The true ground state of ν = 0 (charge neutrality) monolayer graphene quantum Hall has long been debated. Famously the symmetry of the monolayer graphene at ν = 0 (charge neutrality) was analyzed by J. Alicea and P. A. Fisher in 2006 (PRB 74, 075422), and canted anti-ferromagnet (CAF) was predicted by I. F. Herbut in 2007 (PRB 75, 165411). However, the complete picture of the Hamiltonian was missing until the seminal paper by M. Kharitonov in 2012 (PRB 85, 155439) which predicts a phase transition from a vanilla insulator (CAF) to a topological insulator Ferromagnetic phase (F) as one changes the Zeeman energy keeping the cyclotron energy fixed. This was later confirmed in the experiment by A. F. Young et. al. in 2014 (Nature 505, 528). Motivated by recent experiments (L. He et. al. PRB 100, 085437, Ali Yazdani et. al. Science abm3770, B. Sacepe arXiv:2110.02811) we revisit this phase diagram. We show that, generically, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models and argue that the coexistence phase naturally provides an explanation for unreconciled experimental observations on the quantum Hall effect in graphene.
Ref: Phys. Rev. Lett. 128, 106803, (2022)
