Collective Bulk and Edge Modes through the Quantum Phase Transition in Graphene at $\nu=0$

TL;DR

This paper investigates the quantum phase transition in undoped graphene under strong magnetic fields, revealing distinct bulk and edge collective modes in canted antiferromagnetic and ferromagnetic phases through theoretical analysis.

Contribution

It provides a detailed theoretical study of collective excitations across the CAF-FM transition in graphene, highlighting differences in bulk and edge modes using the time-dependent Hartree-Fock approximation.

Findings

CAF has gapless neutral bulk modes

FM has gapped bulk modes but gapless edge states

Edge response functions can distinguish the two phases

Abstract

Undoped graphene in a strong, tilted magnetic field exhibits a radical change in conduction upon changing the tilt-angle, which can be attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor $\nu=0$. This behavior signifies a change in the nature of the collective ground state and excitations across the transition. Using the time-dependent Hartree-Fock approximation, we study the collective neutral (particle-hole) excitations in the two phases, both in the bulk and on the edge of the system. The CAF has gapless neutral modes in the bulk, whereas the FM state supports only gapped modes in its bulk. At the edge, however, only the FM state supports gapless charge-carrying states. Linear response functions are computed to elucidate their sensitivity to the various modes. The response functions demonstrate that the two phases can be distinguished by the evolution of a local charge pulse at the edge.