Shot noise and higher current moments in dimensions 2, 3 & 4

TL;DR

This paper investigates shot noise and higher current moments in disordered conductors across dimensions 2, 3, and 4, providing analytical and numerical insights into their behavior at criticality and in the metallic regime.

Contribution

It introduces a comprehensive analysis of current moments and shot noise in the Anderson model, deriving analytical expressions and confirming microscopic theory predictions.

Findings

Identifies stable and unstable limiting values of Fano factor and ratios C_M in different regimes.

Provides analytical formulas for current cumulants at 3D criticality.

Numerically confirms Nazarov's microscopic theory predictions.

Abstract

Shot noise and higher current moments T_M=<Tr (t^+t)^M> are studied within the Anderson model of disordered conductors in dimensions d= 2, 3 and 4. Here t denotes a transmission matrix. We calculate the conductance G=T_1, shot noise S=T_1-T_2, Fano factor F=S/G and ratios C_M=T_M/G, and we show indications that all of them are as good order parameters as the conductance itself. In the limit of infinite system size, two limiting values of F and C_M are found; the stable one in the metallic regime, and the unstable one, characterizing the critical point for d > 2. We present analytical expressions for both limiting values, together with a compact formula for current cumulants at 3D criticality. Our data confirm also Nazarov's microscopic theory [PRB 52, 4720 (1995)], as we show numerically for special linear combinations of T_M.