Most theories of the metallic state (including Fermi liquid and marginal Fermi liquid theories) assume/assert/embody that adding electrons or holes to the ground state requires the same amount of energy. In a similar vein quasi-particle peaks in spectral functions should be symmetric.
There are two important exceptions to theories which assert dynamical particle-hole symmetry:
The hidden Fermi liquid theory of Anderson
The extremely correlated Fermi liquid theory of Shastry
Shastry points out that there is already some experimental evidence for asymmetry. The figure below [taken from a Science paper by Pasupathy et al. about a different issue] shows the differential conductivity [roughly proportional to the local density of states] from an STM measurement on an overdoped sample of BSCCO. The relevant point is that the background has a significant slope. If there was particle-hole symmetry the background would be flat, as it is for simple metals.
This slope is much larger than the small asymmetry expected from band structure that arises due to the proximity of the Fermi energy to a van Hove singularity.
In light of the theoretical issues discussed above this seems to be an important result and needs to be checked.
There are a few puzzles.
1. Earlier tunneling experiments do not see such a large asymmetry.
2. As the doping decreases the asymmetry does not increase, which is what I would have expected, since the system is effectively becoming more correlated.
3. The above data show no sign of a van Hove singularity.
I thank Jure Kokalj for helpful discussions about this topic.