Harmonic Fingerprint of Unconventional Superconductivity in Twisted Bilayer Graphene

TL;DR

This paper introduces the harmonic fingerprint (HFP) as a tool to connect microscopic parameters with the structure of unconventional superconducting pairing in twisted bilayer graphene, revealing how nonlocal interactions influence pairing symmetry and gap anisotropy.

Contribution

It develops the harmonic fingerprint concept to analyze the orbital-resolved pairing wave function and demonstrates its sensitivity to microscopic interaction changes in TBG.

Findings

Nonlocal interactions increase higher harmonic contributions.

Changes in HFP affect gap anisotropy in unconventional superconductors.

Different pairing states exhibit distinct harmonic fingerprints.

Abstract

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 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.