We developed a microscopic theory for the point-contact conductance between a metallic electrode and a strongly correlated material using the nonequilibrium Schwinger-Kadanoff-Baym-Keldysh formalism. We explicitly show that, in the classical limit, contact size shorter than the scattering length of the system, the microscopic model can be reduced to an effective model with transfer matrix elements that conserve in-plane momentum. We found that the conductance dI/dV is proportional to the effective density of states, that is, the integrated single-particle spectral function A(omega = eV) over the whole Brillouin zone. From this conclusion, we are able to establish the conditions under which a non-Fermi liquid metal exhibits a zerobias peak in the conductance. This finding is discussed in the context of recent point-contact spectroscopy on the iron pnictides and chalcogenides, which has exhibited a zero-bias conductance peak.
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