Finite-size effect in shot noise in hopping conduction

Abstract

We study a current shot noise in a macroscopic insulator based on a two-dimensional electron system in GaAs in a variable range hopping (VRH) regime. At low temperature and in a sufficiently depleted sample a shot noise close to a full Poissonian value is measured. This suggests an observation of a finite-size effect in shot noise in the VRH conduction and demonstrates a possibility of accurate quasiparticle charge measurements in the insulating regime.As first shown by Schottky for the case of a vacuum tube, electric current can be viewed as a sequence of uncorrelated pulses corresponding to arrivals of individual electrons at the anode [1]. A mean-squared current fluctuation (shot noise) in this random Poissonian process has a spectral density of S I = 2qI, where q ≡ e is the elementary charge and I is the average current. A direct shot noise measurement of the charge q of a quasiparticle is intriguing in application to various solid state materials, where q can be renormalized by interactions (q = e) [2,3]. This list includes nontrivial many-body insulating states in charge-density wave compounds [4], in cooper pair insulators [5,6] and in the bulk of a two-dimensional (2D) system in fractional quantum Hall effect [7].

Noise insights into electronic transport

“…The observation of F = 1 in B = 0 reproduces our previous result 39 and signals that transport in zero field occurs via VRH conduction in the regime of finite-size effect, when the width of the gate, L, is not greater than the size of the critical cluster, ξ. Compared to longer devices with L ξ in which the random resistance network is very well interconnected 17 , see the sketch c1 of fig.…”

“…In this case, the Fano factor is inversely proportional to the number of hardhops, F ∼ 1/N , and for N = 1 can reach F ∼ 1, as predicted by theory 38 and consistent with experiments. Remarkably, in GaAs 2DES at low T and deep enough in the insulating regime the Poissonian noise with F = 1 ± 0.1 was demonstrated 39 . This motivates us to study shot noise in quantizing magnetic fields, where Poissonian current statistics would enable, e.g., a direct measurement of the quasiparticle charge in the bulk of the insulating state in the FQHE.…”

Zero energy states at a normal-metal/cuprate-superconductor interface probed by shot noise

“…This is a plausible situation for our junctions, in which the quasiparticle density of states in the nodal direction increases linearly with voltage. We note thatΓ = 2/3 was predicted for a diffusive conductor on the basis of the random matrix theory [35]; this fact was used in [36] to calculate the shot noise.Γ between 0 and 0.4, similar to what we used to fit the data, was observed in [37] for transport through a barrier in GaAs structures.…”

“…We note that Γ = 2/3 was predicted for a diffusive conductor on the basis of the random matrix theory [35]; this fact was used in [36] to calculate the shot noise. Γ between 0 and 0.4, similar to what we used to fit the data, was observed in [37] for transport through a barrier in GaAs structures.…”

Tunneling mechanism in a (Ga,Mn)As/GaAs-based spin Esaki diode investigated by bias-dependent shot noise measurements

“…When the tunnel barrier is thick, multiple hopping through the LS network becomes dominant [21]. In this case, F decreases from unity, depending on the number of hopping events (N), the network structure, and dimensionality [22][23][24][25][26][27][28]. In a simple one-dimensional network with N identical barriers, theory gives F = 1/N [22].…”