Spin-fluctuation-induced pairing in twisted bilayer graphene

TL;DR

This paper models the microscopic origin of superconductivity in twisted bilayer graphene, revealing chiral d-wave pairing driven by magnetic fluctuations, with distinctive vortex and magnetic field patterns that are experimentally detectable.

Contribution

It introduces a microscopic model combining tight-binding and RPA to analyze pairing mechanisms, identifying chiral d-wave superconductivity and vortex structures in twisted bilayer graphene.

Findings

Chiral d-wave pairing dominates in large parameter regions.

Superconducting vortices are localized in AA regions.

Distinct magnetic field patterns are predicted for experimental detection.

Abstract

We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the \AA ngstr\"om scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this parameter space, we find chiral $d$-wave pairing regimes, spontaneously breaking time-reversal symmetry, separated by magnetic instabilities at integer band fillings. Interestingly, the $d$-wave pairing is strongly concentrated in the AA regions of the moir\'e unit cell and exhibits phase windings of integer multiples of $2\pi$ around these superconducting islands, i.e. pinned vortices. The spontaneous circulating current creates a distinctive magnetic field pattern. This signature of the chiral pairing should be measurable by state-of-the-art experimental techniques.