  We theoretically investigate the non-equilibrium quantum phase transition in
a generic setup: the pseudogap Kondo model where a quantum dot couples to
two-left (L) and right (R)-voltage-biased fermionic leads with power-law
density of states (DOS) with respect to their Fermi levels {\mu}_L/R,
{\rho}_c,L(R) ({\omega}) \propto |{\omega} - {\mu}_L(R) |r, and 0 < r < 1. In
equilibrium (zero bias voltage) and for 0 < r < 1/2, with increasing Kondo
correlations, in the presence of particle-hole symmetry this model exhibits a
quantum phase transition from a unscreened local moment (LM) phase to the Kondo
phase. Via a controlled frequency-dependent renormalization group (RG)
approach, we compute analytically and numerically the non-equilibrium
conductance, conduction electron T-matrix and local spin susceptibility at
finite bias voltages near criticality. The current-induced decoherence shows
distinct nonequilibrium scaling, leading to new universal non-equilibrium
quantum critical behaviors in the above observables. Relevance of our results
for the experiments is discussed.
