  Massless Dirac fermions in graphene at charge neutrality form a strongly
interacting system in which both charged and neutral (energy) modes play an
important role. These modes are essentially decoupled in the absence of a
magnetic field, but become strongly coupled when a field is applied. We show
that these ideas explain the recently observed giant magnetodrag, arising in
classically weak fields when electron density is tuned near charge neutrality.
We predict strong Hall drag in this regime, which is in stark departure from
the weak coupling regime, where theory predicts the absence of Hall drag.
Energy-driven magnetodrag and Hall drag arise in a wide temperature range and
at weak magnetic fields, and feature an unusually strong dependence on field
and carrier density.
