High Density Electrons on a Thin Helium Film over an Amorphous Metal Substrate*

Electrons on helium offer a unique platform for understanding two-dimensional electron systems. The high mobilities and low densities characteristic of the system allow us to probe different regimes of phase space than typical solid state structures. However, observing a degenerate liquid has yet to be conclusively demonstrated. This has been difficult due to a hydrodynamic instability which limits electron densities on bulk helium. This restriction can be circumvented by using a thin film of helium, but typically substrate surface roughness can make electron detection difficult. In this work, we use an amorphous metal as a substrate and show that we can stably support densities of electrons that should be Fermi degenerate. The amorphous metal is grown with a surface roughness less than 100pm, and has no grain boundaries that would act to impede electron transport. We have evidence of electron densities around 10¹¹ cm^-2, which at 1.8K is expected to be a degenerate liquid. These measurements were taken using a kelvin probe technique, which as we will discuss is dependent on not only the charge density, but also the deformation of the helium surface.