  Interaction driven symmetry breaking in a metallic (doped) Dirac system can
manifest in the spontaneous gap generation at the nodal point buried below the
Fermi level. Across this transition linear conductivity remains finite making
its direct observation difficult in linear transport. We propose the nonlinear
Hall effect as a direct probe of this transition when inversion symmetry is
broken. Specifically, for a two-dimensional Dirac material with a tilted
low-energy dispersion, we first predict a transformation of the characteristic
inter-band resonance peak into a non-Lorentzian form in the collisionless
regime. Furthermore, we show that inversion-symmetry breaking quantum phase
transition is controlled by an exotic tilt-dependent line of critical points.
As this line is approached from the ordered side, the nonlinear Hall
conductivity is suppressed owing to the scattering between the strongly coupled
incoherent fermionic and bosonic excitations. Our results should motivate
further studies of nonlinear responses in strongly interacting Dirac materials.
