Extracting the scaling dimension of quantum Hall quasiparticles from current correlations

Abstract

Fractional quantum Hall quasiparticles are generally characterized by two quantum numbers: electric charge Q and scaling dimension ∆. For the simplest states (such as the Laughlin series) the scaling dimension determines the quasiparticle's anyonic statistics (the statistical phase θ = 2π∆). For more complicated states (featuring counterpropagating modes or non-Abelian statistics) knowing the scaling dimension is not enough to extract the quasiparticle statistics. Nevertheless, even in those cases knowing the scaling dimension facilitates distinguishing different candidate theories for describing the quantum Hall state at a particular filling (such as PH-Pfaffian and anti-Pfaffian at ν = 5/2). Here we propose a scheme for extracting the scaling dimension of quantum Hall quasiparticles from thermal tunneling noise produced at a quantum point contact. Our scheme features the level of robustness and simplicity comparable to extracting the quasiparticle charge from tunneling shot noise.

Does delta-$T$ noise probe quantum statistics?

“…Ref. [49]). The determination of the sign of the noise by ∆ T indicates that negative delta-T noise is not a unique feature of anyonic systems (e.g., Laughlin FQH edges), but can be generated by interactions in many 1D electrons systems.…”

“…At this point, we note that the C (n) coefficients can be viewed as corresponding Fano factors for the delta-T noise. Where the Fano factor for weak, voltage biased tunneling, reveals the charges of the tunneling particles, the C ( n) coefficients can be used to extract scaling dimensions [49] and (in some cases) the quantum statistics of the particles.…”

“…( 78) is expressed in terms of the scaling dimension of the full tunneling operator (44) (see also Ref. [49]). A major observation in the present work is therefore that, in the weak tunneling limit, negative delta-T noise will, in fact, be generated when two identical subsystems are bridged by a leading relevant inter-edge tunneling operator satisfying two conditions:…”

“…In contrast to the voltage-induced noise, the delta-T noise does not require a net flow of a non-equilibrium charge current. Since initial theoretical [42][43][44][45][46][47][48][49] and experimental [41,[50][51][52][53][54][55] work, it has been shown that non-equilibrium noise in the absence of currents is, in fact, a more general phenomenon than delta-T noise [56]. Still, what properties of nanoscale conductors-and, in particular, facets of their strongly-correlated nature-this class of zerocurrent non-equilibrium noise might reveal, remains an open and interesting question.…”

“…Further, a very recent work, Ref. [49], specifically emphasized the role of scaling dimension in the delta-T noise. In particular, the authors proposed to use delta-T noise to extract scaling dimensions of particles tunneling between complex FQH edges.…”