Uniquely identifying quantum Hall phases in charge-neutral graphene

Charge-neutral graphene in the quantum Hall regime is an example of a quantum Hall ferromagnet in a complex spin-valley space. This system exhibits a plethora of phases, with the particular spin-valley order parameters chosen by the system depending sensitively on the short-range anisotropic couplings, the Zeeman field, and the sublattice symmetry breaking field. A subset of order parameters related to lattice symmetry breaking have been observed by scanning tunneling microscopy. However, other order parameters, particularly those that superpose spin and valley, are more elusive, making it difficult to pin down the nature of the phase. We propose a solution to this problem by examining two types of experimentally measurable quantities: transport gaps and collective mode dispersions. We find that the variation of the transport gap with the Zeeman and sublattice symmetry-breaking fields, in conjunction with the number of Larmor and gapless modes, provides a unique signature for each theoretically possible phase.