The field of ion transport through carbon nanotubes (CNTs) is marked by a large variability of the ionic conductance values reported by different groups. There is also a large uncertainty concerning the relative contributions of channel and access resistances in the experimentally measured currents, both depending on experimental parameters (nanotube length and diameter). In this perspective article, we discuss the ionic conductance values reported so far in the case of 2 individual CNTs and compare them with standard nano-fluidic models considering both the access and channel resistances. With a view toward guiding experimentalists, we thus show in which conditions the access or the channel resistance can predominate in CNTs. We explain in particular that it is not justified to use phenomenological models neglecting the channel resistance in the case of micrometer-long CNTs. This comparison reveals that most experimental conductance values can be explained in the framework of current nanofluidic models by considering experimental variations of slip length and surface charge density and that just a few extraordinarily high values cannot be accounted for even using extreme parameter values. Finally, we discuss how to complete existing models and how to improve the statistical reliability of experimental data in the field.

Helium is recognized as a model system for the study of phase transitions. Of particular interest is the superfluid phase in two dimensions. We report measurements on superfluid helium films adsorbed on the surface of a suspended carbon nanotube. We measure the mechanical vibrations of the nanotube to probe the adsorbed helium film. We demonstrate the formation of helium layers up to five atoms thickness. Upon increasing the vapor pressure, we observe layer-by-layer growth with discontinuities in both the number of adsorbed atoms and the speed of the third sound in the adsorbed film. These hitherto unobserved discontinuities point to a series of first-order layering transitions. Our results show that helium multilayers adsorbed on a nanotube are of unprecedented quality compared to previous works. They pave the way to new studies of quantized superfluid vortex dynamics on cylindrical surfaces, of the Berezinskii-Kosterlitz-Thouless phase transition in this new geometry, and perhaps also to supersolidity in crystalline single layers as predicted in quantum Monte Carlo calculations.

Helium-4 atoms are bosons, with the capability to turn superfluid at very low temperature. Remarkably, this property is conserved even when the thickness of the Helium film is reduced down to few atoms thick only. The study of 2D helium films has led to several breakthrough in condensed matter physics including the study of third sound and topological phase transitions, the latter being rewarded by the 2016 Nobel Prize.In most experimental studies helium was adsorbed on large scale substrates, such as mm2 scale grafoil plates or Mylar. Recent advances in the field of optomechanics and nanomechanics now opens up the possibility to study fluids and superfluids of smaller dimensions.In this talk, we present our recent experiments on helium films probed through the mechanical vibrations of a carbon nanotube. We observed a strong discontinuity in the adsorption of He on the nanotube surface, that we attributed to a layering transition. In addition, the low-temperature dependence of the mechanical mode of the nanotube exhibit a mode softening. Thanks to the tunability of the nanotube resonator, we confirmed the spring nature of this effect and drawn a link with the propagation of third sound in He 2D films.

When cooling Helium-4 atoms at very low temperature the system becomes superfluid, a quantum state of matter. Remarkably, this property is conserved even when the thickness of the Helium film is reduced down to few atoms thick only. The study of 2D helium films has led to several breakthrough in condensed matter physics including the study of third sound and topological phase transitions, the latter being rewarded by the 2016 Nobel Prize.Up to now, most experimental studies focused on large scale substrates, such as mm2 scale grafoil plates or Mylar. Recent advances in the field of optomechanics and nanomechanics now opens up the possibility to study fluids and superfluids of smaller dimensions.I will present our recent experiments on helium films growed on individual carbon nanotube, and probed through the mechanical vibrations of the nanotube. We observed a strong discontinuity in the adsorption of He on the nanotube surface, that we attributed to a layering transition. In addition, the low-temperature dependence of the mechanical mode of the nanotube exhibit a mode softening. Thanks to the tunability of the nanotube resonator, we confirmed the spring nature of this effect and drawn a link with the propagation of third sound in He 2D films.

Mechanical resonators based on a singlecarbon nanotube are exceptional sensors of mass and force.The force sensitivity in these ultralight resonators is oftenlimited by the noise in the detection of the vibrations. Here,we report on an ultrasensitive scheme based on a RLCresonator and a low-temperature amplifier to detect nanotubevibrations. We also show a new fabrication process ofelectromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrodedown to ∼150 nm. These advances in detection and fabrication allow us to reach 0.5pm/ Hz displacement sensitivity.Thermal vibrations cooled cryogenically at 300 mK are detected with a signal-to-noise ratio as high as 17 dB. We demonstrate4.3zN/ Hz force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is animportant step toward imaging individual nuclear spins and studying the coupling between mechanical vibrations and electronsin different quantum electron transport regimes.