Negative spin ∆T noise induced by spin-flip scattering and Andreev reflection

We study charge ∆T noise, followed by an examination of spin ∆T noise, in the normal metal-spin flipper-normal metal-insulator-superconductor (N-sf-N-I-S) junction. Our analysis reveals a key contrast: while charge ∆T noise remains strictly positive, spin ∆T noise undergoes a sign reversal from positive to negative, driven by the interplay between spin-flip scattering as well as Andreev reflection. In contrast, charge quantum shot noise remain positive and sign-definite, which is valid for spin quantum shot noise also. The emergence of negative spin ∆T noise has two major implications. First, it establishes a clear distinction between spin resolved ∆T noise and quantum shot noise: the former is dominated by opposite-spin correlations, whereas the latter is led by same-spin correlations. Second, it provides access to scattering mechanisms that are not captured by quantum shot noise alone. Thus, negative spin ∆T noise serves as a unique probe of the cooperative effects of Andreev reflection and spin flipping. We further place our results in context by comparing them with earlier reports of negative ∆T noise in strongly correlated systems, such as fractional quantum Hall states, and in multiterminal hybrid superconducting junctions. Overall, this work offers new insights into the mechanisms governing sign reversals in ∆T noise and highlights their role as distinctive fingerprints of spin-dependent scattering in superconducting hybrid devices.