Interrelation of elasticity and thermal bath in nanotube cantilevers

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.This work is supported by ERC advanced (Grant No. 692876), ERC PoC (Grant No. 862149), Marie Skłodowska-Curie (Grant No. 665884), PROBIST (Grant No. 754510), the Cellex Foundation, the CERCA Programme, AGAUR (Grant No. 2017SGR1664), Severo Ochoa (Grant No. SEV2015-0522), MICINN (Grants No. RTI2018-097953-B-I00 and No. PGC2018-096955-B-C44), the Fondo Europeo de Desarrollo Regional, the Grant No. MAT2017-82970-C2-2-R of Spanish MINECO and the Project No. E13_17R from Aragon Regional Government (Construyendo Europa desde Aragón). F. A. acknowledges support from European Research Council (ERC) starting Grant No. 802093. P. V. acknowledges support from European Research Council (ERC) starting grant 758794 “Q-ROOT.”Peer reviewe