  Different channels over which electrons scatter between parts of the Fermi
surface are the key to various electronic quantum matters, such as
superconductivity and density waves. We consider an effective model in higher
dimensions where each of the two pockets in the original model maps to (the
Landau levels of) two Dirac fermions. We discover an emergent channel when two
Dirac fermions from different pairs annihilate, where the presence of a strong
density wave is essential. We support our analysis with numerical calculations
on model examples in the vicinity of ferromagnetic and antiferromagnetic
orders. We also discuss interesting consequences on electron interaction
channels that beyond-mean-field fluctuations may induce.
