Δ_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 Δ_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 Δ_T noise can discriminate between S₊₊ and S_+- pairing symmetries, which are relevant to iron-based superconductors. We introduce Δ_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 Δ_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.