$\Delta_T$ Noise as a Robust Diagnostic for Chiral, Helical and Trivial Edge Modes

In this article we demonstrate that $\Delta_T$ noise provides a sensitive, practical probe for distinguishing chiral edge modes from topological helical and trivial (non-topological) helical edge transport. Measured under zero-current conditions, $\Delta_T$ noise reveals contrasts that conventional conductance measurements typically miss. Crucially, $\Delta_T$ requires no external energy input in the form of an applied voltage bias, yet encodes the same intrinsic information that shot noise yields in the zero-temperature, finite-bias limit, without the distorting effects of Joule heating. This absence of bias-induced heating makes $\Delta_T$ noise both more precise and more reliable than conventional shot-noise approaches. Moreover, the diagnostic power of $\Delta_T$ noise persists at finite frequencies $\omega$ too. The frequency-dependent signal $\Delta_{T}(\omega)$ exhibits distinctive spectral signatures (including sign changes) that further enhance its utility as an experimentally accessible fingerprint of edge-mode topology.