Tomonaga-Luttinger Liquid parameters in Multi-wall Nanotubes

Tomonaga-Luttinger liquid (TLL) theory is a canonical formalism used to describe one-dimensional (1D) metals, where the low energy physics is determined by collective bosonic excitations. In this work, we present a theoretical model to compute the parameters of Tomonaga-Luttinger liquid (TLL) in multi-wall nanotubes (MWNTs). MWNTs introduce additional complexity to the usual fermionic chains due to interactions and hybridization between their multiple coaxial shells. We consider a model in which conducting paths along the length of the MWNTs are randomly distributed among the shells. Since the valley degree of freedom remains a good quantum number, the TLL description in addition to spin and charge, contains also valley degree of freedom, hence four mode description applies. The values of all four TLL parameters are obtained for this model. A surprising outcome is that the compressibility of the holon mode becomes a universal quantity, while the parameters of neutral modes will depend on the details of inter-shell coupling. Finally, we propose experiments where our predictions can be tested.