Coulomb interaction,phonons, and superconductivity in twisted bilayer graphene

The polarizability of twisted bilayer graphene, due to the combined effect of electron–hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron–hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.

Twisted bilayer graphene (TBG) shows a complex phase diagram which combines superconducting and insulating phases (1, 2) and resembles strongly correlated materials previously encountered in condensed matter physics (3–6). On the other hand, superconductivity seems more prevalent in TBG (7–11), while in other strongly correlated materials magnetic phases are dominant.The pairing interaction responsible for superconductivity in TBG has been intensively studied. Among other possible pairing mechanisms, the effect of phonons (12–19) (see also ref. 20), the proximity of the chemical potential to a van Hove singularity in the density of states (DOS) (21–25) and excitations of insulating phases (26–28) (see also refs. 29–31), and the role of electronic screening (32–35) have been considered.In the following, we analyze how the screened Coulomb interaction induces pairing in TBG. The calculation is based on the Kohn–Luttinger formalism (36) for the study of anisotropic superconductivity via repulsive interactions. The screening includes electron–hole pairs (37), plasmons (38), and phonons (note that acoustic phonons overlap with the electron–hole continuum in TBG). Our results show that the repulsive Coulomb interaction, screened by plasmons and electron–hole pairs only, leads to anisotropic superconductivity, although with critical temperatures of order T_c ∼ 10⁻³ to 10⁻² K. The inclusion of phonons in the screening function substantially enhances the critical temperature, to T_c ∼ 1 to 10 K.