Pomeranchuk instability in doped graphene

TL;DR

This paper investigates how Coulomb interactions at Van Hove singularities in doped graphene can lead to a Pomeranchuk instability, potentially causing symmetry breaking, and explores the competition with ferromagnetism, revealing a complex phase diagram.

Contribution

It demonstrates the likelihood of a Pomeranchuk instability in doped graphene at Van Hove filling due to Coulomb interactions, and analyzes the competition with ferromagnetic order.

Findings

Pomeranchuk instability can occur in doped graphene at Van Hove filling.

Ferromagnetism is also possible due to on-site Hubbard interactions.

The phase diagram shows regions of different instabilities and stability of the Fermi liquid.

Abstract

The density of states of graphene has Van Hove singularities that can be reached by chemical doping and have already been explored in photoemission experiments. We show that in the presence of Coulomb interactions the system at the Van Hove filling is likely to undergo a Pomeranchuk instability breaking the lattice point group symmetry. In the presence of an on--site Hubbard interaction the system is also unstable towards ferromagnetism. We explore the competition of the two instabilities and build the phase diagram. We also suggest that, for doping levels where the trigonal warping is noticeable, the Fermi liquid state in graphene can be stable up to zero temperature avoiding the Kohn--Luttinger mechanism and providing an example of two dimensional Fermi liquid at zero temperature.