Colored ΔT noise probes the topological character of edge-modes

Abstract

We investigate colored ΔT noise, i.e., finite-frequency ΔT noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored ΔT noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since ΔT noise is driven solely by a temperature and voltage bias under zero average charge current conditions, it eliminates current-induced Joule heating and directly probes intrinsic thermal fluctuations. We show that chiral, spin-conserving helical, and spin-flip helical (trivial) EMs exhibit distinct colored ΔT-noise signatures under appropriate bias protocols. Incorporating energy-dependent scattering through a quantum point contact, we demonstrate that electron–hole asymmetry significantly modifies the finite-frequency spectrum while preserving these distinguishing features. Notably, colored ΔT noise exhibits a frequency-dependent sign reversal absent in the corresponding white (ω=0) ΔT noise. We further investigate zero-temperature colored quantum shot noise and find that it vanishes identically for chiral EMs, whereas the spin-conserving helical response changes sign with frequency. By contrast, spin-flip helical (trivial) edge-mode (Ems) exhibit a positive colored shot-noise spectrum. However, the corresponding colored ΔT noise retains its characteristic sign reversal, providing a robust distinction between spin-conserving helical and spin-flip helical (trivial) EM transport. These results establish colored ΔT noise as a robust, experimentally accessible, complementary probe for identifying chiral, spin-conserving helical, and spin-flip helical (trivial) EM transport in mesoscopic topological systems.