  We calculate the differential conductance as a function of temperature and
bias voltage, $G(T,V)$, through Au monoatomic chains with a substitutional Co
atom as a magnetic impurity, connected to a four-fold symmetric lead. The
system was recently proposed as a possible scenario for observation of the
overscreened Kondo physics. Stretching the chain, the system could be tuned
through a quantum critical point (QCP) with three different regimes,
overscreened, underscreened and non Kondo phases. We present calculations of
the impurity spectral function by using the numerical renormalization group
(NRG) for the three different regimes characterizing the QCP. Non trivial
behaviour of the spectral function is reported near the QCP. Comparison with
results using the non crossing approximation (NCA), shows that the latter is
reliable in the overscreened regime, when the anisotropy is larger than the
Kondo temperature. For these parameters, which correspond to realistic previous
estimates, $G(T,V)$ calculated within NCA exhibits clear signatures of the
non-Fermi liquid behaviour within the overscreened regime.
