Stability of C2-odd pairing under the gap equation

Ascertain whether a superconducting order parameter that is odd under the in-plane C2 rotation in twisted bilayer nodal d-wave superconductors constitutes a stable, self-consistent solution of the superconducting gap equation.

Background

The paper analyzes twisted bilayer nodal d-wave superconductors and shows that Bogoliubov flat bands can emerge when the superconducting order parameter is odd under the in-plane C2 rotation. Using a low-energy 4×4 effective Hamiltonian, the authors identify conditions for the formation and flattening of Bogoliubov quasiparticle bands.

While the spectral consequences of assuming such a C2-odd pairing are explored, the self-consistent stability of this pairing structure was not addressed. Establishing whether this pairing solves the gap equation remains necessary to validate the physical realization of the proposed flat-band phenomenology.