Phonon-assisted tunnelling in interacting suspended single-wall carbon nanotubes

Wataru Izumida,Milena Grifoni

doi:10.1088/1367-2630/7/1/244

Abstract

Transport in suspended metallic single-wall carbon nanotubes in the presence of strong electron–electron interaction is investigated. We consider a tube of finite length and discuss the effects of the coupling of the electrons to the deformation potential associated to the acoustic stretching and breathing modes. Treating the interacting electrons within the framework of the Luttinger liquid model, the low-energy spectrum of the coupled electron–phonon system is evaluated. The discreteness of the spectrum is reflected in the differential conductance which, as a function of the applied bias voltage, exhibits three distinct families of peaks. The height of the phonon-assisted peaks is very sensitive to the parameters. The phonon peaks are best observed when the system is close to the Wentzel–Bardeen singularity.

Highlights

DEUTSCHE PHYSIKALISCHE GESELLSCHAFT between phonons and plasmons
The experimental observation of the phonon peak would be an indication of the strong fluctuation of the superconducting order parameter, which corresponds to the WB singularity, in SWNTs
Long-range Coulomb interaction is dominant in isolated SWNTs, because the electrons are spread out around the circumference of the tube, and the probability of two electrons to be near to each other is of the order 1/N, where N is the number of atoms on the circumference

Summary

Low-energy Hamiltonian

This cannot occur, not even for the smallest SWNT radii. The breathing mode yields a renormalization of the electron–electron interaction parameter as g∗ = vF/v∗c+ = g/aB This results in the increase of the electron–phonon coupling in equation (12) with (I∗)2 = I2/a. We notice that Umklapp scattering processes should reduce the charge velocity [31] This effect would be dominant near half-filling, where a strong coupling with the stretching mode is expected [29]. This situation has not been considered in our calculation, since SWNTs are usually away from half-filling [11]

Phonon-assisted tunnelling

Conclusion