becomes the most dominant process governing transport and thus the Drude theory, where momentum-relaxing scatterings such as electron-impurity scattering are assumed to be dominant, is no longer valid. This regime is called the hydrodynamic regime and described by an emergent hydrodynamic theory. Here, we develop a basic framework of optical responses in the hydrodynamic regime. Based on the hydrodynamic equation, we reveal the existence of a ``hydrodynamic mode'' resulting from the viscosity effect and compute the reflectance and the transmittance in three-dimensional electron fluids. Our theory also describes how to probe the hydrodynamic effects and measure the viscosity through simple optical techniques.