Generalized Gumbel distribution of current fluctuations in purple membrane monolayers

TL;DR

This paper explores a generalized Gumbel distribution model to describe current fluctuations in bacteriorhodopsin monolayers, revealing a transition from bimodal to unimodal distributions with changing bias voltage.

Contribution

It introduces a generalized Gumbel distribution framework to model charge transport fluctuations in biological monolayers, linking distribution shape changes to bias voltage.

Findings

Current fluctuations follow a generalized Gumbel distribution.

Distribution shape transitions from bimodal to unimodal with bias.

Different shape parameters correspond to distinct fluctuation regimes.

Abstract

We investigate the nature of a class of probability density functions, say G(a), with a the shape parameter, which generalizes the Gumbel distribution. These functions appear in a model of charge transport, when applied to a metal-insulator-metal structure, where the insulator is constituted by a monolayer of bacteriorhodopsin. Current shows a sharp increase above about 3 V, interpreted as the cross-over between direct and injection sequential-tunneling regimes. In particular, we show that, changing the bias value, the probability density function changes its look from bimodal to unimodal. Actually, the bimodal distributions can be resolved in at least a couple of $G(a)$ functions with different values of the shape parameter.