Euler-obstructed nematic nodal superconductivity in twisted bilayer graphene

Abstract

Signatures of nematic nodal superconductivity have been experimentally observed in magic angle twisted bilayer graphene (MATBG). Here, we propose a general topological mechanism explaining how a nematic pairing leads to nodal superconductivity in MATBG. By focusing on the intervalley ${C}_{2z}\mathcal{T}$-invariant Cooper pairing order parameter, we show that the pairing order parameter can always be split into a trivial channel and an Euler obstructed channel, owing to the nontrivial normal-state band topology. When the pairing is spontaneously nematic, we find that a sufficiently-dominant Euler obstructed channel with two zeros typically leads to nodal superconductivity. The mechanism is general since it is independent of the specific interaction that accounts for the required pairing. Under the approximation of exactly-flat bands, we analytically find that the mean-field zero-temperature superfluid weight is bounded from below, and thus the Berezinksii-Kosterlitz-Thouless (BKT) critical temperature can be nonzero, even if the Euler obstructed pairing is dominant. We also numerically find that a spontaneously-nematic dominant Euler obstructed pairing can arise from a local attractive interaction.