  When phonons couple to fermions in 2D semimetals, the interaction may turn
the system into an insulator. There are several insulating phases in which the
time reversal and the sublattice symmetries are spontaneously broken. Examples
are many-body states commensurate to Haldane's staggered flux model or to
lattice models with periodically modulated strain. We find that the effective
field theories of these phases exhibit characteristic Chern-Simons terms, whose
coefficients are related to the topological invariants of the microscopic
model. This implies that the corresponding quantized Hall conductivities
characterize these insulating states.
