  This paper aims to clarify the nature of a surprising ordered phase recently
reported in biased Bernal bilayer graphene that occurs at the phase boundary
between the isospin-polarized and unpolarized phases. Strong nonlinearity of
transport at abnormally small currents, with $dI/dV$ vs. $I$ sharply rising and
then falling back, is typical for a charge/spin-density-wave state (CDW or SDW)
sliding transport. Here, however, it is observed at an isospin-order phase
boundary, prompting a question about the CDW/SDW mechanism and its relation to
the quantum critical point. We argue that the observed phase diagram cannot be
understood within a standard weak-coupling picture. Rather, it points to a
mechanism that relies on an effective interaction enhancement at a quantum
critical point. We develop a detailed strong-coupling framework accounting for
the soft collective modes that explain these observations.
