Topological Classification of Shot Noise on Fractional Quantum Hall Edges

Abstract

Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited by the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "anti-ballistic". Correspondingly, the noise either vanishes, decays algebraically or is constant up to exponentially small corrections in the edge length.Electrical and thermal transport on fractional quantum Hall (FQH) edges are quantized, reflecting the bulk topological order [1][2][3]. In particular, the electrical Hall and two-terminal conductances, G H and G,are determined by the bulk filling factor ν ∈ Q. Furthermore, the thermal Hall and two-terminal conductances, G Q H and G Q , arXiv:1906.05623v1 [cond-mat.mes-hall]

Quantized charge fractionalization at quantum Hall Y junctions in the disorder dominated regime

“…This is consistent with the plasmon (charge density wave) transport model (see Methods) shown in Fig. 5a, where interaction and scattering are characterized by distributed capacitances and scattering conductances, respectively [46][47][48] . The transport eigenmodes generally deviate from the pure charge and neutral modes at higher frequencies.…”

Conductance plateaus and shot noise in fractional quantum Hall point contacts

“…These distinct noise characteristics were shown in Ref. 37 to provide a topological classification of the Abelian FQH states and provides an indirect probe of upstream heat transport on the edge.…”

“…It was shown in Ref. 37 that these topologically distinct cases exhibit three different noise characteristics. For completeness, the derivation of this result is outlined next.…”

“…It was shown in Ref. 37 that Eq. (22) allows three different types of heat transport along the edge.…”

“…To simplify our treatment of the edge structure, we shall hereafter assume that all edge channels with a given chirality equilibrate into effective hydrodynamic modes on the length scale ∼ a which thus serves as the UV cutoff of the model (see Ref. 37 for a detailed discussion). The resulting two modes, labelled by n = ±, have effective filling factor discontinuities…”