Shot noise and higher current moments in dimensions 2, 3 & 4
Abstract
Shot noise and higher current moments TM=<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=T1, shot noise S=T1-T2, Fano factor F=S/G and ratios CM=TM/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 CM 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 TM.
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