Effect of Bogoliubov flat bands on zero-energy edge states in d-wave superconductors

Determine the effect of the Bogoliubov flat band on the zero-energy edge states in d-wave superconductors, including how the presence of twist-induced Bogoliubov flat bands influences the midgap Andreev surface bound states characteristic of d-wave pairing.

Background

The authors show that interlayer coupling and twist in bilayer nodal d-wave superconductors can generate Bogoliubov flat bands near newly created nodes on the C2 rotation axis. Zero-energy edge states (midgap surface states) are a hallmark of d-wave superconductors and have been extensively studied in the literature.

The interplay between these well-known d-wave surface states and the newly proposed Bogoliubov flat bands has not been established. Understanding this interaction is important for interpreting spectroscopic signatures and potential topological or transport consequences at edges and interfaces.