Waves in electron hydrodynamics

I sometimes have research ideas that I think are cool, but that don’t make sense for me to pursue. I generally just make a note of them and move on. This is the 22nd post in a series describing some of the ideas I’ve accumulated. This idea is closely related to conversations I’ve had over the years to with George Varnavides.

Waves in electron hydrodynamics

What’s the idea?

In some materials, electron scattering is momentum-conserving (on some relevant length- and time-scale). These materials exhibit electron hydrodynamics, where the electrons flow following the Navier-Stokes equation. Presumably that also means they can exhibit waves, and I think this could be an exciting phenomenon to understand.

Why is this important?

It would be a fundamentally novel phenomenon in a weird class of materials.

How can I get started?

I’d start by thinking about waves in a viscous medium. Realistic electronic fluids are likely limited to modest Reynolds numbers (1-10) in the near term (because of limitations in sample purity, mostly). Then I’d just map out the phenomenology of those waves (assuming this hasn’t already been done), keeping in mind that the viscosity need not be isotropic.

I’d also think about experimental setups where these waves can be forced and perhaps observed.

Finally, it seems useful to think about the relationship between these waves and e.g. plasmons. My intuition is that they are fundamentally different, but I could well be wrong and if this is what plasmons are that is also useful to know.