Nodal nematic superconductivity in multiple flat-band systems

In this work, we propose a mechanism of inducing stable nodal superconductivity for multiple-flat-band systems. This mechanism is based on the degenerate flat band nature, so that not only intra-eigenband pairing, but also inter-eigenband pairing has a significant influence on the superconductivity properties. Based on the Bogoliubov-de Gennes formalism of the heavy fermion model for the twisted bilayer graphene as an example, we show that although the nodal nematic Euler obstructed pairing has higher energy around the nodal points compared to the fully gapped chiral d-wave pairing in the momentum space, the inter-eigenband pairing can lower the energy in other momenta away from the nodes, so that the nematic Euler obstructed pairing is energetically favored for its overall condensation energy. This type of mechanism is particular to multiple-flat-band systems with no Fermi surfaces.