Colored ${\Delta }_T$ noise probes the topological character of edge modes

Abstract

We investigate colored ${\Delta }_T$ noise, i.e., finite-frequency ${\Delta }_T$ noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored ${\Delta }_T$ noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since ${\Delta }_T$ 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 ${\Delta }_T$-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 ${\Delta }_T$ noise exhibits a frequency-dependent sign reversal absent in the corresponding white ($\omega =0$) ${\Delta }_T$ 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) EMs exhibit a positive colored shot-noise spectrum. However, the corresponding colored ${\Delta }_T$ 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 ${\Delta }_T$ 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.

7 pages, 2 figures, 2 tables, accepted for publication in Applied Physics Letters (2026)

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