Spin-fluctuation-induced pairing in twisted bilayer graphene

Physical review. B./Physical review. B, vol. 103

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 angstrom scale. For local on-site 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 a 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 $2\ensuremath{\pi}$ 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.

Authors 4

1. Ammon Fischer Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany

2. Lennart Klebl Aachen Institute for Theory of Statistical Physics

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany

3. Carsten Honerkamp Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany

4. Dante Marvin Kennes Aachen Institute for Theory of Statistical Physics

   Jülich Aachen Research Alliance · Center for Free-Electron Laser Science · Max Planck Institute for the Structure and Dynamics of Matter · RWTH Aachen University

   Affiliation as printed

   Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany

   Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, 22761 Hamburg, Germany