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Magic-angle twisted bilayer graphene (MATBG) hosts normal-state nearly-flatbands with nonzero Euler numbers and shows superconductivity. In this work, westudy the effects of the nontrivial normal-state band topology on theintervalley $C_{2z}\mathcal{T}$-invariant mean-field Cooper pairing orderparameter in MATBG. We show that the pairing order parameter can always besplit into a trivial channel and an Euler obstructed channel in all gauges forthe normal-state basis, generalizing the previously-studied channel splittingin the Chern gauge. The nonzero normal-state Euler numbers require the pairinggap function of the Euler obstructed channel to have zeros, while the trivialchannel can have a nonvanishing pairing gap function. When the pairing isspontaneously nematic, we find that a sufficiently-dominant Euler obstructedchannel with two zeros typically leads to nodal superconductivity. Under theapproximation of exactly-flat bands, we find that the mean-fieldzero-temperature superfluid weight is generally bounded from below, no matterwhether the Euler obstructed channel is dominant or not, generalizing thepreviously-derived bound for the uniform s-wave pairing. We numerically verifythese statements for pairings derived from a local attractive interaction. Ourwork suggests that Euler obstructed Cooper pairing may play an essential rolein the superconducting MATBG.

Euler Obstructed Cooper Pairing in Twisted Bilayer Graphene: Nematic Nodal Superconductivity and Bounded Superfluid Weight