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arXiv:2607.17354

Colored $Δ_T$ noise probes the topological character of edge modes

Sachiraj Mishra, Colin Benjamin

cond-mat.mes-hallhep-thmath-phphysics.app-phquant-phSubmitted Jul 19, 2026• Announced Jul 21, 2026
v1 · Jul 19, 2026v2 · Aug 10, 2026
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Abstract

We investigate colored $Δ_T$ noise, i.e., finite-frequency $Δ_T$ noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored $Δ_T$ noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since $Δ_T$ 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 $Δ_T$-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 $Δ_T$ noise exhibits a frequency-dependent sign reversal absent in the corresponding white ($ω=0$) $Δ_T$ 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 $Δ_T$ 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 $Δ_T$ 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.

Journal reference
Applied Physics Letters 129, 093101 (2026)
DOI
10.1063/5.0353027
Comments
7 pages, 2 figures, 2 tables

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Colored ΔTΔ_TΔT​ noise probes the topological character of edge modes
We investigate colored ΔTΔ_TΔT​ noise, i.e., finite-frequency ΔTΔ_TΔT​ noise, as a probe of edge-mode (EM) transport in quantum Hall and quantum spin Hall systems. Colored ΔTΔ_TΔT​ noise probes finite-frequency nonequilibrium current fluctuations and dynamical transport properties that are often obscured in DC measurements of conductance and noise. Since ΔTΔ_TΔT​ 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 ΔTΔ_TΔT​-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 ΔTΔ_TΔT​ noise exhibits a frequency-dependent sign reversal absent in the corresponding white (ω=0ω=0ω=0) ΔTΔ_TΔT​ 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 ΔTΔ_TΔT​ 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 ΔTΔ_TΔT​ 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.
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We study delta-T noise -- excess charge noise at zero voltage but finite temperature bias -- for weak tunneling in 1D interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process (more specifically, its scaling dimension). We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Boson-like particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This particularly implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the thermal noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons. Our findings show that delta-T noise can probe the nature of collective excitations in interacting 1D systems.
Effect of electron-hole asymmetry on ΔTΔ_TΔT​ noise in metal/quantum point contact/metal and metal/quantum point contact/superconductor junctions
This work examines charge ΔTΔ_TΔT​ noise in two-terminal hybrid nanostructures featuring a quantum point contact (QPC), realized either between two normal metallic leads (NQN) or between a normal metal and a superconducting lead (NQS). The energy-dependent transmission of a QPC breaks electron-hole (e-h) symmetry, leading to a finite thermovoltage under an applied temperature and voltage bias. In contrast, in earlier studies on hybrid junctions incorporating insulating barriers, as electron-hole symmetry is preserved, have vanishing thermovoltage, and consequently, charge ΔTΔ_TΔT​ noise is calculated at zero thermovoltage. In our setup, the broken e-h symmetry allows for a finite thermovoltage, at which we compute the corresponding charge ΔTΔ_TΔT​ noise. Unlike earlier studies restricted by electron-hole symmetry and vanishing thermovoltage, our work establishes a self-consistent thermoelectric noise framework in mesoscopic hybrid junctions, revealing how Andreev reflection fundamentally reshapes charge ΔTΔ_TΔT​ noise once electron-hole symmetry is broken. This broad access to charge fluctuation signatures provides a more comprehensive understanding of non-equilibrium transport in linear response. To the best of our knowledge, this is the first work that systematically explores the interplay between Andreev reflection and electron-hole symmetry breaking in the context of quantum noise and ΔTΔ_TΔT​ noise in mesoscopic hybrid structures.
Quantum point contacts (QPCs) are essential tools for transport experiments in solid-state systems, enabling the detection of fractional charges and anyonic braiding statistics. Realizing analogous transport setups in isolated quantum-simulation platforms, such as ultracold atoms, remains challenging, since it typically requires coupling to external reservoirs. Here we show that the scattering properties of chiral edge states at a QPC can instead be extracted directly from the stationary edge currents of an isolated, reservoir-free lattice system. Exploiting the sensitivity of this scattering to Aharonov-Bohm-type phases, we propose an equilibrium protocol to detect local magnetic fluxes from ground-state edge currents. We further introduce a dynamical scheme, robust against finite temperature and particle-number fluctuations, based on the post-quench evolution following a sudden potential-bias removal. Since anyonic excitations are themselves associated with a local, quantized magnetic flux, our approach should extend to probing anyonic statistical phases in quantum-engineered platforms.
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We study nonequilibrium noise in chiral Luttinger liquids using the Landauer-Buttiker scattering approach, obtaining the current and voltage noise spectrum for a four-terminal measurement scheme. Experimental consequences of the tunneling of charges are present in the four-terminal measurement of both the low-frequency shot noise (\ensuremath{\omega} near 0), and the high-frequency Josephson noise (\ensuremath{\omega} near ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=e∗{\mathit{e}}^{\mathrm{*}}e∗V/\ensuremath{\Elzxh}). Within perturbation theory, an algebraic singularity is present at the Josephson frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{J}}$=e∗{\mathit{e}}^{\mathrm{*}}e∗V/\ensuremath{\Elzxh}, whose position depends on the charge e∗{\mathit{e}}^{\mathrm{*}}e∗ of the tunneling particles, either electrons or fractionally charged quasiparticles. These two types of tunneling are related by a strong-weak--coupling duality transformation. We show in a nonperturbative calculation for an exactly solvable point that the singularity at the quasiparticle frequency exists only in the limit of vanishing coupling, whereas the singularity at the electron frequency is present for all coupling strengths. The vanishing coupling limit corresponds to perfectly quantized Hall conductance in the case of quasiparticle tunneling between edge states in the fractional quantum Hall regime, and thus tunneling destroys the singularity at the quasiparticle frequency concomitantly with the quantized current. \textcopyright{} 1996 The American Physical Society.