Nodal Nematic Superconductivity in Multiple-Flat-Band Land

TL;DR

This paper introduces a mechanism for stable nodal nematic superconductivity in multiple-flat-band systems, emphasizing the role of inter-eigen-band pairing in energy stabilization, demonstrated through a heavy fermion model of twisted bilayer graphene.

Contribution

It proposes a novel mechanism for nodal superconductivity in flat-band systems, highlighting the importance of inter-eigen-band pairing for energy stability.

Findings

Inter-eigen-band pairing lowers overall energy in flat-band systems.

Nematic d-wave pairing is energetically favored despite higher energy at nodal points.

The mechanism is specific to systems without Fermi surfaces.

Abstract

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-eigen-band pairing, but also inter-eigen-band 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 d-wave pairing has higher energy around the nodal points compared to the chiral d-wave pairing in the momentum space, the inter-eigen-band pairing can lower the energy in other momenta away from the nodes, so that the nematic d-wave pairing is energetically favored for its overall condensation energy. This type of mechanism is particular to multiple-flat-band systems with no Fermi surfaces.