Hydrodynamics

Hydrodynamics is a universal description of fluids which emerges at length and time scales much larger than those that govern microscopic processes.  While it has been useful in almost all fields of physics, its applications in solid state physics have been fairly restricted. Recently, however, important strongly correlated systems have been found which exhibit universal transport properties which cannot be explained by a single particle picture, and for which a non-perturbative approach like hydrodynamics is warranted. The opportunity provided by these systems is twofold: it enables the study of novel regimes of transport with unique properties, and it also generates exotic types of hydrodynamic theories which would not occur otherwise ``in vacuum''. 

Experiments in 2D materials (e.g. graphene, PdCoO2) have recently amplified interest for a regime of transport in which electrons behave like a viscous fluid, and for which Ohm's law is replaced by the much richer Navier-Stokes equation. 

I gave a colloquium about this topic at U of T (see embedded youtube video on the left).

Electron hydrodynamic and Hall viscosity

A viscous electronic flow leads to even richer phenomenology than previously observed in classical viscous fluids, like honey or tar, by virtue of the electron being charged. Under an applied magnetic field, the electronic fluid should undergo a force perpendicular to its velocity and proportional to the velocity gradient. This so-called viscous Hall effect was predicted theoretically and, in analogy with the regular Hall effect, has a quantized version in the limit of large magnetic fields. In [1], we proposed a way of measuring the Hall viscosity of electronic fluids by measuring transport in mesoscopic samples of high-mobility 2D metals. Shortly after, the first measurement of the electronic viscous Hall effect was reported in graphene [2].

Visualizing a Poiseuille flow of electrons

In an ongoing collaboration with the groups of Shahal Ilani and Andre Geim, we put the theory to the test by providing the first direct imaging of a viscous flow of electrons in graphene. One of the key advances behind this work was the use of a magnetic field, which made it possible to deduce the local current profile based on the local Hall voltage (the latter being measured thanks to a single-electron transistor local voltage probe). This story was published in Nature and featured in a popular science article in PhysicsWorld!

What is the conductance of a wormhole?

Surprisingly, this far-fetched question is directly related to the very practical problem of making small electronic devices with the highest possible conductance. In a recent preprint, we show that, by a judicious choice of geometry, it is possible to reach an arbitrarily large conductance when electrons are a in novel regime of transport called hydrodynamic.

Geometric origin of the superballistic flow of electrons

In an ongoing experiment-theory collaboration with the groups of Shahal Ilani, Ady Stern, and Andre Geim, we have recently provided (see the preprint here) a demonstration of the geometric origin of the "superballistic" conductance of hydrodynamic electrons described in the post above. The experiment was done with a graphene sample in a Corbino geometry (which is just a disk with a hole in the middle), which is much easier to realize than a wormhole!