INAUGURAL ARTICLE by a Recently Elected Academy Member:Theory of point contact spectroscopy in correlated materials

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 zero-bias 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.Heavy 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 Σ(ω) ～ 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, a direct link between the two remains missing as there is no rigorous argument relating the PCS signal in strongly correlated systems to the single-particle density of states. The theoretical foundations for the tunneling density of states have been well established (8, 9), but we stress here that PCS is not tunneling, and this work establishes a clear connection between PCS conductance and an effective density of states arising from NFL behavior.In this paper, we build on earlier work (10) to fill in this missing link and as a result are able to establish the circumstances under which the PCS signal is a direct measure of the single-particle density of states in strongly correlated electron systems and hence offers a window into a key probe of non-Fermi liquid behavior, namely the imaginary part of the single-particle self-energy. Of course, PCS is an old field dating back to the pioneering work of Yanson’s (11) in 1974 when he was attempting to measure the tunneling conductance across a superconducting/insulator/normal-metal (SIN) planar junction. According to Harrison’s theorem (12), when the superconductor is driven normal, the resulting planar tunneling conductance must be ohmic: assuming a one-dimensional model, which holds for good planar tunnel junctions, in the standard tunneling conductance formula that assumes weakly correlated electron (conventional) materials, the Fermi velocity v_f = (1/?)(dk_x/dE) exactly divides out the density of states D(E) = (L/π)(dE/dk_x). Yanson discovered weak conductance nonlinearities in an SIN junction above the critical field (S = Pb) and that the second harmonic of the conductance (d²I/dV²) revealed the Eliashberg function, α²F(ω), the strength of about 1% of the background conductance. This behavior resulted from the junctions being leaky with nanoscale metallic shorts between S and N, allowing electrons to be directly injected through the junction without any tunneling processes; hence, Harrison’s theorem did not apply. He went on to show that when the junction is large such that the mean free path is smaller than the junction (thermal regime), no spectroscopic information can be obtained, but if the junction is smaller than the elastic (Sharvin or ballistic limit) or inelastic (diffusive regime) mean free path, spectroscopic information is revealed. Quasiparticles backscattered through the junction reveal the phonon spectrum; therefore, this technique is also called quasiparticle scattering spectroscopy (QPS). Researchers in the field proceeded to map out bosonic spectra (phonons and magnons) in a variety of materials (13, 14), quasiparticle scattering from Kondo impurities (13), spin and charge density waves (15, 16), and recently a Kondo insulator (17). With the advent of the Blonder-Tinkham-Klapwijk (BTK) theory (18), in a clean S/N junction, Andreev scattering was shown to reveal details of the superconducting gap structure, including magnitude and symmetry (19). This technique has been shown to be particularly useful in superconductors that are difficult to grow in thin film form, e.g., heavy-fermion superconductors (10, 20, 21) and the iron-based high-temperature superconductors (22). In the heavy-fermions, the Fano background could be accounted for via multichannel tunneling models (10, 23–25). Our focus here is on establishing a clear link between the suggestive relationship that excess zero-bias signal measured in PCS is a direct measure of the effective density of states arising from electron correlations (6, 19, 21, 26, 27).To this end, we use the Schwinger-Kadanoff-Baym-Keldysh (SKBK) formalism (28–30), coupled with certain reasonable assumptions, to show that the conductance measured from PCS is proportional to the effective density of states (31–37). Because the effective density of states is defined as the integrated single-particle spectral function A(ω = eV) over the whole Brillouin zone, it contains the information about the single particle self energy Σ(ω). We show that a fingerprint of non-Fermi liqud behavior with ν < 1 is an enhancement of the PCS conductance at zero bias. As a comparison, we also discuss the case of a junction in the thermal regime, in which only DC resistivity is detected. We highlight here that the DC resistivity is fundamentally different from the PCS conductance. The former is corresponding to the current-current correlation function evaluated by Kubo formula, whereas the latter is related to the single particle Green function as described by the SKBK formalism. Consequently, we conclude that the zero-bias peak in the PCS could be identified as a unique signature of non-Fermi liquid metal.