Microscopic details such as interactions and Fermiology determine the structure of superconducting pairing beyond the spatial symmetry classification along irreducible point group representations. From the effective pairing vertex, the pairing wave function related to superconducting order unfolds in its orbital-resolved Fourier profile which we call the harmonic fingerprint (HFP). The HFP allows us to formulate a concise connection between microsopic parameter changes and their impact on superconductivity. From a random phase approximation analysis of twisted bilayer graphene (TBG) involving $d+id$-, $s_{\pm }$-, and $f$-wave order, we find that nonlocal interactions, which unavoidably enter the low-energy electronic description of TBG, not only increase the weight of higher lattice harmonics but also have a significant effect on the orbital structure of these pairing states. For gapped unconventional superconducting order such as $s_{\pm }$ and $d+id$, a change in HPF induces enhanced gap anisotropies. Experimental implications to distinguish the different gaps and HPFs are also discussed.

• Received 12 September 2019
• Revised 12 March 2020
• Accepted 24 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.134517