Delta_T Noise, Quantum Shot Noise, and Thermoelectric Clues to the Pairing Puzzle in Iron Pnictides

Quantum noise has long served as a powerful probe of quantum transport in mesoscopic junctions. Recently, temperature-driven noise, or $\Delta_T$ noise, has attracted growing interest due to its presence even in the absence of average charge current. In this work, we investigate a normal metal-insulator-iron-pnictide junction and demonstrate how thermovoltage, Seebeck coefficient, zero temperature quantum shot noise, finite temperature quantum noise and $\Delta_T$ noise can discriminate between $S_{++}$ and $S_{+-}$ pairing symmetries, which are relevant to iron-based superconductors. We introduce $\Delta_T$ noise as a novel probe for distinguishing between the two pairing symmetries. In contrast to conductance, which exhibits a single peak for both $S_{++}$ and $S_{+-}$ states with only a difference in magnitude, the $\Delta_T$ noise reveals qualitatively distinct features: a twin-peak structure for the $S_{++}$ pairing symmetry and a single-peak profile for the $S_{+-}$ state. A similar symmetry-dependent contrast is observed in both zero temperature quantum shot noise and finite temperature quantum noise, where the $S_{++}$ state consistently exhibits a twin-peak structure, while the $S_{+-}$ state shows a single-peak response. Furthermore, both the thermovoltage and the Seebeck coefficient display sign reversals for the two pairing symmetries, with opposite trends in the $S_{++}$ and $S_{+-}$ cases. Our results demonstrate that noise-based measurements, together with Seebeck coefficient and thermovoltage, form a mutually reinforcing set of probes that enables reliable identification of superconducting gap symmetry in Iron Pnictide superconductors.