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 makes only minimal assumptions about the edge structure and features the level of robustness, simplicity, and model independence comparable to extracting the quasiparticle charge from tunneling shot noise.

Charge, spin, and heat shot noises in the absence of average currents: Conditions on bounds at zero and finite frequencies

“…Then, we demonstrate that the zero-current shot noise is limited by the remaining terms also at finite frequency, see Eq. (28). Notably, the zero-frequency limit of this bound is stricter than Eq.…”

“…The bound (28) implies that, in the absence of charge current, the finite-frequency charge shot noise is always smaller than the remaining noise contributions, S I sh (ω) ≤ S I rest (ω), when the noise measurement is performed in the colder reservoir. This can be understood from the fact that R(ω) as well as Θ L (ω) are always positive quantities.…”

“…More recently, charge noise as a response to a temperature gradient and in the absence of a voltage bias -dubbed delta-T noise -has been investigated in several theoretical [20][21][22][23][24][25][26][27][28][29][30] and experimental [31][32][33][34][35][36][37] works. These works demonstrate that delta-T noise offers additional insights beyond the traditional shot noise, e.g., for quantifying local temperature gradients [25,32] or as a potential tool for extracting scaling dimensions and exchange statistics of anyons [23,28,29]. Still, the full scope of delta-T noise remains to be understood.…”

Delta-T noise for fractional quantum Hall states at different filling factor

“…In recent years, systems connected to reservoirs kept at different temperatures, when no voltage is applied, have been experimentally [15][16][17][18] and theoretically [19][20][21][22][23][24] considered. The presence of a temperature gradient leads to a non-equilibrium contribution to the charge current noise known as delta-T noise.…”

“…This opposite regime requires a weak-strong duality relation [27] in order to be addressed. This analysis aims to deepen our knowledge on delta-T noise in order to move towards more involved applications concerning the possibility of investigating the statistics [28,29] and the scaling dimension of the carriers [24].…”