I am very impressed with how over the past two decades the quality and resolution of Angle Resolved PhotoEmission Spectroscopy (ARPES) data has improved so significantly.
Nigel Hussey brought to my attention a beautiful paper Anisotropic quasiparticle scattering rates in slightly underdoped to optimally doped high-temperature La2−xSrxCuO4 superconductors
This allows one to clearly see real quantum many-body effects with the "naked eye".
The Figure below shows an intensity plot as a function of energy and momentum from
an cuprate superconductor with approximately optimum doping. The intensity is proportional to the one electron spectral function (imaginary part of the Greens function).
If there are well defined quasi-particles this should have a clear maximum which disperses (i.e. defines an energy vs. momentum curve). The blue dashed line is the bare dispersion one estimates from band structure calculations. One can see that near the Fermi energy the actual dispersion curve has a much smaller slope indicative of signficant renormalisation due to many-body effects. The almost vertical slope between EI and EII is known as the "waterfall" (WF).
Notice that the quasi-particle peak gets broader as one moves away from the Fermi energy as one would expect for a "Fermi liquid" (or something similar).
Using a model bare dispersion one can extract both the energy and momentum dependence of the self energy. It turns out that the imaginary part has the form
where phi is the angle around the Fermi surface.
The first term is associated with disorder and the second with inelastic scattering in a marginal Fermi liquid (which scales linearly with frequency).
[In a Fermi liquid the scattering scales quadratically with frequency.].
The momentum (phi) dependence has a "d-wave" form will cold spots near the nodes.
I also found this particularly interesting because angle-dependent magnetoresistance measurements from Nigel Hussey's group on an overdoped cuprate found a similar angular dependence for the inelastic scattering rate and an approximately linear temperature dependence. (A Nature Physics paper describes this result and a PRL shows how the strength of the anisotropic scattering increases as the doping is reduced.)
If two different groups using different techniques on different materials observe the same physics it suggests that there is a significant effect here.