Pairing in magic-angle twisted bilayer graphene: role of phonon and plasmon umklapp

TL;DR

This paper investigates how phonons and plasmons contribute to superconductivity in magic-angle twisted bilayer graphene, highlighting the importance of umklapp processes and Coulomb interactions in pairing mechanisms.

Contribution

It introduces a theoretical framework analyzing the cooperative effects of phonons and plasmons on pairing, emphasizing the role of umklapp processes in enhancing superconductivity in MATBG.

Findings

Umklapp phonon processes significantly enhance pairing.

Screened Coulomb interactions can boost superconductivity at specific fillings.

Spectral features in tunneling density of states reflect umklapp phonon frequencies.

Abstract

Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a non-trivial structure of the underlying Bloch wavefunctions. We perform a theoretical study of the cooperative effects due to phonons and plasmons on pairing in order to disentangle the distinct role played by these modes on superconductivity. We consider a variant of MATBG with an enlarged number of fermion flavors, $N \gg 1$, where the study of pairing instabilities reduces to the conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving mini-optical phonon modes, which arise physically as a result of the folding of the original acoustic branch of graphene due to the moir\'e superlattice structure, contribute significantly towards enhancing pairing. We also investigate the role played by the dynamics of the screened Coulomb interaction on pairing, which leads to an enhancement in a narrow window of fillings, and study the effect of external screening due to a metallic gate on superconductivity. At strong coupling the dynamical pairing interaction leaves a spectral mark in the single particle tunneling density of states. We thus predict such features will appear at specific frequencies of the umklapp phonons corresponding to the sound velocity of graphene times an integer multiple of the Brillouin zone size.