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Helium is recognized as a model system for the study of phase transitions. Ofparticular interest is the superfluid phase in two dimensions. We reportmeasurements on superfluid helium films adsorbed on the surface of a suspendedcarbon nanotube. We measure the mechanical vibrations of the nanotube to probethe adsorbed helium film. We demonstrate the formation of helium layers up tofive atoms thickness. Upon increasing the vapour pressure, we observelayer-by-layer growth with discontinuities in both the number of adsorbed atomsand the speed of sound in the adsorbed film. These hitherto unobserveddiscontinuities point to a series of first-order layering transitions. Ourresults show that helium multilayers adsorbed on a nanotube are ofunprecedented quality compared to previous works. They pave the way to newstudies of quantized superfluid vortex dynamics on cylindrical surfaces, of theBerezinskii-Kosterlitz-Thouless phase transition in this new geometry, perhapsalso to supersolidity in crystalline single layers as predicted in quantumMonte Carlo calculations.

Layering transitions in superfluid helium adsorbed on a carbon nanotube mechanical resonator