Mobile solid $^3$He on carbon nanotube promoted by topological frustration

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 of matter 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. We demonstrate that $^3$He on a nanotube merges both fermionic and bosonic phenomena, with a quantum phase transition between solid 1/3 phase and a fluid-like solid. The bosonic dimer fluid-like solid contains topology-induced vacancies which are delocalized owing to large zero-point motion. We thus observe a quantum phase transition from fermionic $^3$He crystal in to a bosonic one in quasi-1D geometry.