Tomonaga-Luttinger Liquid Parameters in Multiwalled Nanotubes

Tomonaga-Luttinger liquid (TLL) theory is a canonical formalism used to describe 1D metals, where the low-energy physics is determined by collective Bosonic excitations. Herein, a theoretical model to compute the parameters of Tomonaga-Luttinger liquid (TLL) in multiwalled nanotubes (MWNTs) is presented. MWNTs introduce additional complexity to the usual Fermionic chains due to interactions and hybridization between their multiple coaxial shells. A model in which conducting paths along the length of the MWNTs are randomly distributed among the shells is considered. 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 and 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 intershell coupling. Finally, experiments where predictions can be tested are proposed.