We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65) ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

We report on an electrical detection method of ultrasensitive carbon nanotube mechanical resonators. The noise floor of the detection method is reduced using a RLC resonator and an amplifier based on a high electron mobility transistor cooled at 4.2 K. This allows us to resolve the resonance frequency of nanotube resonators with an unprecedented quality. We show that the noise of the resonance frequency measured at 4.2 K is limited by the resonator itself, and not by the imprecision of the measurement. The Allan deviation reaches ∼10^-5 at 125 ms integration time. When comparing the integration time dependence of the Allan deviation to a power law, the exponent approaches ∼1/4. The Allan deviation might be limited by the diffusion of particles over the surface of the nanotube. Our work holds promise for mass spectrometry and surface science experiments based on mechanical nano-resonators.