Shot Noise near Quantum-Criticality

TL;DR

This paper investigates shot noise near quantum criticality in heavy-fermion compounds, using marginal Fermi liquid theory to explain experimental observations and revealing how noise behavior transitions with temperature.

Contribution

It applies MFL theory to calculate shot noise in YbRh$_2$Si$_2$, explaining experimental results and elucidating the role of fermion collisions and scattering mechanisms.

Findings

Fair agreement between theory and experiment in noise magnitude and temperature dependence.

At high temperatures, shot noise becomes temperature independent, matching Johnson-Nyquist noise.

Fano factor decreases to zero at high temperatures regardless of voltage.

Abstract

Shot-noise measures the correlations of fluctuations of current for a voltage applied much larger than the temperature and reveals aspects of correlations in fermions beyond those revealed in the conductivity. Recent measurements of shot-noise in the quantum-critical region of the heavy-fermion compound YbRh$_2$Si$_2$ (YRS) have presented a conceptual challenge to old theory and those devised following the experiments. Since the measured resistivity and the specific heat in YRS follow the predictions of marginal Fermi liquid (MFL) theory, we use it to calculate noise using the method developed by Nagaev. We get fair agreement with the magnitude and temperature dependence in the experiments using parameters from resistivity measurements. To achieve this, we find it necessary that the collisions between fermions by exchanging the MFL fluctuations conserve energy but lose momentum through Umklapp scattering and that the fermions and their fluctuations are locally in mutual equilibrium. %and that the self-energy rides the local chemical potential. At low temperatures, impurity scattering determines the noise and at high temperatures the MFL scattering. We show that the noise for MFL scattering for high T alone is the same as the Johnson-Nyquist noise, which in this case is temperature independent. Therefore the Fano factor crosses over to $0$ at high temperatures independent of the voltage applied.