Competing many-body instabilities and unconventional superconductivity in graphene

TL;DR

This paper investigates the competition of many-body instabilities in graphene near van Hove singularities, predicting a phase diagram with unconventional superconductivity and other correlated phases using functional renormalization group methods.

Contribution

It provides a detailed phase diagram of graphene's many-body phases near VHS, highlighting the emergence of d+id-wave superconductivity and spin density wave phases.

Findings

Prediction of d+id-wave superconductivity with topological properties

Identification of spin density wave phase at VHS

Presence of singlet and triplet superconducting phases near VHS

Abstract

The band structure of graphene exhibits van Hove singularities (VHS) at doping x=+- 1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d+id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d+id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d+id-wave as well as triplet f-wave SC phases.