Harmonic Fingerprint of Unconventional Superconductivity*

The structure of superconducting pairing is determined by microscopic details such as the interaction profile and Fermiology beyond the spatial symmetry classification along irreducible point group representations of the underlying lattice. The pairing wave function unfolds in its orbital-resolved Fourier profile which we call the harmonic fingerprint (HFP), allowing us to formulate a concise connection between microsopic parameter changes and their impact on superconductivity. We present an analysis - based on random phase approximation calculations - of twisted bilayer graphene (TBG) involving d+id, s±, and f-wave order. Including nonlocal interactions - which unavoidably enter the low-energy electronic description of TBG - increases the weight of higher lattice harmonics and furthermore has a significant effect on the orbital structure of the paring states.