Antiferromagnetism and competing charge instabilities of electrons in strained graphene from Coulomb interactions

TL;DR

This study uses the TU-fRG method to analyze how strain and electron interactions influence antiferromagnetism and charge order in graphene, revealing a dominant antiferromagnetic phase under long-range interactions.

Contribution

It applies the TU-fRG approach to explore electron interactions in strained graphene, extending beyond previous methods by avoiding the sign problem and examining a broader parameter space.

Findings

Finite biaxial strain induces a quantum phase transition to an ordered state.

Antiferromagnetic spin-density wave dominates under long-range interactions.

Charge density waves are prevalent under medium-range interactions.

Abstract

We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex' wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic \emph{ab initio} interaction parameters and confirm that the application of a finite biaxial strain can induce a quantum phase transition towards an ordered ground state. In contrast to lattice QMC simulations, the TU-fRG is not limited in the choice of tight-binding and interaction parameters to avoid the occurrence of a sign problem. Therefore, we also investigate a range of parameters relevant to the realistic graphene material which are not accessible by numerically exact methods. Although a plethora of charge density waves arise under medium-range interactions, we find the antiferromagnetic spin-density wave to be the prevailing instability for long-range interactions. We further explore the impact of an extended tight-binding Hamiltonian with second-nearest neighbor hopping and a finite chemical potential for a more accurate description of the band structure of graphene's $p_z$ electrons.