Recently, several new approaches have been suggested to experimentally measure the viscosity of the electron fluid in a metallic crystal. Previously, I posted about how ultrasound attenuation can be used to indirectly measure the viscosity. However, that method is arguably not sensitive enough for the small viscosities [of the order n hbar, where n is the electron density] that are of particular relevance to possible quantum limits to the viscosity.
Forcella, Zaanen, Valentinis, and van Der Marel considered electromagnetic properties of viscous charged fluids, finding new possible signatures due to the viscosity such as negative refractive index, a frequency dependent peak in the reflection coefficient, and a strong frequency dependence of the phase. However, they note that these effects may be difficult to observe for viscosities of the order
of the quantum limit, n hbar.
Tomadin, Vignale, and Polini considered a two-dimensional electron fluid in a Corbino disk device
in the presence of an oscillating magnetic flux. They showed that the viscosity could be determined from the dc potential difference that arises between the inner and the outer edge of the disk. In particular, for viscosities of the order of n hbar, the potential difference varied significantly oscillation frequencies in the MHz range.
Levitov and Falkovich recently considered the flow of an electron fluid in a micrometer scale channel in the hydrodynamic regime, where the electron-electron collision rate is much larger than the momentum relaxation rate. They found that when the viscosity to resistance ratio is sufficiently large viscous flow occurs producing vorticity and a negative nonlocal voltage. [See the figure below].
Spatially resolved measurements of the voltage allow determination of the magnitude of the viscosity.
Torre, Tomadin, Geim, and Polini considered the electron liquid in graphene in the hydrodynamic regime and showed that the shear viscosity could be determined from measurements of non-local resistances in multi-terminal Hall bar devices.
Although these last three proposals are promising for the two-dimensional electron fluids in graphene and semiconductor heterostructures fabrication of the relevant micron-scale devices will be particularly challenging for bad metals such as cuprates and organic charge transfer salts.