Probing Nonlinear Luttinger liquid Physics in Semiconducting Single Walled Carbon Nanotubes

Quantum-confined electrons in one dimension (1D) constitute a Luttinger liquid, which features charge spin separation and other intriguing properties distinctly different from the Fermi liquid. Single walled carbon nanotubes (SWNTs) provide the ideal platform to explore such Luttinger liquid physics due to strong lateral quantum confinement and the presence of nanotubes of different species. But in many 1D materials including semiconducting SWNTs, the deviation from linear dispersion can greatly alter the electron behaviors. In order to describe the high-energy electron behaviors in 1D materials with nonlinear band structures, novel theoretical approaches have been employed to replace the linear dispersion with a generic one, which is known as the nonlinear Luttinger liquid theory. Here we probe the nonlinear Luttinger liquid physics in semiconducting SWNTs by combining electronic transport and infrared nano-imaging methods. The electron behaviors in semiconducting SWNTs are well captured by the nonlinear Luttinger liquid theory and are in strong contrast to the linear Luttinger liquid as in metallic SWNTs. Our findings provide novel insight into 1D systems beyond the conventional linear Luttinger liquid paradigm.