Topologically protected mobile solid $^3$He on carbon nanotube

Low dimensional fermionic quantum systems are exceptionally interesting because they reveal distinctive physical phenomena, including among others, topologically protected excitations, edge states, frustration, and fractionalization. Two-dimensional $^3$He has indeed shown a remarkable variety of phases including the unusual quantum spin liquid. Our aim was to lower the dimension of the $^3$He system even more by confining it on a suspended carbon nanotube. In our measurements the mechanical resonance of the nanotube with adsorbed sub-monolayer of $^3$He was measured as a function of coverage and temperature down to 10\;mK. At lowest temperatures and low coverages we have observed a liquid-gas coexistence which transforms to the famous 1/3 commensurate solid phase at intermediate densities. However, at larger monolayer densities we have observed a quantum phase transition from 1/3 solid to a completely new, soft and mobile solid phase. We interpret this mobile solid phase as a bosonic commensurate crystal consisting of helium dimers with topologically protected zero-point vacancies which are delocalized at low temperatures. We thus demonstrate that $^3$He on a nanotube merges both fermionic and bosonic phenomena, with a quantum phase transition between fermionic solid 1/3 phase and a newly observed bosonic dimer solid. The mobility and softness of the bosonic dimer solid are conditioned by topology-induced vacancies which become delocalized at low temperatures owing to a large zero-point motion.