Real Space Imaging of One-Dimensional Standing Waves: Direct Evidence for a Luttinger Liquid

TL;DR

This paper provides direct real-space imaging of electronic standing waves in a carbon nanotube, offering concrete evidence for Luttinger liquid behavior through high-resolution spectroscopy and analysis of spin and charge excitations.

Contribution

It presents the first direct real-space observation of spin and charge bosonic excitations in a Luttinger liquid using scanning tunneling spectroscopy.

Findings

Observation of two distinct standing waves caused by spin and charge excitations

Evidence of increased charge group velocity and power-law decay of amplitudes

Detection of density of states suppression near the Fermi level

Abstract

Electronic standing waves with two different wavelengths were directly mapped near one end of a single-wall carbon nanotube as a function of the tip position and the sample bias voltage with highresolution position-resolved scanning tunneling spectroscopy. The observed two standing waves caused by separate spin and charge bosonic excitations are found to constitute direct evidence for a Luttinger liquid. The increased group velocity of the charge excitation, the power-law decay of their amplitudes away from the scattering boundary, and the suppression of the density of states near the Fermi level were also directly observed or calculated from the two different standing waves.