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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., Comment: 36 pages, including 19 pages of the main text and 17 pages of the Methods section, 4 Figures, all in the main text

Graphene and carbon nanotubes (CNTs) share the same atomic structure of hexagonal carbon lattice. Yet, their synthesis differs in many aspects, including the shape and size of the catalyst. Here, we demonstrate a floating-catalyst chemical vapor deposition (FCCVD) technique for substrate-free, single-step growth of CNT-graphene heterostructures (CNT-G-H) using ethylene as a carbon source. The formation of CNT-G-H is directly evidenced by lattice-resolved (scanning) transmission electron microscopy (STEM) and electron diffraction experiments, corroborated by atomic force microscopy (AFM). Our experiments show the relative number density of graphene-nanoflakes can be tuned by optimizing the synthesis conditions. Since in the applied process the formation of the structures take place in gas-suspension, the as-synthesized CNT-G-H films can be deposited on any surface in ambient temperature with an arbitrary thickness. Moreover, this process of CNT-G-H synthesis with strong universality has also been realized in multiple systems of ethylene-based FCCVD with various catalysts and set-ups.

Transparent and conductive films (TCFs) are of great technological importance. The high transmittance, electrical conductivity and mechanical strength make single-walled carbon nanotubes (SWCNTs) a good candidate for their raw material. Despite the ballistic transport in individual SWCNTs, however, the electrical conductivity of their networks is limited by low efficiency of charge tunneling between the tube elements. Here, we demonstrate that the nanotube network sheet resistance at high optical transmittance is decreased by more than 50% when fabricated on graphene and thus provides a comparable improvement as widely adopted gold chloride ($\mathrm{AuCl_3}$) doping. However, while Raman spectroscopy reveals substantial changes in spectral features of doped nanotubes, no similar effect is observed in presence of graphene. Instead, temperature dependent transport measurements indicate that graphene substrate reduces the tunneling barrier heights while its parallel conductivity contribution is almost negligible. Finally, we show that combining the graphene substrate and $\mathrm{AuCl_3}$ doping, the SWCNT thin films can exhibit sheet resistance as low as 36 $\Omega$/sq. at 90% transmittance., Comment: 21 pages, 6 figures