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(ω = 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.correlated electron materials | point contact spectroscopy | electronic nematicity | non-Fermi liquid | iron-based superconductors H eavy fermion systems (1, 2), high-T c cuprates (3, 4), and very recently the iron-based superconductors (5, 6) all exhibit symptoms of quantum criticality. The most striking feature of quantum criticality is that the quantum fluctuations associated with the quantum critial point (QCP) couple strongly to itinerant electrons, giving rise to drastic changes in the electronic properties. Typically, such emergent properties are non-Fermi liquid like and hence fall outside the standard theory of metals. Although measurements of several physical properties, for example, the heat capacity, magnetic susceptibility, and DC electrical resistivity, have been identified with non-Fermi liquid (NFL) behavior, a direct probe of the hallmark feature of a NFL, namely the imaginary part of the single-particle self energy ΣðωÞ ∼ ω ν with ν < 1, is still lacking. In principle, the temperature dependence of the DC electrical resistivity is expected to be related to ν, but it is also sensitive to many other factors, rendering such measurements inconclusive. In this context angle-resolved photoemission (ARPES) is an ideal probe of this hallmark feature. However, the resolution of the ARPES data are typically not high enough to pin-down ν conclusively. As a result, a reliable experimental setup to judge whether ν is larger or smaller than 1 is one of the most important topics in this field.We demonstrate here how point contact spectroscopy (PCS) can be used to resolve this problem. Our work here is motivated by recent PCS experiments on iron-pnictide superconductors in which an excess zero-bias conductance was measured well above the temperature associated with the structural rearrangement. Based on an analogy with earlier theoretical work on nematic quantum phase transitions (7), Lee et al. argued that the excess zero-bias conductance measured experimentally is likely due to an excess density of states associated with fluctuations near the orbital-ordering quantum phase transition. However,...