Correlation of Distinct Physical Properties in Luttinger Liquid

Quantum-confined electrons in one dimension (1D) behave as Luttinger liquid, a strongly correlated electronic matter that features suppressed spectral density at the Fermi energy and spin-charge separation. Metallic single-walled carbon nanotubes (SWNTs) provide the ideal platform to explore 1D Luttinger liquid physics. However, unambiguous demonstration of Luttinger liquid phenomena in SWNTs has been challenging because the Luttinger liquid interaction parameters are not known a priori. Here we combine electrical transport and optical nanoscopy measurements to correlate completely different physical properties in the same Luttinger liquid. The Luttinger liquid interaction parameters independently determined from the two measurements agree quantitatively with each other. Such combined electrical and optical studies can open up new opportunities in exploring 1D Luttinger liquid physics, such as non-equilibrium transport and ultrafast dynamics.