Local Spectral Weight of a Luttinger Liquid: Effects from Edges and Impurities

TL;DR

This paper investigates how edges and impurities affect the local spectral weight in a Luttinger liquid, revealing oscillations and asymmetries that influence STM measurements of one-dimensional electron systems.

Contribution

It provides a detailed calculation of the finite-temperature local spectral weight near boundaries in a Luttinger liquid, highlighting characteristic oscillations and Fano-like asymmetry.

Findings

Oscillations in spectral weight near boundaries indicate spin-charge separation.

Fano-like asymmetry arises from electron interactions and boundary scattering.

Results inform interpretation of STM experiments on 1D systems like carbon nanotubes.

Abstract

We calculate the finite-temperature local spectral weight (LSW) of a Luttinger liquid with an "open" (hard wall) boundary. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the interplay between electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence scanning tunneling microscopy (STM) of one-dimensional electron systems at low temperatures and voltage bias. Applications to STM on single-walled carbon nanotubes are discussed.