Wannier Pairs in the Superconducting Twisted Bilayer Graphene and Related Systems

TL;DR

This paper investigates the pairing symmetries in twisted bilayer graphene and related systems, revealing an extended s-wave symmetry in TBG with unique nodal features, contrasting with other graphene-based materials.

Contribution

It provides a comparative analysis of pairing symmetries in TBG, GBN, and SLG using a unified theoretical framework based on Wannier states and spin-fluctuation mediated pairing.

Findings

TBG exhibits extended s-wave pairing with same-phase Wannier pairs.

GBN shows p+ip-wave pairing with odd-parity phase.

SLG has d+id-wave pairing with even-parity phase.

Abstract

Unconventional superconductivity often arises from Cooper pairing between neighboring atomic sites, stipulating a characteristic pairing symmetry in the reciprocal space. The twisted bilayer graphene (TBG) presents a new setting where superconductivity emerges on the flat bands whose Wannier wavefunctions spread over many graphene unit cells, forming the so-called Moir\'e pattern. To unravel how Wannier states form Cooper pairs, we study the interplay between electronic, structural, and pairing instabilities in TBG. For comparisons, we also study graphene on boron-nitride (GBN) possessing a different Moir\'e pattern, and single-layer graphene (SLG) without a Moir\'e pattern. For all cases, we compute the pairing eigenvalues and eigenfunctions by solving a linearized superconducting gap equation, where the spin-fluctuation mediated pairing potential is evaluated from materials specific tight-binding band structures. We find an extended $s$-wave as the leading pairing symmetry in TBG, in which the nearest-neighbor Wannier sites form Cooper pairs with same phase. In contrast, GBN assumes a $p+ip$-wave pairing between nearest-neighbor Wannier states with odd-parity phase, while SLG has the $d+id$-wave symmetry for inter-sublattice pairing with even-parity phase. Moreover, while $p+ip$, and $d+id$ pairings are chiral, and nodeless, but the extended $s$-wave channel possesses accidental {\it nodes}. The nodal pairing symmetry makes it easily distinguishable via power-law dependencies in thermodynamical entities, in addition to their direct visualization via spectroscopies.