Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures

Abstract

The electronic transport properties of conventional three-dimensional metals are successfully described by Fermi-liquid theory. But when the dimensionality of such a system is reduced to one, the Fermi-liquid state becomes unstable to Coulomb interactions, and the conduction electrons should instead behave according to Tomonaga-Luttinger-liquid (TLL) theory. Such a state reveals itself through interaction-dependent anomalous exponents in the correlation functions, density of states and momentum distribution of the electrons. Metallic single-walled carbon nanotubes (SWNTs) are considered to be ideal one-dimensional systems for realizing TLL states. Indeed, the results of transport measurements on metal-SWNT and SWNT-SWNT junctions have been attributed to the effects of tunnelling into or between TLLs, although there remains some ambiguity in these interpretations. Direct observations of the electronic states in SWNTs are therefore needed to resolve these uncertainties. Here we report angle-integrated photoemission measurements of SWNTs. Our results reveal an oscillation in the pi-electron density of states owing to one-dimensional van Hove singularities, confirming the one-dimensional nature of the valence band. The spectral function and intensities at the Fermi level both exhibit power-law behaviour (with almost identical exponents) in good agreement with theoretical predictions for the TLL state in SWNTs.

Finite-temperature charge transport in the one-dimensional Hubbard model

“…The interest in the one-dimensional (1D) version of the model arises because of the existence of an exact solution based on the Bethe ansatz [4] and its relevance for quasi-1D materials [5][6][7][8][9], nanostructures [10][11][12] and realizations with ultracold atomic gases in optical lattices [3,13]. A recent optical-lattice experiment has investigated the non-equilibrium charge transport in the twodimensional Hubbard model [14].…”

Quasi-particle tunneling at a constriction in a fractional quantum Hall state

“…In particular cleaved-edge overgrowth (CEO) was used to produce clean and long quantum wires: temperature power laws as well as resonant transport were measured and compared with LL predictions [4]. Finally carbon nanotubes are emerging as a promising model system for the verification of LL physics [5,6].Edge FQH states are expected to lead to a particularly robust realization of a LL: edge channels at ν = 1/q with q odd integer, in fact, can only propagate in one direction and do not suffer from backscattering by random impurities. No localization occurs and the residual * Electronic address: roddaro@sns.it disorder only affects the electrons giving a mere phase shift.…”

“…In particular cleaved-edge overgrowth (CEO) was used to produce clean and long quantum wires: temperature power laws as well as resonant transport were measured and compared with LL predictions [4]. Finally carbon nanotubes are emerging as a promising model system for the verification of LL physics [5,6].…”

Tomonaga-Luttinger Liquid and Coulomb Blockade in Multiwall Carbon Nanotubes under Pressure

“…where E 0 is calculated from the measured nanotube diameter (~30nm), the α T = 0,P ( ) values are obtained from the power law region II and by using the two parameters extracted from the previous scaling of expression (3) shown on the lower panel of Fig. 3:…”