Experimental Studies of the 2D Superfluid Transition in He4 Films and the Kosterlitz Thouless Transition

All normal liquids have a viscosity. It can be large, like cold maple syrup, or small like water, but all conventional liquids have a non-zero viscosity. However, superfluids have zero viscosity. They are the fluid analogs of superconductors, which, unlike normal metals, can have zero resistance at low temperatures.  

In our experiments, we studied a 2D version of superfluidity, in He4, with films only an atomic layer or two thick. A normal liquid that thin could not flow; its viscosity would lock it to the substrate. However, 2D superfluids, because they have zero viscosity, can flow. We built a very sensitive torsional microbalance to study the flow of these atomically thin superfluid He4 films. What we observed puzzled us at first. The superfluid density, a measure of the fraction of superfluid within the entire liquid, did not go continuously from a finite value to zero at the transition temperature, the way it did for 3D systems. In 2D systems, it dropped precipitously from a finite value to zero at the transition.  

Others helped us to understand this result. David Nelson at Harvard University suggested the results might be explained by the Kosterlitz Thouless (KT) theory. He and his collaborators, Vinay Ambegaokar (Cornell University), Bert Halperin (Harvard University), and Eric Siggia (Rockefeller University) reworked the theory into a form applicable to our system, and the agreement with that theory was astonishingly good.   

While we had not set out to verify the KT theory, that was precisely what we ended up doing.