Why it is so hard to detect Luttinger liquids in ARPES?

TL;DR

This paper investigates the challenges in detecting Luttinger liquids via ARPES, highlighting how disorder and scattering effects obscure the TLL signatures, and provides an analytic approach to understand these effects.

Contribution

It identifies the key roles of disorder and scattering in obscuring TLL states in ARPES and derives an exact analytic solution for photo-electron propagation under specific conditions.

Findings

Disorder significantly obscures TLL states in ARPES.

Scattering path operator affects the ARPES final state.

Photon energy can reduce photo-current intensity.

Abstract

The problem of photoemission from a quasi-1D material is studied. We identify two issues that play a key role in the detection of gapless Tomonaga-Luttinger liquid (TLL) phase. Firstly, we show how a disorder -- backward scattering as well as forward scattering component, is able to significantly obscure the TLL states, hence the initial state of ARPES. Secondly, we investigate the photo-electron propagation towards a sample's surface. We focus on the scattering path operator contribution to the final state of ARPES. We show that, in the particular conditions set by the 1D states, one can derive exact analytic solution for this intermediate stage of ARPES. The solution shows that for particular energies of incoming photons the intensity of photo-current may be substantially reduced. Finally, we put together the two aspects (the disorder and the scattering path operator) to show the full, disruptive force of any inhomogeneities on the ARPES amplitude.