Why it is so hard to detect Luttinger liquids in angle resolved photo-emission spectroscopy?

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 angle resolved photo-emission spectroscopy (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 an exact analytical 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.