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 ν = 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.
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The authors thank the Aspen Center for Physics (NSF Grant No. PHY-1066293) for its hospitality and acknowledge support by the Simons Foundation (E.S.). This work was supported by the US-Israel Binational Science Foundation (BSF), Grant No. 2012120 (E.S., G.M., H.A.F.), the Israel Science Foundation (ISF), Grant No. 231/14 (E.S.), and NSF-DMR 1306897 (G.M.), and by NSF-DMR 1506460.
Murthy, Ganpathy; Shimshoni, Efrat; and Fertig, H. A., "Collective Bulk and Edge Modes Through the Quantum Phase Transition in Graphene at ν = 0" (2016). Physics and Astronomy Faculty Publications. 440.