Charge fluctuations, phonons and superconductivity in multilayer graphene

TL;DR

This paper investigates the emergence of superconductivity in multilayer graphene using a Kohn-Luttinger mechanism, predicting critical temperatures and order parameters that align with experimental data and suggesting potential for high-temperature superconductivity in certain stacks.

Contribution

It introduces a parameter-free theoretical framework to predict superconductivity in various multilayer graphene stacks based on electronic interactions and compares their critical temperatures.

Findings

Superconductivity can be driven by electronic interactions alone in AB bilayer and ABC trilayer graphene.

ABC trilayer graphene has the highest predicted critical temperature of about 100 mK.

Ising spin-orbit coupling significantly enhances the critical temperature, especially in AB bilayer graphene.

Abstract

Motivated by the recent experimental detection of superconductivity in Bernal bilayer (AB) and rhombohedral trilayer (ABC) graphene, we study the emergence of superconductivity in multilayer graphene based on a Kohn-Luttinger (KL)-like mechanism in which the pairing glue is the screened Coulomb interaction. We find that electronic interactions alone can drive superconductivity in AB bilayer graphene and ABC trilayer graphene with the critical temperatures in good agreement with the experimentally observed ones, allowing us to further predict superconductivity from electronic interactions in Bernal ABA trilayer and ABAB tetralayer and rhombohedral ABCA tetralayer graphene. By comparing the critical temperatures ($T_c$) of these five non-twisted graphene stacks, we find that the ABC trilayer graphene possesses the highest $T_c\sim100$ mK. After considering the enhancement of superconductivity due to Ising spin-orbit coupling, we observe that the AB bilayer graphene has the largest enhancement in the critical temperature, increasing from 23 mK to 143 mK. The superconducting behaviors in these non-twisted graphene stacks could be explained by the order parameters (OPs). The OPs of Bernal stacks preserve intravalley $C_3$ symmetry, whereas rhombohedral stacks break it. In all stacks, the OPs have zeroes and change signs between valleys, which means that these multilayers of graphene are nodal spin-triplet superconductors. Moreover, dressing the purely electronic interaction with acoustic phonons, we observe minor changes of the critical temperatures in these five stacks. We adopt the KL-like mechanism to investigate the tendency of superconductivity in multilayer graphene without fitting parameters, which could provide guidance to future experiments exploring superconductivity in non-twisted graphene.